期刊
COMPUTER-AIDED DESIGN
卷 129, 期 -, 页码 -出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.cad.2020.102915
关键词
Mesh adaptation; Metric-conforming; Four-dimensional; Function approximation; High-order finite elements
资金
- CAPS project: AFRL [FA8050-14-C-2472]
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. (C) 2020 Elsevier Ltd. All rights reserved.
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