rekka / fdm_wave

Finite difference method for the wave equation in Rust

fdm_wave

Implementation of a finite difference stepper for the wave equation with SIMD optimization.

Currently only the following are supported:

• methods

  • central-in-time, central-in-space finite difference discretization

• boundary data

  • zero Neumann boundary data

Simple example

The following code advances the solution by performing one step of the finite difference method for the wave equation with zero Neumann boundary data, with given dt and dx. v is the current solution, and u is the solution at the previous time step, and w is the new solution. The dimension of the mesh is (2, 2) = (rows, columns). Arrays are stored in the row-major order (C order).

extern crate fdm_wave;

fn main() {
    let u = vec![1., 2., 3., 4.];
    let v = vec![3., 2., 1., 4.];
    let mut w = vec![0.; 4];

    let dt = 1.;
    let dx = 2.;

    fdm_wave::wave_step(&u, &v, &mut w, (2, 2), dt * dt / dx * dx);

    println!("{:?}", w);
}

Usage

This crate works with Cargo. Add it to Cargo.toml as

[dependencies.fdm_wave]
git = "https://github.com/rekka/fdm_wave.git"

To use the SIMD-optimized routines, you need to use a nightly compiler and add the simd feature:

[dependencies.fdm_wave]
git = "https://github.com/rekka/fdm_wave.git"
features = ["simd"]

Supports SSE2 and AVX. Make sure that you are passing correct flags to Cargo/rustc (target-cpu=native; possibly using RUSTFLAGS).

The SIMD versions are mainly useful for small problem sizes. The algorithm is limited by memory bandwidth if it spills out of caches.

License

MIT license: see the LICENSE file for details.