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 twodimensional (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.

A Divide-and-Conquer Algorithm for 3-D Capacitance Extraction

“…Several fast algorithms have been proposed to solve (2), such as FastCap [11], the pre-corrected FFT algorithm [12], the singular value decomposition algorithm IES 3 [9], hierarchical refinement algorithm HiCap [13], geometry independent approximation [10], and others [2,5]. Although these algorithms use the fact that charges far away can be approximated, the entire interconnect geometry is carried throughout the algorithm.…”

A simple a-posteriori error estimation for adaptive BEM in elasticity

“…The adaptive BEM has also been applied to different kinds of engineering problems [8,15,24,25]. Even though, the efficiency and flexibility of the above developed BEM algorithms deserve further research.…”

“…In the boundary element method, research in this field began in the early 1980s [3][4][5]. Similar in FEM, the adaptive schemes in BEM comprise h-type [6-8], p-type [9-11], r-type [12-15], and their combinations [16-20], and there are diverse strategies for the local and global error estimations, see further [21-23].The adaptive BEM has also been applied to different kinds of engineering problems [8,15,24,25]. Even though, the efficiency and flexibility of the above developed BEM algorithms deserve further research.…”

Improving boundary element methods for parasitic extraction

“…The adaptive refinement scheme [15,17] and high order basis functions [5] are popular ways used to reduce the first type of error. In [1], the adaptive meshing idea of constructing an optimal mesh based on a coarse initial discretization was studied. However, no implementation and running time were reported.…”