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.

中文翻译：

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一种用于模拟具有浮动电位导体的静电问题的可混合不连续伽辽金方法

在静电模拟中，必须在隔离导体的表面上强制执行具有未定义/浮动电位值的等电位条件。如果该导体带电，则还需要非零充电条件。虽然使用传统的有限元方法 (FEM) 实现这些条件并不简单，但它们可以很容易地离散化并合并到不连续伽辽金 (DG) 方法中。然而，与 FEM 相比，DG 离散化会导致更多的未知数。在这项工作中，提出了一种可混合的 DG（HDG）方法来缓解这个问题。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电位边界条件，并且在 HDG 的全局问题中弱强制执行。全局 HDG 问题的未知数仅与网格骨架上的节点相关，它们的数量远小于 DG 所需的未知数总数。数值算例表明，所提出的方法与DG一样准确，同时显着提高了计算效率。