The PDE, Boundary Elements Interface
About Boundary Elements Interfaces
Physics interfaces based on the boundary element method (BEM) differs from those based on the finite element method (FEM) in that they only use mesh elements on the boundaries of the modeled regions (curves in 2D and surfaces in 3D). Physics interfaces based on BEM can be used for physics modeling in three types of volumetric regions: domains,
finite voids, and an infinite void. Physics interfaces based on FEM only supports the domain type. COMSOL Multiphysics uses a direct method in the BEM formulation; that is, the boundary element method directly discretizes the field and flux at the boundaries.
Domains can contain a volumetric finite element mesh; however, the physics interfaces based on BEM only utilize the boundary elements of such domains. A volumetric finite element mesh can be used for FEM-based physics in combination with BEM-based physics. Finite voids and the infinite void cannot contain a volumetric finite element mesh, and the mesh generator will only generate boundary elements adjacent to such regions. Only BEM-based physics can be defined in finite voids and the infinite void.
Unlike FEM, which produces sparse system matrices, BEM leads to filled (dense) matrices when using a direct solver. This means that even though BEM uses less degrees of freedom, as compared to the corresponding FEM discretization of the domain, the memory requirements for using a direct solver grow faster with BEM than with FEM. The problem with handling potentially large filled matrices resulting from BEM is avoided in the physics interfaces based on BEM by using iterative solvers in combination with far-field approximations. These methods avoid explicitly constructing these large matrices. Iterative solvers with far-field approximations is the default setting; however, the options of using a direct solver and no far-field approximations are also available.