Partial differential equations (PDEs) with spatially varying coefficients arise throughout
science and engineering, modeling rich heterogeneous material behavior. Yet conventional …

It is well known that there is no analytic expression for the electrical capacitance of the unit
cube. However, there are several Monte Carlo methods that have been used to numerically …

We aim here at presenting a new procedure to numerically estimate the Fekete points of a
wide variety of compact sets in R3. We understand the Fekete point problem in terms of the …

The monograph is devoted to spherical and plane integral operators for high-dimen sional
boundary value problems of mathematical physics. The derived integral opera tors are used …

In this paper, a hybrid approach for solving the Laplace equation in general three-
dimensional (3-D) domains is presented. The approach is based on a local method for the …

The previously reported neBEM solver has been used to solve electrostatic problems having
three-dimensional edges and corners in the physical domain. Both rectangular and …

With the advancement of fabrication technology, the electrostatic coupling has increasing
impact on the performance of very large-scale integrated (VLSI) circuits and micro …

In this chapter, we describe high-accuracy parasitic extraction by both fast integral equation
methods as well as random-walk-based methods. For any extraction application, the …

Abstract Sparsified Randomization Monte Carlo (SRMC) algorithms for solving large
systems of linear algebraic equations are presented. We construct efficient stochastic …

Dielectric continuum or implicit solvent models provide a significant reduction in
computational cost when accounting for the salt-mediated electrostatic interactions of …