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 paper gives some global and uniform convergence estimates for a class of subspace
correction (based on space decomposition) iterative methods applied to some …

We present a sparse grid/hyperbolic cross discretization for many-particle problems. It
involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the …

A multigrid method is proposed to solve the eigenvalue problem by the finite element
method based on the combination of the multilevel correction scheme for the eigenvalue …

This paper gives an overview for the method of subspace corrections. The method is first
motivated by a discussion on the local behavior of high-frequency components in a solution …

We analyze the convergence rate of an asynchronous space decomposition method for
constrained convex minimization in a reflexive Banach space. This method includes as …

This paper proposes several domain decomposition methods to compute the smallest
eigenvalue of linear self-adjoint partial differential operators. Let us be given a partial …

In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission
eigenvalue problem on polygonal domains that are not necessarily able to be covered by …

This work presents some space decomposition algorithms for a convex minimization
problem. The algorithms has linear rate of convergence and the rate of convergence …

Kron's method has been used successfully by engineers for over 30 years to find
eigenvalues of large symmetric matrices. These matrices arise from domain decomposition …