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arXiv · 1502.07703

Orthogonal bases for vertex-mapped pyramids

Jesse Chan·T. Warburton
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Abstract

Discontinuous Galerkin (DG) methods discretized under the method of lines must handle the inverse of a block diagonal mass matrix at each time step. Efficient implementations of the DG method hinge upon inexpensive and low-memory techniques for the inversion of each dense mass matrix block. We propose an efficient time-explicit DG method on meshes of pyramidal elements based on the construction of a semi-nodal high order basis, which is orthogonal for a class of transformations of the reference pyramid, despite the non-affine nature of the mapping. We give numerical results confirming both expected convergence rates and discuss efficiency of DG methods under such a basis.

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Jesse Chan, T. Warburton. 2015-02-26. Orthogonal bases for vertex-mapped pyramids. https://arxiv.org/abs/1502.07703

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