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A space–time discontinuous Galerkin method for the solution of the wave equation in the time domain
Author(s) -
Petersen Steffen,
Farhat Charbel,
Tezaur Radek
Publication year - 2008
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.2485
Subject(s) - discontinuous galerkin method , galerkin method , partial differential equation , classification of discontinuities , wave equation , mathematics , basis function , mathematical analysis , finite element method , space time , spacetime , space (punctuation) , dimension (graph theory) , physics , computer science , quantum mechanics , chemical engineering , pure mathematics , engineering , thermodynamics , operating system
In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the wave equation. We present a space–time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the homogeneous wave equation. The use of hierarchical wave‐like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space–time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd.