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GPU-accelerated discontinuous Galerkin methods on hybrid meshes. (English) Zbl 1349.65443

Summary: We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities.computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.

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
65Y10 Numerical algorithms for specific classes of architectures

Software:

OCCA; PyFR; Gmsh; Netgen
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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