Anisotropic ‘helmholtz’ Equations: Massively Parallel Structured Multifrontal Solver Using Nested Dissection Based Domain Decomposition with Separators of Variable Thickness

Abstract. We consider the discretization and approximate solution of inhomogeneous anisotropic ‘Helmholtz’ equations in 3D. The anisotropy comprises general (tilted) TI symmetries. In particular, we are concerned with solving these equations on a large domain, for a large number of different sources. We make use of a nested dissection based domain decomposition in a massively parallel multifrontal solver combined with Hierarchically SemiSeparable (HSS) matrix compression. The anisotropy requires the introduction of separators with variable thickness in the nested dissection; the development of these and their integration with the multifrontal solver is the main topic of this paper.