This book offers a comprehensive presentation of some of the most successful and popular
domain decomposition preconditioners for finite and spectral element approximations of …

Domain decomposition methods are iterative methods for the solution of linear or nonlinear
systems that use explicit information about the geometry, discretization, and/or partial …

Efficient solution of the Navier–Stokes equations in complex domains is dependent upon the
availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the …

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 …

This article is the first of two articles on the adaptive multilevel finite element treatment of the
nonlinear Poisson–Boltzmann equation (PBE), a nonlinear eliptic equation arising in …

An abstract framework of auxiliary space method is proposed and, as an application, an
optimal multigrid technique is developed for general unstructured grids. The auxiliary space …

Given the measurement of temperature at a fixed time θ> 0 and the measurement of
temperature in a subregion of the physical domain, we investigate the simultaneous …

In this paper, we investigate the numerical identifications of physical parameters in parabolic
initial-boundary value problems. The identifying problem is first formulated as a constrained …

We consider additive Schwarz domain decomposition preconditioners for piecewise linear
finite element approximations of elliptic PDEs with highly variable coefficients. In contrast to …

Adaptive multilevel finite element methods are developed and analyzed for certain elliptic
systems arising in geometric analysis and general relativity. This class of nonlinear elliptic …