ASSESSMENT OF THE REFLECTION-TRANSMISSION ERROR FOR RECIPROCAL MASS MATRICES

Abstract eng:
The majority of methods for wave propagation relies on compatible finite elements with a diagonal mass matrix or a discontinuous approximation, e.g. hybridizable discontinuous Galerkin [1]. Recently, several methods were proposed to directly construct a sparse inverse of a mass matrix also called reciprocal mass matrix [2,3,4]. This matrix faciliates direct computation of acceleration from the force vector. This enables efficient explicit computation for compatible finite elements that does not have accurate diagonal mass matrices [5]. Initial analysis showed that these reciprocal mass matrices may be optimized for a low dispersion error inside a homogeneous domain. In case of heterogeneous domains, reflection and transmission on the interfaces may be a source of a leading term in the overall error of the discretization [1]. In this contribution, the reflection-transmission error is studied for several formulations of the reciprocal mass matrix for 1D and 2D cases.

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