The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems
The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems
复制标题
用于嵌入式域计算的移位边界方法。
DOI：
10.1016/j.jcp.2017.10.026
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
G. Scovazzi
中科院分区：
文献类型：
--
作者：
A. Main;G. Scovazzi
我们提出了一种新的有限元方法嵌入域计算，这福尔斯属于代理/近似边界算法的范畴。该方法的主要特点是将边界条件的施加位置从真实边界转移到替代边界，并适当地修改转移的边界条件，以保持数值解的最佳收敛速度。这个过程产生的方法，在我们看来，是简单的，有效的，也是强大的，因为它是不受小切细胞的问题。虽然一般的性质，在这里，我们将这个新概念的泊松和斯托克斯问题。我们特别提出了完整的分析的情况下的泊松算子的稳定性和收敛性，和数值试验的泊松和斯托克斯方程，几何形状的逐步更高的复杂性。
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 ofshiftingthe location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify theshiftedboundary 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.