Module solver 

Linear solvers for BEM

This module provides various solvers for BEM systems:

• direct - Direct LU factorization (for small systems)
• cgs - Conjugate Gradient Squared (for iterative solving)
• bicgstab - BiCGSTAB (alternative iterative solver)
• gmres - GMRES (recommended for large BEM problems)
• fmm_interface - Interface to use FMM operators with iterative solvers
• preconditioner - Basic preconditioners
• ilu_preconditioner - ILU preconditioner (recommended for BEM)
• batched_blas - Batched BLAS operations for optimized matrix computations

Solver Selection Guide

For BEM systems, we recommend:

System Size	Solver	Configuration
N < 1000	Direct LU	-
N < 10000	GMRES(50) + ILU	GmresConfig::for_small_problems()
N > 10000	GMRES(100) + ILU	GmresConfig::for_large_bem()

GMRES is generally preferred for large BEM problems due to:

• Monotonic convergence (unlike CGS which can be erratic)
• Better handling of non-symmetric matrices
• Configurable memory usage via restart parameter

Preconditioning Strategy

BEM systems are ill-conditioned. Simple diagonal (Jacobi) preconditioning is not sufficient. Use ILU preconditioning:

use bem::core::solver::{
    gmres_solve_with_ilu, GmresConfig, IluMethod, IluScanningDegree
};

let config = GmresConfig::for_large_bem();
let solution = gmres_solve_with_ilu(
    &matrix,
    &rhs,
    IluMethod::Tbem,
    IluScanningDegree::Fine,
    &config,
);

Re-exports

pub use fmm_interface::CsrOperator;

pub use fmm_interface::DenseOperator;

pub use fmm_interface::DiagonalPreconditioner;

pub use fmm_interface::LinearOperator;

pub use fmm_interface::MlfmmOperator;

pub use fmm_interface::SlfmmOperator;

pub use fmm_interface::ilu_diagnostics;

pub use fmm_interface::solve_tbem_with_ilu;

pub use fmm_interface::solve_with_ilu;

pub use fmm_interface::solve_with_ilu_operator;

pub use fmm_interface::IluDiagnostics;

pub use fmm_interface::IluOperator;

pub use fmm_interface::gmres_solve_with_ilu;

pub use fmm_interface::gmres_solve_with_ilu_operator;

pub use fmm_interface::solve_gmres;

pub use fmm_interface::gmres_solve_fmm_hierarchical;

pub use fmm_interface::gmres_solve_with_hierarchical_precond;

pub use fmm_interface::gmres_solve_fmm_batched;

pub use fmm_interface::gmres_solve_fmm_batched_with_ilu;

pub use fmm_interface::recommended_mesh_resolution;

pub use fmm_interface::mesh_resolution_for_frequency_range;

pub use fmm_interface::estimate_element_count;

pub use fmm_interface::AdaptiveMeshConfig;

pub use preconditioner::BlockDiagonalPreconditioner;

pub use preconditioner::DiagonalPreconditioner as BasicDiagonalPreconditioner;

pub use preconditioner::HierarchicalFmmPreconditioner;

pub use preconditioner::IdentityPreconditioner;

pub use preconditioner::Preconditioner;

pub use preconditioner::RowScalingPreconditioner;

pub use preconditioner::SparseNearfieldIlu;

pub use ilu_preconditioner::IluMethod;

pub use ilu_preconditioner::IluPreconditioner;

pub use ilu_preconditioner::IluScanningDegree;

pub use ilu_preconditioner::IluSetup;

pub use gmres::gmres_solve;

pub use gmres::gmres_solve_preconditioned;

pub use gmres::GmresConfig;

pub use gmres::GmresSolution;

pub use batched_blas::SlfmmMatvecWorkspace;

pub use batched_blas::slfmm_matvec_batched;

pub use batched_blas::create_batched_matvec;

pub use batched_blas::batched_t_matrix_apply;

pub use batched_blas::batched_s_matrix_apply;

pub use batched_blas::batched_d_matrix_apply;

pub use batched_blas::batched_near_field_apply;

Modules

batched_blas

Batched BLAS operations for complex matrices

bicgstab

BiCGSTAB (Bi-Conjugate Gradient Stabilized) solver

cgs

Conjugate Gradient Squared (CGS) solver

direct

Direct solver (LU factorization)

fmm_interface

FMM-solver interface

gmres

GMRES (Generalized Minimal Residual) solver

ilu_preconditioner

Incomplete LU (ILU) Preconditioner

preconditioner

Preconditioners for iterative solvers