# SIMD (2D FDTD)

**SIMD** lets one CPU instruction operate on multiple grid values. FDTD CUDA's OpenMP `v2` marks its inner field loops for vectorization:

```cpp
#pragma omp simd
for (std::size_t i = block.i0; i < block.i1; ++i) {
    const std::size_t k = row + i;
    Hx[k] = Chx1[k] * Hx[k] - Chx2[k] * invDy * (Ez[k + pitch] - Ez[k]);
}
```

The loop advances across one row. Each iteration writes a distinct $H_x$ value and reads electric samples that remain unchanged throughout the magnetic phase. This independence permits simultaneous lane updates.

Threads share rows through `omp for`; SIMD handles several columns within each thread. It does not replace the barriers between field phases. The compiler still chooses the actual vector instructions based on the build target. Compare `v1` and `v2` to isolate the effect of the explicit inner-loop directive.

Source: [fdtd_tmz_backend_omp_v2.h](https://github.com/yanevskiv/fdtd-cuda/blob/main/include/fdtd/TMz/backends/omp/fdtd_tmz_backend_omp_v2.h).