Mixed-Order Meshes through rp-adaptivity for Surface Fitting to Implicit Geometries
CoRR(2024)
摘要
Computational analysis with the finite element method requires geometrically
accurate meshes. It is well known that high-order meshes can accurately capture
curved surfaces with fewer degrees of freedom in comparison to low-order
meshes. Existing techniques for high-order mesh generation typically output
meshes with same polynomial order for all elements. However, high order
elements away from curvilinear boundaries or interfaces increase the
computational cost of the simulation without increasing geometric accuracy. In
prior work, we have presented one such approach for generating body-fitted
uniform-order meshes that takes a given mesh and morphs it to align with the
surface of interest prescribed as the zero isocontour of a level-set function.
We extend this method to generate mixed-order meshes such that curved surfaces
of the domain are discretized with high-order elements, while low-order
elements are used elsewhere. Numerical experiments demonstrate the robustness
of the approach and show that it can be used to generate mixed-order meshes
that are much more efficient than high uniform-order meshes. The proposed
approach is purely algebraic, and extends to different types of elements
(quadrilaterals/triangles/tetrahedron/hexahedra) in two- and three-dimensions.
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