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• W4379932414 abstract "In this paper, a diamond scheme for heterogeneous and anisotropic diffusion problems is proposed on unstructured polyhedral meshes through a certain linearity-preserving approach. This scheme has both cell-centered primary unknowns and cell-vertex auxiliary unknowns. The main feature of our new scheme is that auxiliary unknowns are expressed as linear combinations with the surrounding cell-centered unknowns by the least square technique combined with the graph search algorithm to handle arbitrary discontinuities. The search algorithm is local, and for the problem with a continuous diffusion coefficient, the resulting vertex interpolation algorithm naturally degenerates to the classical least squares interpolation algorithm. Our second-order 3D interpolation formula is simple and allows for an arbitrary diffusion tensor and arbitrary grid topology. Numerical experiments confirm that our extended Least Square Weight (eLSW) is robust and linearity-preserving for the heterogeneous (possibly discontinuous) diffusion tensor on general unstructured grids, as expected. Moreover, our linearity-preserving diamond scheme achieves nearly optimal accuracy for all test cases." @default.
• W4379932414 created "2023-06-09" @default.
• W4379932414 creator A5032792997 @default.
• W4379932414 creator A5045721913 @default.
• W4379932414 date "2023-08-01" @default.
• W4379932414 modified "2023-09-26" @default.
• W4379932414 title "A linearity-preserving diamond scheme with extended least square interpolation for the heterogeneous and anisotropic diffusion problems on polyhedral meshes" @default.
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• W4379932414 doi "https://doi.org/10.1016/j.camwa.2023.05.022" @default.
• W4379932414 hasPublicationYear "2023" @default.
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