Enhanced multipole acceleration technique for the solution of large Poisson computations

Abstract

The solution of Poisson's simulations in large, geometrically complex domains with various boundary conditions are of interest in many physical computations. In this paper, we focus on electrostatic analysis. This is important for microactuator (MEMS) and interconnect modeling and also in the simulation of the electrostatic properties in VLSI chips, such as CCD sensors and DRAM cells. The computation of the static electric potential and field distribution involves the solution of the Poisson's equation, or in case of charge free space, Laplace's equation. The boundary element method has proven to be well suited for the solution of these partial differential equations in both 2- and 3-D. The required computational resources can be significantly reduced with the use of multipole acceleration techniques. An enhanced multipole (MP) acceleration technique is presented, allowing for reduced computational time and memory requirements in all stages of the computational process: the assembly of the global system of equations, the solution of the system and the evaluation of the potential and flux at specified internal positions. Contrary to previous applications of MP acceleration to Poisson's equation, the method allows the treatment of a wider class of boundary conditions, including Neumann and floating. The method is applicable both in two and three dimensions using a constant or high order boundary elements.