A high-performance 3D FDTD solver for Maxwell's equations in C++ with OpenMP parallelization, Roden-Gedney PML absorbing boundaries, and Rerun-based 3D visualization.

AC current loop radiating electromagnetic waves, visualized with Rerun. E-field in viridis, H-field in inferno.

Implements the Yee algorithm on a staggered grid using leapfrog time-stepping in H-field formulation with per-cell material coefficients.

$$\frac{\partial \mathbf{H}}{\partial t} = -\frac{1}{\mu}\nabla \times \mathbf{E}$$

$$\frac{\partial \mathbf{E}}{\partial t} = \frac{1}{\varepsilon}\nabla \times \mathbf{H} - \frac{\sigma}{\varepsilon}\mathbf{E} - \frac{\mathbf{J}}{\varepsilon}$$

Discretized with precomputed loss-incorporating coefficients:

$$E_i^{n+1} = C_a \cdot E_i^n + C_b \cdot \left(\nabla \times \mathbf{H} - \mathbf{J}\right)_i \qquad H_i^{n+1} = H_i^n - D_b \cdot (\nabla \times \mathbf{E})_i$$

where $C_a = \frac{1 - \sigma\Delta t / 2\varepsilon}{1 + \sigma\Delta t / 2\varepsilon}$, $C_b = \frac{1}{\varepsilon/\Delta t + \sigma/2}$, and $D_b = \Delta t / \mu$.

The time step satisfies the CFL condition: $\Delta t \leq \frac{\alpha}{c \sqrt{1/\Delta x^2 + 1/\Delta y^2 + 1/\Delta z^2}}$

• Yee-grid leapfrog with per-cell ε, μ, σ and precomputed Ca/Cb/Db coefficients via public bake_coefficients()
• Roden-Gedney PML absorbing boundaries (σ/α grading with κ = 1; no coordinate stretching), per-axis σ_max for anisotropic grids, and material-correct ψ application using per-cell Cb/Db
• Monolithic AlignedSoA<T> memory - 27 field/material/coefficient arrays in one SIMD-aligned contiguous block with compile-time width detection (AVX-512/AVX2/SSE2)
• OpenMP parallelization with collapse(2) outer loops, #pragma omp simd inner loops, RESTRICT/ASSUME_ALIGNED hints
• Four source types: AC current loop, AC concentric rings, straight wire, point source, Gaussian pulse
• Double-buffered binary I/O with persistent writer thread overlapping computation
• Plane wave validation tracking energy drift, phase correlation, and numerical dispersion
• Rerun 3D visualization with volume rendering, vector cones, and time-series energy plots
• Tests across 7 suites including analytical curl checks, multi-axis PML reflection (dB), non-unity material regression, lossy baking, independent H/E half-step verification, and anisotropic coefficient validation

mkdir -p build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j
./main
python ../render.py  # optional visualization

Windows (MinGW):

cmake .. -G "MinGW Makefiles" -DCMAKE_BUILD_TYPE=Release
mingw32-make -j

The scripts/ directory has per-mode scripts for both platforms. Each creates its build directory on first run and does incremental builds on subsequent runs.

Linux / macOS:

./scripts/build-debug.sh
./scripts/build-test.sh
./scripts/build-release.sh

Windows (PowerShell / MinGW):

.\scripts\build-debug.ps1
.\scripts\build-test.ps1
.\scripts\build-release.ps1

cmake .. -DCMAKE_BUILD_TYPE=Test
make -j
ctest --output-on-failure

# or run individual suites:
./run_tests PML
./run_tests Integration

Parameters in config.cfg (key = value, # comments). Missing keys use compiled defaults; unknown keys warn.

Derived: dt (CFL-limited), pml_thickness (from grid volume, clamped to [4, 25]), pml_sigma_max_x/y/z (per-axis Berenger formula).

├── config.cfg                          # Runtime parameters
├── CMakeLists.txt                      # Three-tier build system
├── render.py                           # Rerun 3D visualization
├── scripts/
│   ├── build-debug.{sh,ps1}            # Debug build
│   ├── build-test.{sh,ps1}             # Test build
│   └── build-release.{sh,ps1}          # Release build
├── src/
│   ├── main.cpp                        # Entry point
│   ├── Utilities/
│   │   ├── aligned_soa.hpp             # SIMD-aligned SoA allocator
│   │   └── macros.hpp                  # RESTRICT, ASSUME_ALIGNED macros
│   └── Classes/
│       ├── Config/config.hpp           # Config parser & derived quantities
│       ├── Grid/grid.{hpp,cpp}         # Field storage, Yee kernels, bake_coefficients
│       ├── Source/source.{hpp,cpp}     # Source types (loop, wire, point, Gaussian)
│       ├── PML/pml.{hpp,cpp}           # PML coefficients & ψ updates
│       ├── Simulation/simulation.{hpp,cpp}
│       ├── Write_Output/output.{hpp,cpp}
│       └── Validation/validation.{hpp,cpp}
├── tests/
│   ├── test_framework.hpp              # Header-only test framework
│   ├── test_aligned_soa.cpp            # Allocation & alignment (7)
│   ├── test_grid.cpp                   # Grid, sources, config, lossy, H/E split (19)
│   ├── test_pml.cpp                    # Coefficients, anisotropic, clamping (9)
│   ├── test_integration.cpp            # Physics: conservation, causality, dipole, superposition (14)
│   └── test_output_validation.cpp      # I/O, validation, multi-axis PML reflection (6)
└── output/                             # Generated data (gitignored)