-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathindex.html
More file actions
1196 lines (1105 loc) · 103 KB
/
index.html
File metadata and controls
1196 lines (1105 loc) · 103 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<style type="text/css" media="all">
body {font-family: 'Droid Sans', helvetica,Arial,sans-serif;}
a:link, a:visited, a:active {text-decoration:none}
div.container{width:85%; margin:2%; line-height:140%;}
div.right{float:right;width:150px; margin:1em; padding:1em;}
div.content{margin-left:4%; padding:1em;}
</style>
<title>Allan Peter Engsig-Karup</title>
<meta name="description" content="Academic page of Allan Peter Engsig-Karup">
<meta name="keywords" content="Scientific Computing, Scientific Machine Learning, Physics-Informed Machine Learning, High-Performance Computing, Deep Learning">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta http-equiv="Content-Style-Type" content="text/css">
<meta name="viewport" content="width=device-width, initial-scale=1">
<style type="text/css">
div.foo p {
margin-bottom:0.0em;
margin-top:0.0em;
}
</style>
</head>
<body data-new-gr-c-s-check-loaded="14.1012.0" data-gr-ext-installed="">
<div class="container">
<div class="right"><img alt="" width="250px" src="assets/AllanEngsigKarup2.jpg">
</div>
<div class="content">
<h1 style="text-align: left;">Allan Peter Engsig-Karup</h1>
<p>
Professor (Assoc) in Computational Mathematics / Scientific Machine learning<br><a href="https://www.compute.dtu.dk/~apek">Section for Scientific Computing
</a>, <a href="https://www.compute.dtu.dk/" target="_blank">Department of Applied Mathematics and Computer Science</a>,
<a href="https://www.compute.dtu.dk/sections/sco" target="_blank">Section for Scientitic Computing</a>,
<a href="https://www.compute.dtu.dk/" target="_blank">DTU Compute</a>,
<a href="https://www.dtu.dk/english" target="_blank">Technical University of Denmark</a>.
<br>
<br>
Research interests:
</p>
<ul>
<li><a href="#mathmodelling">Mathematical-Physical Modelling</a> </li>
<li><a href="#scientificcomputing">Scientific Computing</a> </li>
<li><a href="#hpc">High-Performance Computing</a> </li>
<li><a href="#sciml">Scientific Machine Learning</a> </li>
<li><a href="#softwareengineering">Software Engineering</a> </li>
<li><a href="#nlp">Natural language processing (NLP) for Human-Device interfaces enabling Virtual Assistants / Agents</a> </li>
<li><a href="#softwareengineering">AI Engineering</a> </li>
</ul>
<p></p>
<table style="width:85%">
<tbody>
<tr>
<td>
<a href="https://scholar.google.com/citations?user=UbWFbIkAAAAJ&hl=en" target="_blank"><img src="assets/gscholar.png" width="45px" height="45px"></a>
<a href="https://www.linkedin.com/in/allan-peter-engsig-karup-851b984/" target="_blank"><img src="assets/linkedin.jpg" width="45px" height="45px"></a>
<a href="https://www.researchgate.net/profile/Allan-Engsig-Karup" target="_blank"><img src="assets/researchgate-icon-2047x2048-5zkr6kip.png" width="45px" height="45px"></a>
<a href="https://github.com/apengsigkarup" target="_blank"><img src="assets/GitHub-Mark-ea2971cee799.png" width="45px" height="45px"></a>
<p>
E-mail: <a href="mailto:apek@dtu.dk">apek@dtu.dk</a>
</p>
<p>
<img src="https://www2.compute.dtu.dk/~apek/02689_2023_chatGPT4_DallE.png" height="200px"/>
<img src="http://www2.compute.dtu.dk/~apek/SCIML2022/ChrisSciML2022_PicGroup.jpg" height="200px"/>
<img src="https://www2.compute.dtu.dk/~apek/scientificmachinelearning/DALL-ERunnerInMotion.png" height="200px"/>
<a href="https://www.lumi-supercomputer.eu/"><img src="assets/LUMI_supercomputer_2022_web-600x400-c-default.jpg" height="200px"/></a>
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0021999116301255" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="https://www2.compute.dtu.dk/~apek/OceanWave3D/simulationFNPFfr35.gif" alt="Link" height="200px"/>
</a>
<img src="http://www2.imm.dtu.dk/~apek/dambreak2d.gif" alt="Link" height="200px"/>
<br>
<img src="assets/DGFEMsphericaladvection2D_simulation.gif" alt="Link" height="200px"/>
</p>
Teaching:
<ul>
<li><a href="https://kurser.dtu.dk/course/02614" target="_blank">02614 at DTU: High-Performance Computing (Past teaching: GPU Computing)</a></li>
<li><a href="https://kurser.dtu.dk/course/02623" target="_blank">02623 at DTU: The Finite Element Methods for Partial Differential Equations</a></li>
<li><a href="https://kurser.dtu.dk/course/preview/76535/en-GB" target="_blank">02671 at DTU: Data-Driven Methods for Computational Science and Engineering (given in 2023, 2024 and 2025)</a></li>
<li><a href="https://kurser.dtu.dk/course/02687" target="_blank">02687 at DTU: Scientific Computing for Ordinary and Partial Differential Equations</a></li>
<li><a href="https://kurser.dtu.dk/course/02689" target="_blank">02689 at DTU: Advanced Numerical Methods for Differential Equations</a></li>
<li><a href="https://kurser.dtu.dk/course/02456" target="_blank">02456 at DTU (projects): Deep Learning</a></li>
<li><a href="https://kurser.dtu.dk/course/01666" target="_blank">01666 at DTU (projects): Project work - Bachelor of Mathematics and Technology</a></li>
<li><a href="https://kurser.dtu.dk/course/02122" target="_blank">02122 at DTU (projects): Software Technology Project</a></li>
<li><a href="https://kurser.dtu.dk/course/02901" target="_blank">02901 at DTU (projects): Advanced Topics in Machine Learning - Physics-Informed Machine Learning</a></li>
<ul>
<li><a href="https://www2.compute.dtu.dk/courses/02901/02901-2024/" target="_blank">Final program of the summer school (Aug 19-23, 2024)</a></li>
</ul>
</ul>
Seminars:
<ul>
<li><a href="https://dtumods.github.io/">Mathematics of Data Science Seminar Series</a></li>
</ul>
Current research group:
<ul>
<li><a href="" target="_blank">Jens Visbech</a>, PhD student/Inria Bordeaux/DTU Construct</li>
<ul>
<li><a href="https://www.compute.dtu.dk/news/jens-visbeck?id=dc4c5fe9-b11b-443c-8146-4184544b1120">DTU Compute: Jens Visbech receives Elite Research Travel Grants 2025</a></li>
<li><a href="https://dm.dk/forskerforum/magasinet/2025/forskerforum-nr-2-2025/fra-vvs-laerling-til-boelgeforsker/" target="_blank">ForskerForum: Fra VVS-lærling til bølgeforsker (Danish article)</a></li>
</ul>
<li><a href="" target="_blank">Max Bitsch</a>, Industrial PhD student, DTU Compute/DHI Group</li>
<li><a href="" target="_blank">Freja Petersen</a>, Industrial PhD student, DTU Compute/DHI Group</li>
<li><a href="" target="_blank">Niels Skovgaard Jensen</a>, Industrial PhD student, DTU Compute/Ticra</li>
</ul>
<p></p>
Current research collaborations:
<ul>
<li><a href="" target="_blank">Yuanxin Xia</a>, PhD student, DTU Electro/DTU Compute</li>
<li><a href="" target="_blank">Anton Sørensen</a>, PhD student, DTU Sustain/DTU Compute</li>
<li><a href="" target="_blank">Matteo Calafa</a>, PhD student, DTU Electro/DTU Compute</li>
</ul>
</td>
</tr>
</tbody>
</table>
In addition, I supervise many BSc/MSc students.
<p></p><h2><a id="labs">Computing Laboratories</a></h2>
<a href="http://gpulab.compute.dtu.dk"><img src="assets/GPULABlogo.png" height="60px"/></a> <br/><br/>
I am a co-founder of the GPULAB established at DTU Compute in 2008.
<ul>
<li><a href="http://gpulab.compute.dtu.dk">DTU Compute GPULAB</a> (Now hosted by the DTU Computing Center)</li>
</ul>
<h2><a id="research">Research overview</a></h2>
<ul>
<li>Advance and use modern scientific computing for simulation in areas of engineering applications.</li>
<li>Advance and use modern data-driven methods / algorithms for predictive and generative tasks of relevance in areas of science and engineering.</li>
<li>Develop and implement modern state-of-the-art numerical methods / linear algebra for massively parallel high-performance / cloud computing / super computing on modern many-core hardware systems.</li>
<li>Use large language models from areas of natural language processing for human-device interfaces to design workflows that enable virtual assistants and agents.</li>
</ul>
<h3><a id="scientificcomputing">Scientific Computing</a></h3>
Scientific computing for simulation, uncertainty quantification, and high-performance computing:
<ul>
<li><a href="" target="_blank">Mathematical-Physical Modelling</a> </li>
<li><a href="" target="_blank">Advanced Numerical Methods</a> </li>
<li><a href="" target="_blank">Multigrid Methods for Solving Large Systems of Equations</a> </li>
<li><a href="" target="_blank">Massively Parallel CPU-GPU Acceleration</a> </li>
<li><a href="" target="_blank">Computational Fluid Dynamics</a> </li>
<li><a href="" target="_blank">Uncertainty Quantification</a> </li>
</ul>
with examples of applications in different engineering areas
<ul>
<li><a href="" target="_blank">Spread of Disease Modelling</a> </li>
<li><a href="" target="_blank">Marine Hydrodynamics</a> </li>
<li><a href="" target="_blank">Computational Fluid Dynamics</a> </li>
<li><a href="" target="_blank">Room Acoustics</a> </li>
<li><a href="" target="_blank">Railway Vehicle Dynamics</a> </li>
<li><a href="" target="_blank">Reservoir Simulation</a> </li>
</ul>
<h3><a id="sciml">Scientific Machine Learning</a></h3>
Data-driven methods / algorithms for efficient modelling:
<ul>
<li><a href="" target="_blank">High-dimensional Function Approximation</a> </li>
<li><a href="" target="_blank">Sensing</a> </li>
<li><a href="" target="_blank">Reduced Order Modelling</a> </li>
<li><a href="" target="_blank">Neural Operators</a> </li>
<li><a href="" target="_blank">Physics-Informed Neural Networks</a></li>
<li><a href="" target="_blank">Physics-Informed Holomorphic Neural Networks</a></li>
<li><a href="" target="_blank">Multi-fidelity Methods</a></li>
<li><a href="" target="_blank">Generalised Residual Networks</a></li>
<li><a href="" target="_blank">Surrogate Modelling</a></li>
<li><a href="" target="_blank">Neural Ordinary/Partial Differential Equations</a></li>
<li><a href="" target="_blank">Physics Informed Regression</a></li>
</ul>
with examples of application in different engineering areas
<ul>
<li><a href="" target="_blank">Digital Twins</a> </li>
<li><a href="" target="_blank">Finance</a> </li>
<li><a href="" target="_blank">Materials Science</a> </li>
<li><a href="" target="_blank">Room Acoustics</a> </li>
<li><a href="" target="_blank">Marine hydrodynamics</a> </li>
<li><a href="" target="_blank">Life Science</a> </li>
</ul>
<h3><a id="sciml">Software</a></h3>
<ul>
<li><a href="https://github.com/apengsigkarup/OceanWave3D-Fortran90" target="_blank">OceanWave3D (Fortran 90)</a></li>
<li><a href="https://www2.compute.dtu.dk/~apek/OceanWave3D/" target="_blank">MarineSEM: A collection of free surface incompressible flow solvers</a></li>
<li><a href="https://www.sciencedirect.com/science/article/pii/S0045782524006613?via%3Dihub" target="_blank">Physics-Informed Holomorphic Neural Networks (PIHNN) (Python)</a>, <a href="https://www.youtube.com/watch?v=37mDjIVfSho">Online Talk, CRUNCH SEMINAR, Oct 25, 2024</a></li>
<li><a href="http://www.limitcycle.it/dabi/dtu-uq.html" target="_blank">Spectral Tensor Train Decomposition (Python)</a></li>
<li><a href="https://github.com/MarcusGalea/PhysicsInformedRegression.jl">Physics-informed Regression (Julia)</a></li>
</ul>
<!--
<p></p><h3><a id="nlp">Natural language processing</a></h3>
<a href="https://pubmed.ncbi.nlm.nih.gov/23462700/" target="_blank">Search for health informatics</a>, understanding
<a href="https://arxiv.org/abs/2207.08143" target="_blank">large language models in the medical context</a> and developing algorithms for
<a href="https://proceedings.mlr.press/v202/lievin23a.html" target="_blank">end-to-end learning of joint retrieval and generation models</a>.
<p></p><h3><a id="ai4science">AI for science</a></h3>
Making <a href="https://www.nature.com/articles/s41597-022-01870-w" target="_blank">datasets</a> for training
<a href="https://iopscience.iop.org/article/10.1088/2632-2153/aca23e" target="_blank">models</a> that can act as fast
surrogates for physical models such as density functional theory (DFT).
-->
<h2><a id="selected-publications">Publications (selected highlights)</a></h2>
Published collaborative research works are listed here.
<table border="0" cellspacing="2" cellpadding="2"><tbody>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2602.11425" target="_blank">
<!-- Replace with a representative figure if available -->
<img src="assets/SurfaceImpedanceNeuralFields.png" alt="Link to paper" width="180px">
</a>
</td>
<td valign="top">
<b>Surface impedance inference via neural fields and sparse acoustic data obtained by a compact array</b>
<p>
Standardized laboratory characterizations for absorbing materials rely on idealized sound field assumptions, which deviate largely from real-life conditions. Consequently, \emph{in-situ} acoustic characterization has become essential for accurate diagnosis and virtual prototyping. We propose a physics-informed neural field that reconstructs local, near-surface broadband sound fields from sparse pressure samples to directly infer complex surface impedance. A parallel, multi-frequency architecture enables a broadband impedance retrieval within runtimes on the order of seconds to minutes. To validate the method, we developed a compact microphone array with low hardware complexity. Numerical verifications and laboratory experiments demonstrate accurate impedance retrieval with a small number of sensors under realistic conditions. We further showcase the approach in a vehicle cabin to provide practical guidance on measurement locations that avoid strong interference. Here, we show that this approach offers a robust means of characterizing \emph{in-situ} boundary conditions for architectural and automotive acoustics.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=Xia%2C+Yuanxin" target="_blank">Yuanxin Xia</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Li%2C+Xinyan" target="_blank">Xinyan Li</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Calaf%C3%A0%2C+Matteo" target="_blank">Matteo Calafà</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig-Karup%2C+Allan+P" target="_blank">Allan P. Engsig-Karup</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Jeong%2C+Cheol-Ho" target="_blank">Cheol-Ho Jeong</a>
<br>
<em>arXiv:2602.11425 [cs.SD]</em>, submitted Feb 11, 2026.
<br>
<a href="https://arxiv.org/abs/2602.11425" target="_blank">Link to paper</a>.
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2602.05416" target="_blank">
<!-- Replace with a representative figure if you have one -->
<img src="assets/ReducedOrderSurrogates_CoastalOcean.png" alt="Link to paper" width="180px">
</a>
</td>
<td valign="top">
<b>Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models</b>
<p>
While POD-based surrogates are widely explored for hydrodynamic applications, the use of Koopman Autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a flexible Koopman autoencoder formulation that incorporates meteorological forcings and boundary conditions, and systematically compares its performance against POD-based surrogates. The Koopman autoencoder employs a learned linear temporal operator in latent space, enabling eigenvalue regularization to promote temporal stability. This strategy is evaluated alongside temporal unrolling techniques for achieving stable and accurate long-term predictions. The models are assessed on three test cases spanning distinct dynamical regimes, with prediction horizons up to one year at 30-minute temporal resolution. Across all cases, the Koopman autoencoder with temporal unrolling yields the best overall accuracy compared to the POD-based surrogates, achieving relative root-mean-squared-errors of 0.01-0.13 and R2-values of 0.65-0.996. Prediction errors are largest for current velocities, and smallest for water surface elevations. Comparing to in-situ observations, the surrogate yields -0.65% to 12% change in water surface elevation prediction error when compared to prediction errors of the physics-based model. These error levels, corresponding to a few centimeters, are acceptable for many practical applications, while inference speed-ups of 300-1400x enables workflows such as ensemble forecasting and long climate simulations for coastal-ocean modelling.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=Petersen%2C+Freja+H%C3%B8gholm" target="_blank">Freja Høgholm Petersen</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Mariegaard%2C+Jesper+Sandvig" target="_blank">Jesper Sandvig Mariegaard</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Palmitessa%2C+Rocco" target="_blank">Rocco Palmitessa</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig-Karup%2C+Allan+Peter" target="_blank">Allan Peter Engsig-Karup</a>
<br>
<em>arXiv:2602.05416 [cs.CE]</em>, submitted Feb 5, 2026.
<br>
<a href="https://arxiv.org/abs/2602.05416" target="_blank">Link to paper</a>.
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2601.01895" target="_blank">
<!-- Replace with your own image if desired -->
<img src="assets/UnstructuredSubgridShallowWater.png" alt="Link to paper" width="180px">
</a>
</td>
<td valign="top">
<b>An unstructured second-order subgrid method for the shallow water equations</b>
<p>
We propose a new unstructured numerical subgrid method for solving the shallow water equations using a finite volume method with enhanced bathymetry resolution. The method employs an unstructured triangular mesh with support for triangulation of elements to form finer subgrids locally. The bathymetry is represented on the fine mesh, allowing the incorporation of small-scale features, while velocities are defined on the coarse mesh. The governing equations are solved numerically on the coarse mesh, making the method computationally cheaper compared to a traditional fine mesh computation. To accurately represent the velocities, we employ a second-order accurate WENO method and for temporal integration an explicit second-order accurate Runge-Kutta method. Furthermore, we present a novel subgrid face value reconstruction that accounts for partially wet cells, where only some of the subgrid cells are wet. Together with a newly developed gravity source term discretization, we demonstrate that the scheme is well-balanced on the subgrid level. Finally, the subgrid method is validated on several test cases to show: i) that the scheme is well-balanced, ii) confirm the order of the accuracy of the scheme, and iii) demonstrate the capability of handling moving flood and dry boundaries. We also highlight when it is beneficial to increase the number of subgrid cells to improve the results of the finite volume method.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=Bitsch%2C+Max+Ebstrup" target="_blank">Max Ebstrup Bitsch</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Heilmann%2C+Irene+Torpe" target="_blank">Irene Torpe Heilmann</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig-Karup%2C+Allan+Peter" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=S%C3%B8rensen%2C+Ole+Rene" target="_blank">Ole Rene Sørensen</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Grooss%2C+Jesper" target="_blank">Jesper Grooss</a>
<br>
<em>arXiv:2601.01895 [math.NA]</em>, submitted January 5, 2026.
<br>
<a href="https://arxiv.org/abs/2601.01895" target="_blank">Link to paper</a>, <a href="podcasts/LLMNotebookPodcastWater_movement_modeling_breakthrough_speeds_flood_prediction.m4a"><img src="assets/iconGoogleNOTEBOOK.svg">LLMNotebook podcast (English)</a>.
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2512.23648" target="_blank">
<img src="assets/SEMSteadyStateFreeSurfaceFlows.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A High-Order Spectral Element Solver for Steady-State Free Surface Flows</b>
<p>
We present a spectral element solver for the steady incompressible Navier-Stokes equations subject to a free surface. Utilizing the kinematic behaviour of the free surface boundary, an iterative pseudo-time procedure is proposed to determine the a priori unknown free surface profile. The numerical model is implemented in the open-source finite element framework Firedrake, which enables the use of a high-order polynomial basis on unstructured meshes through weak formulations. Additionally, the curvature of the free surface and submerged bodies is incorporated through curvilinear elements obtained via transfinite linear blending, which conserves the high-order convergent properties of the overall scheme. The model is applied to several benchmark cases in two spatial dimensions. Initially, it addresses fixed-domain problems, including the lid-driven cavity flow and flows around bodies such as a cylinder and a NACA airfoil. Subsequently, with the presence of a free surface, it is extended to determine the flow around a bathymetry bump and a submerged NACA airfoil. The results confirm the high-order accuracy of the model through convergence studies and demonstrate a substantial speed-up over low-order numerical schemes.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=Minniti%2C+Simone" target="_blank">Simone Minniti</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Visbech%2C+Jens" target="_blank">Jens Visbech</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Eskilsson%2C+Claes" target="_blank">Claes Eskilsson</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Parolini%2C+Nicola" target="_blank">Nicola Parolini</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig-Karup%2C+Allan+Peter" target="_blank">Allan Peter Engsig-Karup</a>
<br>
<em>arXiv:2512.23648 [math.NA]</em>, submitted Dec 29, 2025.
<br>
<a href="https://arxiv.org/abs/2512.23648" target="_blank">Link to paper</a>, <a href="podcasts/LLMNotebook_210x_Faster_CFD_for_Free_Surface_Flow.m4a"><img src="assets/iconGoogleNOTEBOOK.svg">LLMNotebook podcast (English)</a>.
<!-- Add code / dataset links here if available, e.g.: -->
<!-- <a href="https://github.com/..." target="_blank">Link to code</a>. -->
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2511.18071" target="_blank">
<img src="assets/SubspaceAccelerationWaterWaves.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Subspace Acceleration for Efficient Nonlinear Water Wave Simulation</b>
<p>
Efficient simulation of nonlinear and dispersive free-surface flows governed by the incompressible Navier-Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a time-dependent discretized Poisson problem at every time step to enforce divergence free flow. This is crucial to ensure conservation of mass and requires solving long sequences of time-dependent linear systems typically using iterative methods, such as the preconditioned Krylov subspace methods. In this work, we investigate new subspace acceleration techniques for improving initial guesses to reduce the number of iterations required by iterative solvers, with a focus on nonlinear wave propagation problems. We extend the original subspace acceleration method by incorporating the complete history of previous solutions through an exponentially weighted formulation. This approach eliminates the need for repeated sketching and orthonormalization, resulting in a more efficient and scalable strategy to generate better initial guesses. Our method is implemented within a high-order finite-difference framework using a method-of-lines formulation and a low-storage Runge-Kutta time integration scheme. We demonstrate that subspace acceleration significantly reduces the number of GMRES iterations when solving the Poisson equation in nonlinear water wave simulations. Performance is evaluated on two benchmark problems: nonlinear stream function wave propagation and harmonic wave generation over a submerged bar. In both cases, the new approach achieves substantial improvements in computational efficiency without compromising accuracy. Although demonstrated using high-order finite difference methods, the technique is discretization independent and broadly applicable to incompressible free-surface flow solvers.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=S%C3%B8rensen%2C+Rasmus+Kleist+H%C3%B8rlyck">Rasmus Kleist Hørlyck Sørensen</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Guido%2C+Margherita">Margherita Guido</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig-Karup%2C+Allan+Peter">Allan Peter Engsig-Karup</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Kressner%2C+Daniel">Daniel Kressner</a>
<br>
<em>arXiv:2511.18071 [physics.flu-dyn]</em>, submitted November 25, 2025.
<br>
<a href="https://arxiv.org/abs/2511.18071" target="_blank">Link to paper</a>, <a href="podcasts/LLMNotebook_SubspaceAcceleration.m4a"><img src="assets/iconGoogleNOTEBOOK.svg">LLMNotebook podcast (English)</a>.
</td>
</tr>
<tr>
<td valign="top">
<a href="https://openreview.net/pdf?id=bjyUK5NX0a" target="_blank">
<img src="assets/TICRAAntennaArrays.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Differentiable Simulations for Joint Parameterised Optimisation of Antenna Arrays</b>
<p>
Many modern antenna systems rely on active electronically scanned array technol-
ogy to reconfigure antenna systems in real-time. The scanning of arrays requires
correct array excitation coefficients. To obtain excitation coefficients that satisfy
an ample space of reconfigurability, a considerable number of inverse problems
usually need to be solved. This is either done with heuristics, optimisers or through
costly physical measurements. In this work, we discuss our experience with imple-
menting a batchable and differentiable antenna array simulation tool and utilising it
in combination with neural networks to solve large-scale excitation synthesis using
joint parametric optimisation. The method enables us to train neural networks to
solve a wide range of beam-shaping problems in an end-to-end manner. We have
observed that the method is competitive with direct optimisation methods when
a large number of problems need to be solved. However, the current approach
does not yet achieve the same solution quality as a well-tuned direct optimisation
method.
</p>
<a href="" target="_blank">Niels Skovgaard Jensen</a>,
<a href="" target="_blank">Frederik Faye</a>,
<a href="" target="_blank">Lasse Hjuler Christiansen</a>
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<br>
<em>A workshop @ EurIPS 2025</em>, December 6, 2025.
<br>
<a href="https://openreview.net/pdf?id=bjyUK5NX0a" target="_blank">Link to paper</a>.
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2508.19249" target="_blank">
<!-- <img src="assets/arxiv_logo.png" alt="arXiv link" width="130px"> -->
<img src="assets/VonKarmenVotextSensing.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Physics-Informed Regression: Parameter Estimation in Parameter-Linear Nonlinear Dynamic Models</b>
<p>
We present a new efficient hybrid parameter estimation method based on the idea, that if nonlinear dynamic models are stated in terms of a system of equations that is linear in terms of the parameters, then regularized ordinary least squares can be used to estimate these parameters from time series data. We introduce the term "Physics-Informed Regression" (PIR) to describe the proposed data-driven hybrid technique as a way to bridge theory and data by use of ordinary least squares to efficiently perform parameter estimation of the model coefficients of different parameter-linear models; providing examples of models based on nonlinear ordinary equations (ODE) and partial differential equations (PDE). The focus is on parameter estimation on a selection of ODE and PDE models, each illustrating performance in different model characteristics. For two relevant epidemic models of different complexity and number of parameters, PIR is tested and compared against the related technique, physics-informed neural networks (PINN), both on synthetic data generated from known target parameters and on real public Danish time series data collected during the COVID-19 pandemic in Denmark. Both methods were able to estimate the target parameters, while PIR showed to perform noticeably better, especially on a compartment model with higher complexity. Given the difference in computational speed, it is concluded that the PIR method is superior to PINN for the models considered. It is also demonstrated how PIR can be applied to estimate the time-varying parameters of a compartment model that is fitted using real Danish data from the COVID-19 pandemic obtained during a period from 2020 to 2021. The study shows how data-driven and physics-informed techniques may support reliable and fast -- possibly real-time -- parameter estimation in parameter-linear nonlinear dynamic models.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=Nielsen%2C+Jonas+S%C3%B8eborg" target="_blank">Jonas Søeborg Nielsen</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Jacobsen%2C+Marcus+Galea" target="_blank">Marcus Galea Jacobsen</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Olson%2C+Albert+Brincker" target="_blank">Albert Brincker Olson</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=S%C3%B8rensen%2C+Mads+Peter" target="_blank">Mads Peter Sørensen</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig-Karup%2C+Allan+Peter" target="_blank">Allan Peter Engsig-Karup</a>
<br>
<em>arXiv:2508.19249 [cs.LG]</em>, submitted July 25, 2025.
<br>
<a href="https://arxiv.org/abs/2508.19249" target="_blank">Link to paper</a>. <a href="https://github.com/MEGAjosni/Physics-Informed-Regression/tree/main/scripts">Link to Julia code.</a>, <a href="podcasts/LLMNotebook_PIR.mp4"><img src="assets/iconGoogleNOTEBOOK.svg">LLMNotebook podcast (Danish)</a>, <a href="podcasts/LLMNotebook_PIR_English.mp4"><img src="assets/iconGoogleNOTEBOOK.svg">LLMNotebook podcast (English)</a>.
</td>
</tr>
<tr>
<td valign="top">
<a href="https://www.sciencedirect.com/science/article/pii/S0029801825020694" target="_blank">
<!-- <img src="assets/arxiv_logo.png" alt="Link" width="130px"> -->
<img src="assets/NektarppFNPFsemicircularchannel.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A co-simulation approach to modelling fully nonlinear water waves using the spectral/hp element method</b>
<p>
We present a σ-transformed fully nonlinear potential flow (FNPF) model implemented in the open-source spectral/hp element framework Nektar++. The solver splits the problem into (i) free-surface Zakharov equations and (ii) a σ-transformed Laplace continuity equation, coupled at run-time via the CWIPI code coupler. A linear/nonlinear operator splitting avoids re-factorizing the time-dependent Laplace matrix each step. Convergence, scaling, and three benchmarks (semicircular channel, Whalin shoal, and crescent waves) demonstrate accuracy and practicality.
</p>
<a href="" target="_blank">Claes Eskilsson</a>,
<a href="" target="_blank">Hamidreza Abedi</a>,
<a href="" target="_blank">Allan P. Engsig‑Karup</a>,
<br>
<em>Ocean Engineering</em> <b>340</b> (2025) 122385
<a href="https://doi.org/10.1016/j.oceaneng.2025.122385" target="_blank">Link to article</a>
<br>
<a href="https://www.sciencedirect.com/science/article/pii/S0029801825020694" target="_blank">Link to article</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2507.22678" target="_blank">
<!-- <img src="assets/arxiv_logo.png" alt="arXiv link" width="130px"> -->
<img src="assets/PIHKANmultiplyconnecteddomain.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains</b>
<p>
Physics‑informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to satisfy boundary conditions, often resulting in significantly improved accuracy and computational efficiency compared to traditional physics-informed neural networks (PINNs). In this work, we improve and extend the application of PIHNNs to two-dimensional problems. First, we introduce a novel holomorphic network architecture based on the Kolmogorov‑Arnold representation (PIHKAN), which achieves higher accuracy with reduced model complexity. Second, we develop mathematical extensions that broaden the applicability of PIHNNs to a wider class of elliptic partial differential equations, including the Helmholtz equation. Finally, we propose a new method based on Laurent series theory that enables the application of holomorphic networks to multiply‑connected plane domains, thereby removing the previous limitation to simply‑connected geometries.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=Calaf%C3%A0%2C+Matteo" target="_blank">Matteo Calafà</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Andriollo%2C+Tito" target="_blank">Tito Andriollo</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig‑Karup%2C+Allan+P." target="_blank">Allan P. Engsig‑Karup</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Jeong%2C+Cheol‑Ho" target="_blank">Cheol‑Ho Jeong</a>
<br>
<em>arXiv:2507.22678 [cs.CE]</em>, submitted July 30, 2025.
<br>
<a href="https://arxiv.org/abs/2507.22678" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://www.sciencedirect.com/science/article/pii/S0003682X25004074" target="_blank">
<!-- <img src="assets/arxiv_logo.png" alt="Link" width="130px"> -->
<img src="assets/BalconyConfiguration.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>On the Impact of Building Façade Design on Road Traffic and Rooftop Noise Using the Nodal Discontinuous Galerkin Finite Element Method</b>
<p>
This study numerically assesses the acoustic impact of different building façade design strategies for two sound source locations: one corresponding to road traffic noise and another to rooftop-mounted building services. Using a 3D nodal discontinuous Galerkin finite element method, the simulations capture wave phenomena at low frequencies more accurately than traditional methods. Results show reflections in street canyons can increase rooftop-source noise by up to 12 dB. Balconies exhibited screening or amplifying effects between −3.5 dB and +6.3 dB depending on source placement. Rooftop noise was heavily influenced by façade tilting (−8.4 dB to +4.6 dB), while balconies had minor effects (~±1 dB). The numerical results were validated experimentally with a scale model test. :contentReference[oaicite:1]{index=1}
</p>
<a href="https://ssrn.com/abstract=5043583" target="_blank">Sophia Julia Feriani</a>,
<a href="https://ssrn.com/author=Allan+Peter+Engsig‑Karup" target="_blank">Allan Peter Engsig‑Karup</a>,
<a href="https://ssrn.com/author=Cheol‑Ho+Jeong" target="_blank">Cheol‑Ho Jeong</a>
<br>
<em>Applied Acoustics</em>, 2025.
<br>
<a href="https://www.sciencedirect.com/science/article/pii/S0003682X25004074" target="_blank">Link to article</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2506.09435" target="_blank">
<!-- <img src="assets/arxiv_logo.png" alt="arXiv link" width="130px"> -->
<img src="assets/FNPF-SEM_breakwater.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>FNPF‑SEM: A parallel spectral element model in Firedrake for fully nonlinear water wave simulations</b>
<p>
We present a new parallel spectral element solver, FNPF-SEM, for simulating linear and fully nonlinear potential flow-based water waves and their interaction with offshore structures. The tool is designed as a general-purpose wave model for offshore engineering applications. Built within the open-source framework Firedrake, the new FNPF-SEM model is designed as a computational tool capable of capturing both linear and nonlinear wave phenomena with high accuracy and efficiency, with support for high-order (spectral) finite elements. Additionally, Firedrake provides native support for MPI-based parallelism, allowing for efficient multi-CPU distributed computations needed for large-scale simulations. We demonstrate the capabilities of the high-order spectral element model through h- and p-convergence studies, and weak and strong scaling tests. Validation is performed against analytical solutions and experimental data for several benchmark cases, including nonlinear high-order harmonic generation and linear and nonlinear wave interactions with a cylinder and a breakwater. The new FNPF-SEM model offers a numerical framework for simulating wave propagation and wave-structure interactions, with the following key features: i) the ability to represent complex geometries through flexible, unstructured finite element meshes; ii) reduced numerical diffusion and dispersion by using high-order polynomial expansions; and iii) scalability to full- and large-scale simulations over long time periods through a parallel implementation.
</p>
<a href="https://arxiv.org/search/?searchtype=author&query=Visbech%2C+Jens" target="_blank">Jens Visbech</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Melander%2C+Anders" target="_blank">Anders Melander</a>,
<a href="https://arxiv.org/search/?searchtype=author&query=Engsig‑Karup%2C+Allan+Peter" target="_blank">Allan Peter Engsig‑Karup</a>
<br>
<em>arXiv:2506.09435 [math.NA]</em>, submitted June 11, 2025.
<br>
<a href="https://arxiv.org/abs/2506.09435" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://onlinelibrary.wiley.com/doi/10.1002/fld.5387" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/FreeSurfaceINSSpectral.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A High-Order Hybrid-Spectral Incompressible Navier–Stokes Model for Non-Linear Water Waves</b>
<p>
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier–Stokes equations with a free surface for the accurate simulation of non-linear and dispersive water waves in the time domain. The spatial discretization is based on Chebyshev polynomials in the vertical direction and a Fourier basis in the horizontal direction, allowing for the use of the fast Chebyshev and Fourier transforms for the efficient computation of spatial derivatives. The temporal discretization is done through a generalized low-storage explicit fourth-order Runge–Kutta, and for the scheme to conserve mass and achieve high-order accuracy, a velocity-pressure coupling needs to be satisfied at all Runge–Kutta stages. This results in the emergence of a Poisson pressure problem that constitutes a geometric conservation law for mass conservation. The occurring Poisson problem is proposed to be solved efficiently via an accelerated iterative solver based on a geometric
-multigrid scheme, which takes advantage of the high-order polynomial basis in the spatial discretization and hence distinguishes itself from conventional low-order numerical schemes. We present numerical experiments for validation of the scheme in the context of numerical wave tanks demonstrating that the
-multigrid accelerated numerical scheme can effectively solve the Poisson problem that constitute the computational bottleneck, that the model can achieve the desired spectral convergence, and is capable of simulating wave-propagation over non-flat bottoms with excellent agreement in comparison to experimental results.
</p>
<a href="" target="_blank">Anders Melander</a>,
<a href="" target="_blank">Max Ebstrup Bitsch</a>,
<a href="" target="_blank">Dong Chen</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>
<br>
<em>International Journal of Numerical Methods in Fluids</em>, 2025
<br>
<a href="https://onlinelibrary.wiley.com/doi/10.1002/fld.5387" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://www.medrxiv.org/content/10.1101/2025.01.21.25320878v1" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/CalibratedXGBoost.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Conformal Prediction and Venn-ABERS Calibration for Reliable Machine Learning-Based Prediction of Bacterial Infection Focus</b>
<p>
Finding the focus of bacterial infections can be challenging, especially for hospitalised patients. Conventional microbiological diagnostic methods are either time consuming, expensive, or difficult to interpret due to contamination. The aim of this study was to apply machine learning (ML) to reliably predict the focus of bacterial infections. This study utilised a dataset including samples from 10,153 patients, collected from November 1, 2019 to June 3, 2023 at Rigshospitalet, Denmark. The dataset contains microbiological findings, biochemical data, and vital parameters. The dataset was analysed using ML. The ML-outputs were calibrated using Venn-ABERS calibration and model uncertainty was addressed using conformal risk control. The best performing model was the XGBoost model achieving an AUC of 0.93 ± 0.051 (mean ± SD.). Combining the model with methods from the conformal prediction framework achieves predictive capabilities that surpasses similar studies, while also accounting for model uncertainty by providing statistically robust uncertainty estimates.
</p>
<a href="" target="_blank">Jacob Bahnsen Schmidt</a>,
<a href="" target="_blank">Karen Leth Nielsen</a>,
<a href="" target="_blank">Dmytro Strunin</a>,
<a href="" target="_blank">Nikolai Søren Kirkby</a>,
<a href="" target="_blank">Jesper Qvist Thomassen</a>,
<a href="" target="_blank">Steen Christian Rasmussen</a>,
<a href="" target="_blank">Ruth Frikke-Schmidt</a>,
<a href="" target="_blank">Frederik Boëtius Hertz</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>
<br>
<em>medrxiv.org/content/10.1101/2025.01.21.25320878v1</em>, 2025
<br>
<a href="https://www.medrxiv.org/content/10.1101/2025.01.21.25320878v1" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://publications.isope.org/proceedings/ISOPE/ISOPE%202023/data/pdfs/156-2023-FOWT-14.pdf" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/ModelScaleWindTurbineISOPE.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A High-order Accurate Spectral Element-based Time-Domain Simulation of a Model-Scale Floating Offshore Wind Turbine</b>
<p>
This paper describes a new high-order composite numerical model for simulating moored floating offshore bodies. We focus on a floating offshore wind turbine and its static equilibrium and free decay. The composite scheme models linear to weakly nonlinear motions in the time domain by solving the Cummins equations. Mooring forces are acquired from a discontinuous Galerkin finite element solver. Linear hydrodynamic coefficients are computed by solving a pseudo-impulsive radiation problem in three dimensions using a spectral element method. Numerical simulations of a moored model-scale floating offshore wind turbine were performed and compared with experimental measurements for validation, ultimately showing a fair agreement.
</p>
<a href="" target="_blank">Jens Visbech</a>,
<a href="" target="_blank">Harry B. Bingham</a>,
<a href="" target="_blank">Claes Eskilsson</a>,
<a href="" target="_blank">Johannes Palm</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>
<br>
<em>International Journal of Offshore and Polar Engineering</em>, 2024
<br>
<a href="https://publications.isope.org/proceedings/ISOPE/ISOPE%202023/data/pdfs/156-2023-FOWT-14.pdf" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://link.springer.com/article/10.1007/s42286-024-00098-y" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/Geometric_p-multigrid_pseudospectral.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A p-Multigrid Hybrid-Spectral Model for Nonlinear Water Waves</b>
<p>
To improve both scale and fidelity of numerical water wave simulations to study the evolution of wave fields within offshore engineering, it is of key practical interest to achieve high numerical efficiency. We propose a p-multigrid accelerated time-domain scheme for efficient and
-scalable solution of a hybrid-spectral model for the simulation of highly nonlinear and highly dispersive water waves, the accurate calculation of wave kinematics and taking into account varying water depth. To achieve low numerical dispersive and dissipate errors, a high-order hybrid-spectral collocation scheme is implemented to solve the fully nonlinear potential flow (FNPF) equations, and utilizing a p-multigrid iterative solver scheme for solving the Laplace problem. Hereby, the numerical scheme combines the high accuracy of spectral methods, high efficiency of the fast Fourier transform (FFT) algorithm, and multigrid methods. Numerical analysis is performed to evaluate the performance and confirm the spectral accuracy of the scheme. Numerical experiments are considered for steady nonlinear wave propagation. A Fourier-continuation technique is used to extend the scheme from a periodic domain setup to perform benchmarks in a finite domain setup for numerical wave tanks utilizing conventional techniques for wave generation and absorption, and with results in excellent agreement with experimental measurements.
</p>
<a href="" target="_blank">Anders Melander</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>
<br>
<em>Water Waves</em>, 2024
<br>
<a href="https://link.springer.com/article/10.1007/s42286-024-00098-y" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2407.01088" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/PIHNNLinearElasticity.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving Linear Elasticity Problems</b>
<p>
We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity and, by leveraging the Kolosov-Muskhelishvili representation of the solution in terms of holomorphic potentials, we train a complex-valued neural network to fulfill stress and displacement boundary conditions while automatically satisfying the governing equations. This is achieved by designing the network to return only approximations that inherently satisfy the Cauchy-Riemann conditions through specific choices of layers and activation functions. To ensure generality, we provide a universal approximation theorem guaranteeing that, under basic assumptions, the proposed holomorphic neural networks can approximate any holomorphic function. Furthermore, we suggest a new tailored weight initialization technique to mitigate the issue of vanishing/exploding gradients. Compared to the standard PINN approach, noteworthy benefits of the proposed method for the linear elasticity problem include a more efficient training, as evaluations are needed solely on the boundary of the domain, lower memory requirements, due to the reduced number of training points, and C∞ regularity of the learned solution. Several benchmark examples are used to verify the correctness of the obtained PIHNN approximations, the substantial benefits over traditional PINNs, and the possibility to deal with non-trivial, multiply-connected geometries via a domain-decomposition strategy.
</p>
<a href="" target="_blank">Matteo Calafa</a>,
<a href="" target="_blank">Emil Hovad</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>,
<a href="" target="_blank">Tito Andriollo</a>
<br>
<em>Arxiv preprint</em>, 2024
<br>
<a href="https://arxiv.org/abs/2407.01088" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://openreview.net/forum?id=8SvMFLOXvf&referrer=%5Bthe%20profile%20of%20Freja%20Petersen%5D(%2Fprofile%3Fid%3D~Freja_Petersen1)" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/ICLR2024_multifidelity.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Data-driven Multi-Fidelity Modelling for Time-dependent Partial Differential Equations using Convolutional Neural Networks</b>
<p>
We present a general multi-fidelity (MF) framework which is applied through utilizing flexible-order explicit finite difference numerical schemes using convolutional neural networks (CNNs) by combining low-order simulation data with higher order simulation data obtained from numerical simulations based on partial differential equations (PDEs). This allows for improving the performance of low-order numerical simulation through learning from the data how to correct the numerical schemes to achieve improved accuracy. Through the lens of numerical analysis we evaluate the accuracy, efficiency and generalizability of constructed data-driven MF-models. To illustrate the concept, the construction of the MF models uses CNNs and is evaluated for numerical schemes designed for solving linear PDEs; the heat, the linear advection equation and linearized 1D shallow water equations. The numerical schemes allow for a high level of explainability of data-driven correction terms obtained via CNNs through numerical analysis of truncation errors. It is demonstrated that data-driven MF models is a means to improve the accuracy of LF models through operator correction.
</p>
<a href="" target="_blank">Freja Petersen</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>
<br>
<em>ICLR</em>, 2024
<br>
<a href="https://openreview.net/forum?id=8SvMFLOXvf&referrer=%5Bthe%20profile%20of%20Freja%20Petersen%5D(%2Fprofile%3Fid%3D~Freja_Petersen1)" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://www.sciencedirect.com/science/article/pii/S0045782524001270?via%3Dihub" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/3DMeshFloatingSphere.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Solving the complete pseudo-impulsive radiation and diffraction problem using a spectral element method
</b>
<p>
This paper presents a novel, efficient, high-order accurate, and stable spectral element-based model for computing the complete three-dimensional linear radiation and diffraction problem for floating offshore structures. We present a solution to a pseudo-impulsive formulation in the time domain, where the frequency-dependent quantities, such as added mass, radiation damping, and wave excitation force for arbitrary heading angle,
, are evaluated using Fourier transforms from the tailored time-domain responses. The spatial domain is tessellated by an unstructured high-order hybrid configured mesh and with solutions represented by piece-wise polynomial basis functions in the spectral element space. Fourth-order accurate time integration is employed, making the entire numerical scheme a high-order scheme. The model can use symmetry boundaries in the spatial representation to reduce the computational burden. The key piece of the numerical model – the discrete Laplace solver – is verified through
- and
-convergence studies. Moreover, to highlight the capabilities of the proposed model, we present proof-of-concept examples of simple floating bodies (a hemisphere and a box). Also, an oscillating water column is considered, including generalized modes representing the piston motion and wave sloshing effects inside the wave energy converter chamber. In this case, the spectral element model trivially computes the infinite-frequency added mass, which is a singular problem for conventional boundary element-type solvers. The proposed model serves its practical purpose within the field of offshore engineering for simulations of floating offshore wind turbines, wave energy converters, and much more.
</p>
<a href="" target="_blank">Jens Visbech</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>,
<a href="" target="_blank">Harry Bingham</a>
<br>
<em>CMAME</em>, 2024
<br>
<a href="https://www.sciencedirect.com/science/article/pii/S0045782524001270?via%3Dihub" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://arxiv.org/abs/2404.08464" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/PML_DGFEM_OutdoorAcoustics.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A stable decoupled perfectly matched layer for the 3D wave equation using the nodal discontinuous Galerkin method
</b>
<p>
In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a efficient boundary treatment, the computational cost is lowered. One commonly used boundary treatment is the perfectly matched layer (PML) that dampens outgoing waves without polluting the computed solution in the inner domain. The purpose of this study is to propose and assess a new perfectly matched layer formulation for the 3D acoustic wave equation, using the nodal discontinuous Galerkin finite element method. The formulation is based on an efficient PML formulation that can be decoupled to further increase the computational efficiency and guarantee stability without sacrificing accuracy. This decoupled PML formulation is demonstrated to be long-time stable and an optimization procedure of the damping functions is proposed to enhance the performance of the formulation.
</p>
<a href="" target="_blank">Sophia Julia Feriani</a>,
<a href="" target="_blank">Matthias Cosnefroy</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>,
<a href="" target="_blank">Tim Warburton</a>,
<a href="" target="_blank">Finnur Pind</a>,
<a href="" target="_blank">Cheol-Ho Jeong</a>
<br>
<em>Arxiv preprint</em>, 2024
<br>
<a href="https://arxiv.org/abs/2404.08464" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://sites.dundee.ac.uk/iwwwfb2024/wp-content/uploads/sites/197/2024/04/IWWWFB39_16.pdf" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/NavierStokesEquationsIWWWFB2024.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A High-Order Finite Difference Incompressible
Navier-Stokes model for Water Waves and
Wave-Structure Interaction</b>
<p>
We propose a new high-order finite difference numerical model for the simulation
of nonlinear water waves and wave-structure interaction with fixed structures using the
Navier-Stokes equations. The complete formulation is described in three spatial dimensions (3D) and preliminary validation results are here presented for two spatial dimensions (2D). A spatially fixed computational domain is defined through introducing a
sigma-coordinate that transform the Navier–Stokes equations along the vertical dimension
from the sea bed to the still water level. Numerical experiments highlights both the
correctness of the solution, the high-order convergence property that is attractive for efficient solutions as well as the classical benchmark problem due to Beji & Battjes (1994)
where experimental measurements are available and hence serve as validation of the new
high-order numerical scheme.
</p>
<a href="" target="_blank">Allan P. Engsig-Karup</a>,
<a href="" target="_blank">Anders Melander</a>
<br>
<em>IWWWFB</em>, 2024
<br>
<a href="https://sites.dundee.ac.uk/iwwwfb2024/wp-content/uploads/sites/197/2024/04/IWWWFB39_16.pdf" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://www.pnas.org/doi/10.1073/pnas.2312159120" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="https://www2.compute.dtu.dk/~apek/scientificmachinelearning/SciMLDomeAcousticsDeepONet.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators</b>
<p>
We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization methods are computationally expensive when simulating hundreds of source and receiver positions, making simulations with parametric source positions impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with parametric source positions, achieving millisecond-scale computations.
</p>
<a href="" target="_blank">Nikolas Borrel-Jensen</a>,
<a href="" target="_blank">Somdatta Goswami</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>,
<a href="" target="_blank">George Em Karniadakis</a>,
<a href="" target="_blank">Cheol-Ho Jeong</a>
<br>
<em>PNAS</em>, 2024
<br>
<a href="https://www.pnas.org/doi/10.1073/pnas.2312159120" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://journals.sagepub.com/doi/10.1177/10943420231208948" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/WaveBasedRoomAcoustics.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics</b>
<p>
We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions to handle curvilinear geometries and frequency dependent boundary conditions of relevance in practical room acoustics. The implementation is benchmarked on heterogeneous multi-device many-core computing architectures, and high performance and scalability are demonstrated for a problem that is considered expensive to solve in practical applications. In a benchmark study, scaling tests show that multi-GPU support gives the ability to simulate large rooms, over a broad frequency range, with realistic boundary conditions, both in terms of computing time and memory requirements. Furthermore, numerical simulations on two non-trivial geometries are presented, a star-shaped room with a dome and an auditorium. Overall, this shows the viability of using a multi-device accelerated DGFEM solver to enable realistic large-scale wave-based room acoustics simulations.
</p>
<a href="" target="_blank">Anders Melander</a>,
<a href="" target="_blank">Emil Strøm</a>,
<a href="" target="_blank">Finnur Pind</a>,
<a href="" target="_blank">Allan P. Engsig-Karup</a>,
<a href="" target="_blank">Cheol-Ho Jeong</a>,
<a href="" target="_blank">Tim Warburton</a>,
<a href="" target="_blank">Noel Chalmers</a>,
<a href="" target="_blank">Jan S. Hesthaven</a>
<br>
<em>The International Journal of High Performance Computing Applications</em>, 2023
<br>
<a href="https://journals.sagepub.com/doi/10.1177/10943420231208948" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://www.sciencedirect.com/science/article/pii/S0043135422009198" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/1-s2.0-S0043135422009198-gr2_lrg.jpg" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Accelerating hydrodynamic simulations of urban drainage systems with physics-guided machine learning</b>
<p>
We propose and demonstrate a new approach for fast and accurate surrogate modelling of urban drainage system hydraulics based on physics-guided machine learning. The surrogates are trained against a limited set of simulation results from a hydrodynamic (HiFi) model. Our approach reduces simulation times by one to two orders of magnitude compared to a HiFi model. It is thus slower than e.g. conceptual hydrological models, but it enables simulations of water levels, flows and surcharges in all nodes and links of a drainage network and thus largely preserves the level of detail provided by HiFi models.
</p>
<a href="" target="_blank">Rocco Palmitessa</a>,
<a href="" target="_blank">Morten Grum</a>,
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Roland Lowe</a>
<br>
<em>Water Research</em>, 2022
<br>
<a href="https://www.sciencedirect.com/science/article/pii/S0043135422009198" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://pubs.aip.org/asa/jasa/article-abstract/152/2/851/2839313/Reduced-basis-methods-for-numerical-room-acoustic?redirectedFrom=fulltext" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/FOMvsROMRoomAcoustic.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Reduced basis methods for numerical room acoustic simulations with parametrized boundaries</b>
<p>
The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis method (RBM) to achieve a computational cost reduction relative to a traditional full-order model (FOM) for wave-based room acoustic simulations with parametrized boundaries. The FOM solver is based on the spectral-element method; however, other numerical methods could be applied. The RBM reduces the computational burden by solving the problem in a low-dimensional subspace for parametrized frequency-independent and frequency-dependent boundary conditions. The problem is formulated in the Laplace domain, which ensures the stability of the reduced-order model (ROM). We study the potential of the proposed RBM in terms of computational efficiency, accuracy, and storage requirements, and we show that the RBM leads to 100-fold speedups for a two-dimensional case and 1000-fold speedups for a three-dimensional case with an upper frequency of 2 and 1 kHz, respectively. While the FOM simulations needed to construct the ROM are expensive, we demonstrate that the ROM has the potential of being 3 orders of magnitude faster than the FOM when four different boundary conditions are simulated per room surface.
</p>
<a href="" target="_blank">Hermes Sampedro Llopis </a>,
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Cheol-Ho Jeong</a>,
<a href="" target="_blank">Finnur Pind</a>,
<a href="" target="_blank">Jan S. Hesthaven</a>
<br>
<em>The Journal of the Acoustic Society of America</em>, 2022
<br>
<a href="https://pubs.aip.org/asa/jasa/article-abstract/152/2/851/2839313/Reduced-basis-methods-for-numerical-room-acoustic?redirectedFrom=fulltext" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://pubs.aip.org/asa/jel/article/1/12/122402/219469/Physics-informed-neural-networks-for-one" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/PINNSoundsPropgation1D.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries </b>
<p>
Realistic sound is essential in virtual environments, such as computer games and mixed reality. Efficient and accurate numerical methods for pre-calculating acoustics have been developed over the last decade; however, pre-calculating acoustics makes handling dynamic scenes with moving sources challenging, requiring intractable memory storage. A physics-informed neural network (PINN) method in one dimension is presented, which learns a compact and efficient surrogate model with parameterized moving Gaussian sources and impedance boundaries and satisfies a system of coupled equations. The model shows relative mean errors below 2%/0.2 dB and proposes a first step in developing PINNs for realistic three-dimensional scenes.
</p>
<a href="" target="_blank">Nikolas Borrel-Jensen</a>,
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Cheol-Ho Jeong</a>
<br>
<em>JASA Express Lett.</em>, 2021
<br>
<a href="https://pubs.aip.org/asa/jel/article/1/12/122402/219469/Physics-informed-neural-networks-for-one" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.5011" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/EngsigKarupLaskowskiPMultigrid.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>An efficient p-multigrid spectral element model for fully nonlinear water waves and fixed bodies</b>
<p>
In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave-body interaction with high computational efficiency within a single modeling approach. We design and propose an efficient
-scalable computational procedure based on geometric p-multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high-order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p-multigrid spectral element model can take advantage of the high-order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h-multigrid approaches.
</p>
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Wojciech Laskowski</a>
<br>
<em>International Journal for Numerical Methods in Fluids</em>, 2021
<br>
<a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.5011" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/DenmarkCovid19.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Assessment of the National Test Strategy on the Development of the COVID-19 Pandemic in Denmark</b>
<p>
During the COVID-19 pandemic, Denmark has pursued a mass testing strategy culminating in the testing of 12.167 individuals per 100,000 inhabitants per day during the spring of 2021. The strategy included free access to COVID-19 testing, and since 2021, compulsory documentation for negative tests or vaccination has been required for access to workplace, educational institutions, restaurants, and many other places. Testing and subsequent isolation if testing was positive were voluntary. The present study provides an analysis of whether testing frequency in Denmark showed any correlation to hospitalizations throughout the relevant stages of the pandemic. Mass testing was found not to correlate significantly with the number of hospitalizations during the pandemic. Interestingly, during the highest level of testing in spring 2021 the fraction of positive tests increased slightly; thus, the Danish mass testing strategy, at its best, failed to reduce the prevalence of COVID-19. Furthermore, the relationship between positives in antigen testing and in rt-PCR testing indicated that many patients were not tested early in their infection when the risk of transmission was at the highest. In conclusion, the Danish mass testing strategy for COVID-19 does not appear to have a detectable correlation to the number of hospitalizations due to COVID-19.
</p>
<a href="" target="_blank">Peter Busk</a>,
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Thomas Birk Kristiansen</a>
<br>
<em>Epidemiologia</em>, 2021
<br>
<a href="" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://journals.sagepub.com/eprint/84s23Rh2fCWC49Hust9H/full?justLogout=success" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/DTUComputeGPULABLibraryWeakScaling.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A massively scalable distributed multigrid framework for nonlinear marine hydrodynamics</b>
<p>
The focus is on the parallel scalability of a distributed multigrid framework, known as the DTU Compute GPUlab Library, for execution on graphics processing unit (GPU)-accelerated supercomputers. We demonstrate near-ideal weak scalability for a high-order fully nonlinear potential flow (FNPF) time domain model on the Oak Ridge Titan supercomputer, which is equipped with a large number of many-core CPU-GPU nodes. The high-order finite difference scheme for the solver is implemented to expose data locality and scalability, and the linear Laplace solver is based on an iterative multilevel preconditioned defect correction method designed for high-throughput processing and massive parallelism.
</p>
<a href="" target="_blank">Stefan Lemvig Glimberg</a>,
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Luke N Olson</a>
<br>
<em>The International Journal of High Performance Computing Applications</em>, 2019
<br>
<a href="https://journals.sagepub.com/eprint/84s23Rh2fCWC49Hust9H/full?justLogout=success" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://pubs.aip.org/asa/jasa/article/145/6/3299/939446/Time-domain-room-acoustic-simulations-using-the" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/SEMAcousticSimulation.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Time domain room acoustic simulations using the spectral element method</b>
<p>
This paper presents a wave-based numerical scheme based on a spectral element method,
coupled with an implicit-explicit Runge-Kutta time stepping method, for simulating room
acoustics in the time domain. The scheme has certain features which make it highly attractive for room acoustic simulations, namely a) its low dispersion and dissipation properties
due to a high-order spatio-temporal discretization, b) a high degree of geometric flexibility,
where adaptive, unstructured meshes with curvilinear mesh elements are supported and c) its
suitability for parallel implementation on modern many-core computer hardware. A method
for modelling locally reacting, frequency dependent impedance boundary conditions within
the scheme is developed, in which the boundary impedance is mapped to a multipole rational
function and formulated in differential form. Various numerical experiments are presented,
which reveal the accuracy and cost-efficiency of the proposed numerical scheme.
</p>
<a href="" target="_blank">Finnur Pind</a>,
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Cheol-Ho Jeong</a>,
<a href="" target="_blank">Jan S. Hesthaven</a>,
<a href="" target="_blank">Mikael S. Mejling</a>,
<a href="" target="_blank">Jakob Strømann-Andersen</a>
<br>
<em>The Journal of Acoustic Society of America</em>, 2019
<br>
<a href="https://pubs.aip.org/asa/jasa/article/145/6/3299/939446/Time-domain-room-acoustic-simulations-using-the" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://link.springer.com/article/10.1007/s42241-018-0001-1" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/SpectralElement_NACA00012_INS.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>Spectral/hp element methods: Recent developments, applications, and perspectives</b>
<p>
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
</p>
<a href="" target="_blank">Hui Xui</a>,
<a href="" target="_blank">Chris D. Cantwell</a>,
<a href="" target="_blank">Carlos Monteserin</a>,
<a href="" target="_blank">Claes Eskilsson</a>,
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Spencer J. Sherwin</a>
<br>
<em>Journal of Hydrodynamics</em>, 2018
<br>
<a href="" target="_blank">Link to paper</a>
</td>
</tr>
<tr>
<td valign="top">
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0021999116301255" target="_blank">
<!-- <img src="assets/beyond_pixels.png" alt="Link" width="130px"> -->
<img src="assets/MarineSEMCylinderInteraction.png" alt="Link" width="180px">
</a>
</td>
<td valign="top">
<b>A stabilised nodal spectral element method for fully nonlinear water waves</b>
<p>
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998)
, although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global
projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem.
</p>
<a href="" target="_blank">Allan Peter Engsig-Karup</a>,
<a href="" target="_blank">Claes Eskilsson</a>,
<a href="" target="_blank">Daniele Bigoni</a>
<br>
<em>Journal of Computational Physics</em>, 2016
<br>
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0021999116301255" target="_blank">Link to paper</a>, <a href="podcasts/LLMNotebookPodcastFNPFSEM.mp4"><img src="assets/iconGoogleNOTEBOOK.svg">LLMNotebook podcast</a>
</td>
</tr>
<tr>
<td valign="top">