math-fem

Multigrid Finite Element Method (FEM) solver for the Helmholtz equation, optimized for acoustics.

Installation

Add to your Cargo.toml:

[dependencies]
math-fem = { version = "0.3" }

Features

• 2D and 3D meshes: Triangles, quadrilaterals, tetrahedra, hexahedra
• Lagrange elements: P1, P2, P3 polynomial basis functions
• Boundary conditions: Dirichlet, Neumann, Robin (impedance/absorption), PML
• Optimized Assembly: HelmholtzAssembler for efficient frequency sweeps without CSR topology reconstruction
• Multigrid solver: V-cycle, W-cycle with geometric coarsening
• Parallel processing: Rayon-based parallel matrix and RHS assembly
• Room Acoustics Simulator: CLI tool for frequency-domain room simulation

Usage

use math_audio_fem::{mesh, basis::PolynomialDegree};
use math_audio_fem::assembly::HelmholtzAssembler;
use num_complex::Complex64;

// Create a 3D mesh for a room
let mesh = mesh::box_mesh_tetrahedra(0.0, 5.0, 0.0, 4.0, 0.0, 2.5, 10, 8, 5);

// Create an efficient assembler
let assembler = HelmholtzAssembler::new(&mesh, PolynomialDegree::P1);

// Assemble system for a specific frequency (wavenumber k)
let k = Complex64::new(1.5, 0.01); // k = omega/c + i*damping
let system_matrix = assembler.assemble(k, &std::collections::HashMap::new());

Binaries

roomsim-fem

A high-performance room acoustics simulator. It supports:

• Rectangular and L-shaped geometries
• Configurable wall absorption and impedance
• Directional sound sources with crossovers
• Hierarchical warm-starting for fast frequency sweeps

Documentation: Room Simulator Guide | JSON Schema

cargo run --release --bin roomsim-fem --features "cli native" -- --config room.json

Modules

mesh

Mesh generators for common domains:

use math_audio_fem::mesh::*;

// 3D box mesh with tetrahedra
let box_tet = box_mesh_tetrahedra(0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 5, 5, 5);

basis

Lagrange polynomial basis functions (P1, P2, P3).

boundary

Boundary condition handling including Robin (Impedance) conditions for acoustics.

assembly

High-performance matrix assembly:

• Stiffness & Mass: Stored as f64 for memory efficiency.
• HelmholtzAssembler: Pre-assembles sparsity patterns for lightning-fast frequency updates.
• Boundary Mass: Efficiently integrates terms over boundary surfaces.

multigrid

Geometric multigrid solver for large systems.

Element Types

Feature Flags

• native (default) - Enables rayon parallelism and hardware-specific BLAS
• parallel - Enables rayon for parallel assembly
• cli - Enables CLI dependencies for roomsim-fem

Dependencies

• math-solvers - Iterative solvers (GMRES, AMG, Schwarz)
• math-xem-common - Shared room acoustics types and configurations
• ndarray - N-dimensional arrays for numerical computing
• num-complex - Complex number support for Helmholtz systems