Hybridized Isogeometric Method for Elliptic Problems on CAD Surfaces with Gaps
| Autor: | Tobias Jonsson, Mats G. Larson, Karl Larsson |
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| Rok vydání: | 2022 |
| Předmět: |
Beräkningsmatematik
Mechanical Engineering Computational Mechanics General Physics and Astronomy Trimmed multipatch CAD surfaces Numerical Analysis (math.NA) Computer Science Applications Hybridized method Computational Mathematics Mechanics of Materials FOS: Mathematics Mathematics - Numerical Analysis Interfaces with gaps/overlaps CutIGA and CutFEM |
| DOI: | 10.48550/arxiv.2210.01617 |
| Popis: | We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap between patches. Thus, the hybrid variable is defined on a three-dimensional mesh, and we need to add appropriate normal stabilization to obtain an accurate solution, which we show can be done by adding a suitable term to the weak form. In practical applications, the hybrid mesh may be conveniently constructed using an octree to efficiently compute the necessary geometric information. We prove error estimates and present several numerical examples illustrating the application of the method to different problems, including a realistic CAD model. Originally included in thesis in manuscript form. |
| Databáze: | OpenAIRE |
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