论文标题
杂交的不连续的Galerkin方法，用于模拟具有浮动电势导体的静电问题
A hybridizable discontinuous Galerkin method for simulation of electrostatic problems with floating potential conductors
论文作者
论文摘要
在静电模拟中，必须在隔离导体的表面上执行具有未定义/浮动电位值的等电位条件。如果对该导体充电，则还需要非零充电条件。尽管使用传统的有限元方法（FEM）实施这些条件并不直接，但它们很容易被离散化并将其纳入不连续的Galerkin（DG）方法中。但是，与FEM相比，DG离散化导致越来越多的未知数。在这项工作中，提出了一种杂交DG（HDG）方法来减轻此问题。在每个隔离导体的表面上引入了可能具有不同电荷值的浮动边界条件，并且在HDG的全球问题中弱执行。全局HDG问题的未知数是仅与网格骨架上的节点相关的那些，它们的数量远小于DG所需的未知数总数。数值示例表明，所提出的方法与DG一样准确，同时它可以显着提高计算效率。
In an electrostatic simulation, an equipotential condition with an undefined/floating potential value has to be enforced on the surface of an isolated conductor. If this conductor is charged, a nonzero charge condition is also required. While implementation of these conditions using a traditional finite element method (FEM) is not straightforward, they can be easily discretized and incorporated within a discontinuous Galerkin (DG) method. However, DG discretization results in a larger number of unknowns as compared to FEM. In this work, a hybridizable DG (HDG) method is proposed to alleviate this problem. Floating potential boundary conditions, possibly with different charge values, are introduced on surfaces of each isolated conductor and are weakly enforced in the global problem of HDG. The unknowns of the global HDG problem are those only associated with the nodes on the mesh skeleton and their number is much smaller than the total number of unknowns required by DG. Numerical examples show that the proposed method is as accurate as DG while it improves the computational efficiency significantly.
