Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4963720 | Computer Methods in Applied Mechanics and Engineering | 2017 | 28 Pages |
Abstract
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes.
Keywords
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Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
T.P. Fries, D. Schöllhammer,