Abstract Domain decomposition methods are designed to allow the effective numerical
solution of partial differential equations on parallel computer architectures. They comprise a …

Domain decomposition refers to divide and conquer techniques for solving partial differential
equations by iteratively solving subproblems defined on smaller subdomains. The principal …

These notes serve as an introduction to a subject of study in computational mathematics
referred to as domain decomposition methods. It concerns divide and conquer methods for …

In this paper, we consider the solution of linear systems of algebraic equations that arise
from parabolic finite element problems. We introduce three additive Schwarz type domain …

Two parallel, non-iterative, multi-physics, domain decomposition methods are proposed to
solve a coupled time-dependent Stokes-Darcy system with the Beavers-Joseph-Saffman …

In this paper, we construct, analyze, and numerically validate a linearized Crank-Nicolson
virtual element method (VEM) for solving quasilinear parabolic problems on general …

Decomposition Methods for Differential Equations: Theory and Applications describes the
analysis of numerical methods for evolution equations based on temporal and spatial …

Numerical differentiation formulas based on interpolating polynomials, operators and
lozenge diagrams can be simplified to one of the finite difference approximations based on …

Domain decomposition procedures for solving parabolic equations are considered. The
underlying discretization consists of block-centered finite differences. In these procedures …

Ice melting with dc is one of the key technologies to prevent the Chinese power grid from ice
storms. Especially after the severe ice storm in the southern part of China in early 2008, dc …