A boundary conformal discontinuous Galerkin approach for electro-quasistatic field problems on Cartesian grids
A boundary conformal discontinuous Galerkin approach for electro-quasistatic field problems on Cartesian grids
复制标题
DOI：
10.1504/ijcse.2014.064533
复制
发表时间：
2014-09
期刊：
影响因子：
--
通讯作者：
A. Fröhlcke;E. Gjonaj;T. Weiland
中科院分区：
文献类型：
--
作者：
A. Fröhlcke;E. Gjonaj;T. Weiland
提出了一种在直角网格上用高阶间断Galerkin方法求解三维电性拟静电场问题的边界保角方法。该方法基于一种新的剖分单元离散化方法，该方法仅适用于与弯曲材料边界相交的单元。引入了一种特殊的数值求积方法，使得高阶有限元算子可以在考虑截断单元精确几何的情况下进行精确积分。此外，还提出了在计算区域的均匀部分将割胞方法与传统有限元方法进行一般杂交的方法。数值算例表明，这种离散化方法对实际曲线型问题具有较高的计算精度。
A boundary conformal approach for solving three-dimensional electro-quasistatic field problems with a high order discontinuous Galerkin method on Cartesian grids is proposed. The method is based on a novel cut-cell discretisation which is applied only on elements intersected by curved material boundaries. A particular numerical quadrature is introduced which allows for an accurate integration of the high order finite element operators taking into account the exact geometry of the cut-cells. Furthermore, a general hybridisation of the cut-cell approach with the conventional finite element method in the homogeneous parts of the computational domain is proposed. Numerical examples are presented which demonstrate the accuracy of this discretisation method for practical problems with curved geometries.