Anisotropic “Helmholtz” equations: Frequency domain VTI/TTI modeling via a massively parallel structured direct Helmholtz solver

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 abstract.