Coupling at a Distance HDG and BEM
Coupling at a Distance HDG and BEM
复制标题
HDG 和 BEM 远距离耦合
DOI：
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发表时间：
2012
影响因子：
3.1
通讯作者：
Manuel E. Solano
中科院分区：
文献类型：
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作者：
Bernardo Cockburn;F. Sayas;Manuel E. Solano
我们引入了一种数值求解二阶椭圆方程外狄利克雷边值问题的新技术。它包括将用于解决包含源项支持的有界区域上的所谓内部问题的可混合间断伽辽金 (HDG) 方法与用于解决该区域外部问题的边界元方法 (BEM) 相结合。新颖之处在于 BEM 是在适当选择的平滑人工边界上定义的，而 HDG 方法是在多面体子域上定义的。由于人工边界的选择，我们可以利用 BEM 解的谱收敛性和相应方程的简单性。由于 HDG 方法是在多面体子域上定义的，因此无需尝试将网格拟合到人工边界。相反，HDG 通过使用在人工边界和多面体子域之间的区域中定义的简单 Dirichlet-to-Neumann 算子与 BEM 进行一定距离的耦合。展示了新技术性能的数值实验。即使人工边界和多面体域之间的距离为 $h$ 阶，也可以获得最佳收敛阶。
We introduce a new technique for numerically solving exterior Dirichlet boundary-value problems for second-order elliptic equations. It consists of coupling a hybridizable discontinuous Galerkin (HDG) method used for solving the so-called interior problem on a bounded region containing the support of the source term, with a boundary element method (BEM) for solving the problem exterior to that region. The novelty is that the BEM is defined on a suitably chosen, smooth artificial boundary whereas the HDG method is defined on a polyhedral subdomain. Because of the choice of the artificial boundary, we can take advantage of the spectral convergence of the BEM solution and of the simplicity of the corresponding equations. Because the HDG method is defined on a polyhedral subdomain, there is no need to try to fit the mesh to the artificial boundary. Instead, the HDG is coupled at a distance with the BEM by using simple Dirichlet-to-Neumann operators defined in the region between the artificial boundary and the polyhedral subdomain. Numerical experiments displaying the performance of the new technique are presented. Optimal orders of convergence are obtained even though the distance between the artificial boundary and the polyhedral domain is of order $h$.