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An efficient implicit discontinuous spectral Galerkin method. (English) Zbl 0986.65093
Summary: The paper discusses an implicit discontinuous spectral Galerkin method for the solution of the compressible Euler equations. A matrix-free Newton-Krylov-Schwarz algorithm with one-level and two-level nonoverlapping Schwarz preconditioners is used to solve the implicit systems. The study shows that this method is a factor of 50 faster than an explicit method that employs local time-stepping to accelerate convergence to steady-state solution. Procedures using LU-SGS preconditioner appear to provide the best performance. The two-level procedure is found necessary for relatively fast convergence in the case of large numbers of mesh elements.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
65F35 Numerical computation of matrix norms, conditioning, scaling
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
76M10 Finite element methods applied to problems in fluid mechanics
35L65 Hyperbolic conservation laws
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