The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems
| Autor: | Guglielmo Scovazzi, Alex Main |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Mathematical analysis 010103 numerical & computational mathematics Mixed boundary condition Singular boundary method Boundary knot method 01 natural sciences Robin boundary condition Computer Science Applications 010101 applied mathematics Computational Mathematics Uniqueness theorem for Poisson's equation Modeling and Simulation Free boundary problem Method of fundamental solutions Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Journal of Computational Physics. 372:972-995 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2017.10.026 |
| Popis: | We propose a new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms. The key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify the shifted boundary conditions, enforced weakly, in order to preserve optimal convergence rates of the numerical solution. This process yields a method which, in our view, is simple, efficient, and also robust, since it is not affected by the small-cut-cell problem. Although general in nature, here we apply this new concept to the Poisson and Stokes problems. We present in particular the full analysis of stability and convergence for the case of the Poisson operator, and numerical tests for both the Poisson and Stokes equations, for geometries of progressively higher complexity. |
| Databáze: | OpenAIRE |
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