The default for The Pressure Acoustics, Boundary Elements Interface is to use an iterative solver for 3D models and a direct dense matrix solver for 2D problems. If the Far-Field Approximation is turned off, the direct dense matrix solver will be used in all situations. The dense matrix solver is adequate for small BEM problems but quickly runs out of memory for increasing number of DOFs. It is recommended to use the default settings.

When the Stabilized formulation is used (the default), one iterative solver suggestion is generated in 3D. The solver uses MUMPS as a direct preconditioner (with Block low rank factorization with a low tolerance) and GMRES as the iterative method.

In 3D two iterative solver suggestions are generated when the Stabilized formulation is not used. Make sure to reset the solver to default if changes are made. The default iterative suggestion uses the Space Approximate Inverse (SAI) as preconditioner. This approach is memory efficient but for increasing frequencies the convergence is compromised. In this case the Stabilized formulation can be used (see above). As an alternative to using the stabilized formulation the second iterative suggestion can be used (enable the solver suggestion). This solver uses a Hierarchical LU (HLU) preconditioner which produces LU factors of high quality. This will ensure better convergence for the iterative GMRES solver. The memory consumption is higher for this approach and should be used for small to medium models.

The boundary element method (BEM) used in the Pressure Acoustics, Boundary Elements interface is based on the direct method with Costabel’s symmetric coupling. The adaptive cross approximation (ACA+) fast summation method is used for solving the resulting linear system. This is the compression method (or Far-Field Approximation) used per default. This method uses partial assembly of the matrices where the effect of the matrix vector multiplication is computed. The default iterative solver used is GMRES.

The Far-Field Approximation settings are used for matrix assembly and postprocessing. They allow characterization of interactions occurring in boundary element method into near-field and far-field interactions. While the near-field interactions are represented explicitly, the far-field interactions can be represented in an approximate way. This approach results in considerable memory and performance improvements when used in combination with iterative solvers using matrix-free format or during postprocessing. The near-field part of stiffness matrix is used as input by the Direct and Sparse Approximate Inverse (SAI) preconditioners.