Heat Equation

This code solves the heat equation on the unit cube. The heat source is a gaussian that describes a circle. The code only depends on Kokkos.

This program was mostly written by gemini.

OTI Parameter Analysis

This clone includes an additional oti_heat_analysis executable that runs the Kokkos heat solver with OTI-valued model parameters:

• thermal diffusivity alpha
• source amplitude
• source width sigma

The executable compares the OTI sensitivities against central finite differences of the same discrete solver and writes slice data at several time steps.

The analysis currently uses oti::otinum<3,1>: three active parameters and first-order terms only. The reported OTI timings therefore measure first-order sensitivity propagation, not higher-order OTI algebra.

Build against a Kokkos installation and the neighboring cpp_oti_lib headers:

cmake -S . -B build \
  -DCMAKE_CXX_COMPILER=g++-10 \
  -DCMAKE_PREFIX_PATH=/root/Research/kokkos-install

cmake --build build --parallel 2

Run the analysis:

./build/oti_heat_analysis oti_analysis_output

Higher-fidelity stress runs can increase the uniform mesh size and final time:

./build-cuda/oti_heat_analysis oti_analysis_output_cuda_N41 --N 41 --total-time 0.05
./build-cuda/oti_heat_analysis oti_analysis_output_cuda_N61 --N 61 --total-time 0.05

For performance-only stress tests, skip the six finite-difference validation solves and compare only the base scalar solve against the OTI solve:

./build-cuda/oti_heat_analysis oti_analysis_output_cuda_N61_perf --N 61 --total-time 0.05 --skip-fd

The default oti_heat_analysis target uses double coefficients. The CMake build also creates explicit precision targets for GPU comparisons:

./build-cuda/oti_heat_analysis_double oti_analysis_output_cuda_double_N61_perf --N 61 --total-time 0.05 --skip-fd
./build-cuda/oti_heat_analysis_float oti_analysis_output_cuda_float_N61_perf --N 61 --total-time 0.05 --skip-fd

Each run writes coefficient_precision to run_config.csv and records the base scalar and OTI wall times in timing_summary.csv.

Generate plots:

python3 plot_oti_analysis.py oti_analysis_output

Outputs:

• oti_analysis_output/slice_snapshots.csv
• oti_analysis_output/timing_summary.csv
• oti_analysis_output/plots/*.png