Adaptive H-matrix computations in linear elasticity

Titelangaben

Bauer, Maximilian ; Bebendorf, Mario:
Adaptive H-matrix computations in linear elasticity.
In: Applied Numerical Mathematics. Bd. 201 (2024) . - S. 1-19.
ISSN 0168-9274
DOI der Verlagsversion: https://doi.org/10.1016/j.apnum.2024.02.007

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Abstract

This article deals with the efficient numerical treatment of the Lamé equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM). Using BEM, one is faced with the solution of a system of equations with a fully populated system matrix, which is in general very costly. In order to overcome this difficulty, adaptive and approximate algorithms based on hierarchical matrices and the adaptive cross approximation are proposed. These new methods rely on error estimators and refinement techniques known from adaptivity but are not used here to improve the mesh. We apply these new techniques to both, the efficient solution of Lamé equations and to the multiplication with given data.