Support Floquet periodic boundary conditions #314

simlapointe · 2024-12-13T16:16:15Z

Add support for Floquet periodic boundary conditions and improve flexibility of periodic boundary conditions specifications.

Support Floquet boundary conditions by incorporating the phase delay into Maxwell's equations and solving the modified PDE with periodic boundary conditions.
Automatically detect periodic boundary transformations.
Support both translation and rotation transformations.

…tions

…single operator

hughcars

Looking pretty good, I think there are a few larger changes to take care of first

FP should be part of K, given it has no omega dependence in its construction unlike A2. This will simplify loads of things
The muinv kx should be in the MaterialOperator, (doing this neatly will mean adding the ability to use transpose coefficients in the ceed context)
The geodata.cpp can be shortened and simplified some, I have some initial work on doing this in hughcars/periodic-bc, but I'm sure once you get started you'll probably see even more things to do. The basic thing is a mixing assumptions on sdim and no assumptions on sdim.

hughcars · 2025-01-08T15:38:33Z

docs/src/config/boundaries.md

+attribute to the receiver attribute in mesh units. If neither `"Translation"` or
+`"AffineTransformation"` are specified, the transformation between donor and receiver boundaries


Nit: neither "Translation" nor "AffineTransformation"

hughcars · 2025-01-08T15:39:45Z

docs/src/config/solver.md

+eigenmode simulation type. Ignored if non-zero Floquet wave vector is specified in
+[`config["Boundaries"]["Periodic"]["FloquetWaveVector"]`](boundaries.md##boundaries%5B%%22Periodic%22%5D%22FloquetWaveVector%22%5D)
+or [`config["Boundaries"]["FloquetWaveVector"]`](boundaries.md##boundaries%5B%%22FloquetWaveVector%22%5D).


This is also necessary for London equations, so you'll need to reconcile this.

hughcars · 2025-01-08T15:43:19Z

docs/src/examples/cylinder.md

+distance between them is given by the `"Translation"` vector in mesh units. In `floquet.json`,
+an additional `"FloquetWaveVector"` specifies the phase delay between the donor and receiver
+boundaries in the X/Y/Z directions.


Given the relative simplicity of this example, it would be great if we can derive the expected modes analytically. I suspect it'll be possible to map them to an equivalent set of modes on a full length cylinder without phase shift, at which point analytic results can be compared against like for the waveguide case.

hughcars · 2025-01-08T15:59:00Z

docs/src/guide/boundaries.md

@@ -74,7 +74,7 @@ Periodic boundary conditions on an existing mesh can be specified using the
 ["Periodic"](../config/boundaries.md#boundaries%5B%22Periodic%22%5D) boundary keyword. This
 boundary condition enforces that the solution on the specified boundaries be exactly equal,
 and requires that the surface meshes on the donor and receiver boundaries be identical up to
-translation. Periodicity in *Palace* is also supported through meshes generated
+translation or rotation. Periodicity in *Palace* is also supported through meshes generated


How have you tested the rotational case? Might make for a cool example, thinking plausibly the waveguide cylinder could be split into wedges maybe and analyzed.

hughcars · 2025-01-27T19:34:54Z

palace/fem/libceed/operator.hpp

+
+  CeedOperator GetTranspose(std::size_t i) const { return op_t[i]; }
+


Not seeing any use of this so far, why did you need?

hughcars · 2025-01-30T23:00:27Z

palace/utils/configfile.cpp

+    auto trslt = it->find("Translation");
+    if (trslt != it->end())
+    {
+      MFEM_VERIFY(trslt->is_array(),
+                  "\"Translation\" should specify an array in the configuration file!");
+      data.translation = trslt->get<std::array<double, 3>>();
+    }
+    auto trsfr = it->find("AffineTransformation");
+    if (trsfr != it->end())
+    {
+      MFEM_VERIFY(
+          trsfr->is_array(),
+          "\"AffineTransformation\" should specify an array in the configuration file!");
+      data.affine_transform = trsfr->get<std::array<double, 16>>();
+    }


Use full names for the variables.

hughcars · 2025-01-30T23:01:50Z

palace/utils/configfile.hpp

  // Vector defining the direction and distance for this periodic boundary condition.
  std::array<double, 3> translation = {0.0, 0.0, 0.0};


Can this be encoded into the affine transformation? Given it's going to overlap with the final column in terms of data. I.e. if there's a translation, set the rotation piece to identity and fill the translation in.

hughcars · 2025-01-30T23:05:16Z

palace/utils/geodata.cpp

+  if (translation.Norml2() > mesh_tol)
+  {
+    // Use user-provided translation.
+    for (int i = 0; i < 3; i++)
+    {
+      transformation(i, i) = 1.0;
+      transformation(i, 3) = translation[i];
+    }
+    transformation(3, 3) = 1.0;
+  }
+  else if (affine_vec.Norml2() > mesh_tol)
+  {
+    // Use user-provided affine transformation matrix.
+    for (int i = 0; i < 4; i++)
+    {
+      for (int j = 0; j < 4; j++)
+      {
+        transformation(i, j) = affine_vec[i * 4 + j];
+      }
+    }
+  }


If the translation is written to the affine transformation variable in configfile.cpp, this can be shortened to

mfem::DenseMatrix transformation(4); std::copy(data.affine_transform.begin(), data.affine_transform.end(), transformation.begin()); transformation.Transpose(); if (transformation.Norml2() == 0.0) { ...

hughcars · 2025-01-30T23:11:54Z

palace/drivers/drivensolver.cpp

@@ -8,6 +8,7 @@
 #include "fem/errorindicator.hpp"


Missing the correction on the adaptive branch.

hughcars · 2025-01-30T23:13:36Z

palace/linalg/floquetcorrection.cpp

+template class FloquetCorrSolver<Vector>;
+template class FloquetCorrSolver<ComplexVector>;


Is this ever going to be applied to a real valued case?

simlapointe added 30 commits October 25, 2024 17:39

Try different ways to compute the affine transformation matrix

86d6055

Add periodic boundary operator class for periodic/floquet BCs

31a4a9b

Improve Bloch wave vector specification and fix some bugs

6420322

Initial implementation of floquet periodicity terms in governing equa…

707b32b

…tions

Update surface normal calculation and add planar boundary check

82d1d61

Fix some with floquet operators and their use in eigensolver

1de268d

Remove some prints

95502e2

Add a new matrix for the mass periodic term

6021e8f

Ensure enough mesh elements in the periodic direction

0301a71

Debugging tests

63096b3

Debugging tests

974da2a

Allow non-symmetric material properties and merge floquet terms in a …

3f6bef0

…single operator

Merge floquet periodic terms into one operator

975a274

Remove print

57e6d3a

Use CEED Symmetric operator

c45ef21

Merge branch 'main' into simlapointe/periodic-bc

ff552d2

Disable divergence-free projection when using Floquet BCs

5a4f614

Define vector indices in SetOperator

447df80

Constrain Floquet wave vector components

e2d6e46

Update comments since quadrature data is no longer symmetric

49b29e4

Add floquet periodic mass term to auxiliary operator

e8b0d95

Merge main

3b2700c

Fix formatting

951d70f

Merge branch 'main' into simlapointe/periodic-bc

1557829

Warn against using div-free projection and Floquet BCs

7dfcccc

Combine periodic terms in a single helper functions

e687ab9

Test term to help aux space smoother

967c6e6

Test Floquet terms in divergence free projection

12ab759

Clean and reorganize automated periodic boundary matching

e713a6f

Remove print

b5ef9bd

simlapointe added 11 commits December 12, 2024 15:21

Remove print

9fbe941

Undo Aux space preconditioner tests

b865e9c

Remove print

18eab19

Remove unnecessary include

a01573c

Update regression test results

76e325b

Fix formatting

650dce3

Update CHANGELOG

2e2ae18

Remove prints

102386d

Initialize Floquet correction solver outside of frequency loop

7a1d90e

Remove unnecessary comments

14c8ce3

Update schema for Floquet BCs

7259f7c

simlapointe linked an issue Dec 13, 2024 that may be closed by this pull request

Periodic boundary conditions #125

Open

Fix bug assuming symmetric coefficients

4ea97e0

simlapointe added the enhancement New feature or request label Dec 13, 2024

simlapointe added 12 commits December 13, 2024 09:55

Update waveguide example

d72f40d

Merge branch 'main' into simlapointe/periodic-bc

320b333

Merge branch 'main' into simlapointe/periodic-bc

ed3532e

Remove complex coarse solve code before merging in main

f0e0c2e

Merge branch 'main' into simlapointe/periodic-bc

d7e972a

Fix formatting

494a51a

Update docs

d31c929

Use FP for Floquet periodic term

5ae3cf3

Fix formatting

a4ea4f1

Add comments

c14cb5b

Update docs

d21f1e7

Update docs

81a8fec

simlapointe marked this pull request as ready for review December 31, 2024 01:55

simlapointe requested a review from hughcars December 31, 2024 01:55

Update docs

a029c60

hughcars requested changes Jan 30, 2025

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Support Floquet periodic boundary conditions #314

Support Floquet periodic boundary conditions #314

simlapointe commented Dec 13, 2024 •

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		attribute to the receiver attribute in mesh units. If neither `"Translation"` or
		`"AffineTransformation"` are specified, the transformation between donor and receiver boundaries


		CeedOperator GetTranspose(std::size_t i) const { return op_t[i]; }

		// Vector defining the direction and distance for this periodic boundary condition.
		std::array<double, 3> translation = {0.0, 0.0, 0.0};

		template class FloquetCorrSolver<Vector>;
		template class FloquetCorrSolver<ComplexVector>;

Support Floquet periodic boundary conditions #314

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simlapointe commented Dec 13, 2024 • edited Loading

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simlapointe commented Dec 13, 2024 •

edited

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