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High‐order cut discontinuous Galerkin methods with local time stepping for acoustics
Author(s) -
Schoeder Svenja,
Sticko Simon,
Kreiss Gunilla,
Kronbichler Martin
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6343
Subject(s) - discontinuous galerkin method , discretization , eigenvalues and eigenvectors , mathematics , finite element method , galerkin method , mathematical optimization , set (abstract data type) , mathematical analysis , time domain , computer science , physics , quantum mechanics , thermodynamics , programming language , computer vision
Summary We propose a method to solve the acoustic wave equation on an immersed domain using the hybridizable discontinuous Galerkin method for spatial discretization and the arbitrary derivative method with local time stepping (LTS) for time integration. The method is based on a cut finite element approach of high order and uses level set functions to describe curved immersed interfaces. We study under which conditions and to what extent small time step sizes balance cut instabilities, which are present especially for high‐order spatial discretizations. This is done by analyzing eigenvalues and critical time steps for representative cuts. If small time steps cannot prevent cut instabilities, stabilization by means of cell agglomeration is applied and its effects are analyzed in combination with local time step sizes. Based on two examples with general cuts, performance gains of the LTS over the global time stepping are evaluated. We find that LTS combined with cell agglomeration is most robust and efficient.