▪ Abstract An overview of the current state of the art in unstructured mesh techniques for
computational fluid dynamics is given. The topics of mesh generation and adaptation, spatial …

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

Spectral partitioning methods use the Fiedler vector-the eigenvector of the second-smallest
eigenvalue of the Laplacian matrix-to find a small separator of a graph. These methods are …

We prove an abstract convergence estimate for the Algebraic Multigrid Method with
prolongator defined by a disaggregation followed by a smoothing. The method input is the …

Spectral partitioning methods use the Fiedler vector—the eigenvector of the second-smallest
eigenvalue of the Laplacian matrix—to find a small separator of a graph. These methods are …

The problem of solving large, sparse, linear systems of algebraic equations is vital in
scientific computing, even for applications originating from quite different fields. A Survey of …

We study parallel two-level overlap** Schwarz algorithms for solving nonlinear finite
element problems, in particular, for the full potential equation of aerodynamics discretized in …

An overview of current multigrid techniques for unstructured meshes is given. The basic
principles of the multigrid approach are first outlined. Application of these principles to …

This paper contains the main ideas for an AMGe (algebraic multigrid for finite elements)
method based on element agglomeration. In the method, coarse grid elements are formed …

We propose a fast iterative method to optimize coarse basis functions in algebraic multigrid
by minimizing the sum of their energies, subject to the condition that linear combinations of …