3-D integrated circuits (3-D ICs) make use of the vertical dimension for smaller footprint,
higher speed, lower power consumption, and better timing performance. In 3-D ICs, the inter …

The non-Manhattan conductor geometry existing in some capacitance extraction problems
brings difficulty to the floating random walk (FRW) method using cubic transition domains. In …

The numerical solution of large-scale PDEs, such as those occurring in data-driven
applications, unavoidably require powerful parallel computers and tailored parallel …

We review, implement, and compare numerical integration schemes for spatially bounded
diffusions stopped at the boundary which possess a convergence rate of the discretization …

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of
conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances …

We present an iterative scheme, reminiscent of the Multigrid method, to solve large
boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly …

Despite its generality and powerful convergence properties, Milstein's method for functionals
of spatially bounded stochastic differential equations is widely regarded as difficult to …

The performance of stochastic numerical methods for bounded diffusions (accuracy, speed
and weak rate of convergence) is considered. The backdrop is the pointwise solution, via …

Abstract Three-dimensional integrated circuits (3-D ICs) make use of the vertical dimension
for smaller footprint, higher speed, lower power consumption, and better timing performance …

The non-Manhattan conductor geometry existing in some capacitance extraction problems
brings difficulty to the floating random walk (FRW) method using cubic transition domains. In …