An error indicator and automatic adaptive meshing for electrostatic boundary element simulations

Abstract

Accurate electrostatic simulations are required for the analysis of micro electromechanical systems (MEMS) and interconnects in very large scale integration (VLSI) design. Typical simulations involve complex three-dimensional (3-D) geometries together with various dielectric materials, conductors, and boundary conditions. The boundary element method is well suited for such computations. For highly accurate solutions, the meshing of the geometry becomes increasingly important. A scheme is presented which allows generating an optimal mesh automatically based on a coarse initial discretization, e.g., a CAD model. An error indicator derived from boundary integral equations monitors the solution accuracy in each boundary element. H-type or p-type mesh refinement is applied to areas which contribute strongly to the overall error. The method applies to both two-dimensional (2-D) and 3-D simulations containing elements of various orders and shapes. The generated refined meshes result in significantly higher solution accuracy for a given simulation size.