When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

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

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 …

Schwarz domain decomposition methods are the oldest domain decomposition methods.
They were invented by Hermann Amandus Schwarz in 1869 as an analytical tool to …

Linear solvers for reservoir simulation applications are the objective of this review.
Specifically, we focus on techniques for Fully Implicit (FI) solution methods, in which the set …

Recently a variant of the additive Schwarz (AS) preconditioner, the restricted additive
Schwarz (RAS) preconditioner has been introduced, and numerical experiments showed …

Ill-conditioning of the system matrix is a well-known complication in immersed finite element
methods and trimmed isogeometric analysis. Elements with small intersections with the …

We present a general graph-based modeling abstraction for optimization that we call an
OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical …

The convergence of multiplicative Schwarz-type methods for solving linear systems when
the coefficient matrix is either a nonsingular M-matrix or a symmetric positive definite matrix …

The performance of multigrid methods for the standard Poisson problem and for the
consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes …