Four-Dimensional Anisotropic Mesh Adaptation

Anisotropic mesh adaptation is important for accurately simulating physical phenomena at reasonable computational costs. Previous work in anisotropic mesh adaptation has been restricted to studies in two- or three-dimensional computational domains. However, in order to accurately simulate time-depen...

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Published in:Computer aided design 2020-12, Vol.129, p.102915, Article 102915
Main Authors: Caplan, Philip Claude, Haimes, Robert, Darmofal, David L., Galbraith, Marshall C.
Format: Article
Language:English
Subjects:
Adaptation
Algorithms
Anisotropy
Computer simulation
Computing costs
Domains
Finite element method
Four-dimensional
Function approximation
High-order finite elements
Mesh adaptation
Metric-conforming
Time dependence
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creator Caplan, Philip Claude
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description Anisotropic mesh adaptation is important for accurately simulating physical phenomena at reasonable computational costs. Previous work in anisotropic mesh adaptation has been restricted to studies in two- or three-dimensional computational domains. However, in order to accurately simulate time-dependent physical phenomena in three dimensions, a four-dimensional mesh adaptation tool is needed. This work develops a four-dimensional anisotropic mesh adaptation tool to support time-dependent three-dimensional numerical simulations. Anisotropy is achieved through the use of a background metric field and the mesh is adapted using a dimension-independent cavity framework. Metric-conformity – in the sense of edge lengths, element quality and element counts – is effectively demonstrated on four-dimensional benchmark cases within a unit tesseract in which the background metric is prescribed analytically. Next, the metric field is optimized to minimize the approximation error of a scalar function with discontinuous Galerkin discretizations on four-dimensional domains. We demonstrate that this four-dimensional mesh adaptation algorithm achieves optimal element sizes and orientations. To our knowledge, this is the first presentation of anisotropic four-dimensional meshes. [Display omitted] •A four-dimensional anisotropic mesh adaptation algorithm was implemented.•Anisotropy was achieved via a background metric field and the adaptation algorithm builds upon a local cavity operator framework.•Metric-conformity was demonstrated on benchmark cases, whereby the metric field was prescribed analytically.•Optimal mesh size and aspect ratio distributions were obtained in the approximation of four-dimensional functions.
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subjects Adaptation
Algorithms
Anisotropy
Computer simulation
Computing costs
Domains
Finite element method
Four-dimensional
Function approximation
High-order finite elements
Mesh adaptation
Metric-conforming
Time dependence
title Four-Dimensional Anisotropic Mesh Adaptation
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