This paper presents a fast boundary-element method (BEM) algorithm that is well suited for solving electrostatics problems that arise in traditional and bio-microelectromechanical systems (bio-MEMS) design. The algorithm, FFTSVD, is Green's-function-independent for low-frequency kernels and efficient for inhomogeneous problems. FFTSVD is a multiscale algorithm that decomposes the problem domain using an octree and uses sampling to calculate low-rank approximations to dominant source distributions and responses. Long-range interactions at each length scale are computed using the FFT. Computational results illustrate that the FFTSVD algorithm performs better than precorrected-FFT (pFFT)-style algorithms or the multipole-style algorithms in FastCap.

Computer simulation is an important tool for improving our understanding of biomolecule electrostatics, in part to aid in drug design. However, the numerical techniques used in these simulation tools do not exploit fast solver approaches widely used in analyzing integrated circuit interconnects. In this paper we describe one popular formulation used to analyze biomolecule electrostatics, present an integral formulation of the problem, and apply the precorrected-FFT method to accelerate the solution of the integral equations.