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.

Building

cmake -S . -B build -DKokkos_ROOT=/path/to/kokkos
cmake --build build
./build/heat_solver

Optional: forward-mode sensitivities (OTI automatic differentiation)

heat_oti.cpp is the same solver instantiated on an order-truncated imaginary (OTI) number instead of double, using the header-only cpp_oti_lib (vendored as a submodule under external/). An otinum<M, N> is a truncated multivariate Taylor polynomial, so each temperature value carries its exact derivatives with respect to the seeded parameters — the thermal diffusivity, the source amplitude and the source width — from a single solve, with no finite differencing and no change to the kernels (heat_solver.hpp is templated on the scalar type).

git submodule update --init --recursive
cmake -S . -B build -DKokkos_ROOT=/path/to/kokkos -DHEAT_ENABLE_AD=ON
cmake --build build
./build/heat_solver_oti      # writes output_*.vtk plus dTdalpha/dTdamplitude/dTdsigma_*.vtk

The OTI algebra shape is configurable. Setting the truncation order to zero makes otinum<M, 0> store only the real coefficient, so it reproduces the plain double solve bit-for-bit — double is just the zeroth-order case of the OTI algebra:

cmake -S . -B build -DHEAT_ENABLE_AD=ON -DHEAT_OTI_ORDER=0   # double-equivalent
cmake -S . -B build -DHEAT_ENABLE_AD=ON -DHEAT_OTI_ORDER=1   # first-order sensitivities (default)