Hierarchical Matrices And Adaptive Cross Approximation Applied To The Boundary Element Method With Multi-domain Governed By Iterative Coupling
Free (open access)
199 - 208
T. Grytsenko & A. Peratta
The approach presented in this paper is based on the Adaptive Cross Approximation (ACA) applied to the matrices coming from the Boundary Element Method (BEM) with multi-domain. The algorithm uses a hierarchical matrix (H-matrix) storage approach splitting the coefficient matrices representing the interactions inside the sub-domains into many blocks where rank of the off-diagonal blocks is reduced with the help of ACA approximation. The sub-domains are then coupled through the iterative process. These optimisations of the coefficient matrices in conjunction with highly effective algorithms for manipulation with H-matrices allow one to perform the operation of matrix-vector multiplication with almost linear complexity O(NlogN). The approach allows one to solve the linear systems of equations for BEM with multi-domain having nearly 100.000 DOFs using the usual PC. This paper formulates the approach and demonstrates its numerical properties by means of a theoretical example involving a cube with 27 sub-domains.