Reducing Meshing Requirements for Electrostatic Problems using a Galerkin Boundary Element Method

TL;DR

The paper tackles the challenge of rapid electrostatic simulation for CAD designs by eliminating volumetric meshing through a Galerkin boundary element method that supports non-conforming, trimmed CAD surfaces. It introduces enhanced edge data to connect adjacent trimmed surfaces, enabling accurate boundary integral computations with disjoint surface meshes. Numerical experiments on spherical electrodes and a high-voltage bushing demonstrate close agreement with conforming BEM and analytic solutions, while substantially reducing meshing effort. This approach enables closer CAD integration and faster virtual prototyping for electrostatic devices, with potential extensions to higher-order elements in the future.

Abstract

This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding edges of the CAD model are enhanced with the data required to integrate over non-conforming elements. Finally, we generate a mesh for each CAD surface. The approach is verified via numerical experiments and shows excellent agreement with conforming BEM results.

Figures (11)

• Figure 1: Virtual prototyping example: (a) CAD model of the designed device and (b) the related finite element solution of the electric field in the right cone for virtual design assessment.
• Figure 2: Interior of \ref{['fig:EpoxyU-Verbinder']}, where the right grid indicates the volumetric mesh for FEM simulations.
• Figure 3: Trimmed CAD models: (a) cut through the model as shown to a user and (b) the mathematical representation of its surfaces, which is the basis for the meshing process.
• Figure 4: Electric field between two electrodes (left), its truncated discretization for the analysis with the FEM (middle) and the surface discretization required for the simulation with the BEM.
• Figure 5: Surface-surface intersection (SSI) of two surfaces: (left) the restriction of the NURBS parameter spaces to (right) the visualized surfaces in the CAD display.