BemTool is a C++ header library that only relies on the STL and Boost. Its main purpose is the assembly of classic boundary element matrices. At low level, it contains a set of elementary classes for low dimensional linear algebra (so as to deal with geometric computations) and simplicial meshes in 1D,2D and 3D. It contains basic wrappers for Gmsh as regards mesh generation, and eigen for the treatment of large matrices. Currently it provides routines for the assembly of boundary element matrices for Laplace, Helmholtz, Yukawa (purely dissipative Helmholtz) and Maxwell matrices in 2D and 3D. The available discretisation spaces are P0, continuous P1, continuous P2 and RT0 (lowest order Raviart-Thomas elements).

This library does not currently include functionalities oriented toward complexity reduction techniques such as fast multipoles (FMM) or hierarchical matrices. However the companion library HTool oriented toward this type of method is currently under development.

One of the motivations for the development of this lilbrary was numerical investigation of the performance of the multi-trace formalism. As a consequence the classes for meshes include functionalities specially oriented toward the management of multi-domain geometries, in particular for cases where subdomains are adjacent so as to give rise to junction points.

Htool is an implementation of hierarchical matrices (cf. this reference or this one), it was written to test Domain Decomposition Methods (DDM) applied to Boundary Element Method (BEM). It provides:

  • routines to build hierarchical matrix structures (cluster trees, block trees, low-rank matrices and block matrices),
  • parallel matrix-vector and matrix-matrix product using MPI and OpenMP,
  • preconditioning techniques using domain decomposition methods,
  • the possibility to use Htool with any generator of coefficients (e.g., your own BEM library),
  • an interface with HPDDM for iterative solvers,
  • GUI and several service functions to display informations about matrix structures and timing.

Scattering by a cobra cavity

Below is represented the result of the computation of the acoustic (Helmholltz equation) scattering of a plane wave at 17.5GHz incident on a 2 meters long cobra cavity. This calculation was achieved by P.Marchand and P.-H.Tournier using BemTool and HTool plugged into the library domain decomposition library HPDDM. This involved the solution of a dense linear system of size 50928. The computation was launched on the machine OCCIGEN from GENCI in parallel on 256 cores (using a blend of MPI and OpenMP). The computation overall took 95 seconds.