# Numerical validation (2D FDTD)

**Numerical validation** checks both agreement between implementations and properties of the simulated physics. The repository's stability test checks bounded energy at Courant factor 0.99:

```cpp
Simulation::Options opts;
opts.courant = 0.99;
Simulation sim(64, 64, opts);
const auto history = energy_history(sim, 20, 100);
for (const double e : history) {
    const double ratio = e / history.front();
    CAPTURE(ratio);
    REQUIRE(std::isfinite(ratio));
    CHECK(ratio < 1.01);
    CHECK(ratio > 0.99);
}
```

`energy_history` supplies repeated energy measurements. The assertions check finite energy within one percent of the initial value. A separate test deliberately exceeds the CFL limit with stability checking disabled and expects growth.

Other physical tests examine wave speed, closed-box energy, and PML reflection. Backend comparisons check fields and probes against serial results, using [[fdtd-cuda-floating-point-tolerance|tolerances]] or exact comparisons as configured. Matching the serial backend alone cannot establish physical correctness because implementations can share a numerical mistake.

Source: [test_physics.cpp](https://github.com/yanevskiv/fdtd-cuda/blob/main/tests/test_physics.cpp).