What is HierBEM

HierBEM is a scientific C++ software library that implements the 3D Galerkin boundary element method (BEM), accelerated by hierarchical matrices ($\mathcal{H}$-matrices) to achieve log-linear complexity. HierBEM is built on top of the powerful finite element library deal.II, leveraging its mature infrastructure for mesh handling, finite elements, mappings, linear algebra and data output, etc.

Long Term Objective

To provide a suite of high-performance solvers, including:

• BEM solvers for various physical problems, such as electromagnetics, acoustics, elasticity, etc.
• BEM solvers for problems with multiple homogeneous subdomains, using domain decomposition methods (DDM),
• BEM/FEM coupled solvers for addressing inhomogeneous materials and nonlinear effects.

Technical Features

• Numerical quadrature
  • Accurate evaluation of singular boundary integrals using Sauter quadrature with CUDA acceleration.
  • Sauter Quadrature on curved surfaces via high-order mappings from deal.II.
• $\mathcal{H}$-matrix algebra
  • Formatted addition, matrix/matrix multiplication, matrix/vector multiplication, LU and Cholesky factorization.
  • TBB parallelization for matrix/vector multiplication, LU and Cholesky factorization.
  • Load balancing for parallel $\mathcal{H}$-matrix assembly and matrix/vector multiplication using sequence partitioning.
• Linear solvers and preconditioners
  • Real and complex valued preconditioned CG and GMRES.
  • $\mathcal{H}$-matrix LU and Cholesky factorization as preconditioners.
  • With operator preconditioning based on the pseudo-differential operator theory, the condition number of the preconditioned system becomes independent of discretization, hence applicable to large scale problems.
• BEM solvers
  • Laplace solvers (real and complex) with Dirichlet, Neumann, and mixed boundary conditions.