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Efficient time integration for discontinuous Galerkin approximations of linear wave equations
Author(s) -
Hochbruck Marlis,
Pažur Tomislav,
Schulz Andreas,
Thawinan Ekkachai,
Wieners Christian
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300306
Subject(s) - discontinuous galerkin method , mathematics , discretization , krylov subspace , galerkin method , matrix exponential , mathematical analysis , degree of a polynomial , integrator , linear system , polynomial , finite element method , differential equation , computer science , physics , computer network , bandwidth (computing) , thermodynamics
We consider the combination of discontinuous Galerkin discretizations in space with various time integration methods for linear acoustic, elastic, and electro‐magnetic wave equations. For the discontinuous Galerkin method we derive explicit formulas for the full upwind flux for heterogeneous materials by solving the Riemann problems for the corresponding first‐order systems. In a framework of bounded semigroups we prove convergence of the spatial discretization. For the time integration we discuss advantages and disadvantages of explicit and implicit Runge–Kutta methods compared to polynomial and rational Krylov subspace methods for the approximation of the matrix exponential function. Finally, the efficiency of the different time integrators is illustrated by several examples in 2D and 3D for electro‐magnetic and elastic waves.