Quadrature-free discontinuous Galerkin method with code generation features for shallow water equations on automatically generated block-structured meshes

•Quadrature-free discontinuous Galerkin discretizations have the potential to increase model code performance.•Block-structured grids are a compromise between the structured (not geometrically flexible) and unstructured (difficult to make computationally efficient) ones.•Code generation and domain-s...

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Vydáno v:Advances in water resources Ročník 138; s. 103552
Hlavní autoři: Faghih-Naini, Sara, Kuckuk, Sebastian, Aizinger, Vadym, Zint, Daniel, Grosso, Roberto, Köstler, Harald
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.04.2020
Témata:
algorithms
Block-structured mesh
Code generation domain specific languages (DSL)
equations
Local discontinuous Galerkin method (LDG)
porous media
Python SymPy
Quadrature-free formulation
Shallow water equations
water resources
Shallow water equations
Quadrature-free formulation
Python SymPy
Local discontinuous Galerkin method (LDG)
Code generation domain specific languages (DSL)
Block-structured mesh
ISSN:0309-1708, 1872-9657
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Shrnutí:•Quadrature-free discontinuous Galerkin discretizations have the potential to increase model code performance.•Block-structured grids are a compromise between the structured (not geometrically flexible) and unstructured (difficult to make computationally efficient) ones.•Code generation and domain-specific languages allow for a separation of concerns between applications scientists and code developers. Although discretizations of the shallow water equations (SWE) based on the discontinuous Galerkin (DG) method are well established, their computational performance still generally lags behind that of the finite volume discretizations. In explicit and semi-implicit time stepping schemes commonly used in connection with the SWE models, the most computationally expensive parts of a DG algorithm are the element and edge integrals computed via loops over quadrature points. We propose a quadrature-free DG formulation for the SWE that replaces quadrature integrations by analytical evaluations. The method is implemented within the code generation framework of the ExaStencils project using the SymPy Python library. The new formulation uses block-structured triangular meshes automatically generated for a given number of blocks.
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ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2020.103552