Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations

Efficient additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations

For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal meshsize. Therefore, reliable and effective numerical computations, in particular on adaptively refined meshes, require the development of appropriate preconditioners. We analyze and numerically compare multilevel additive Schwarz preconditioners...

Additive Schwarz Methods for First Kind Integral Equations

1.1 INTRODUCTION This paper gives a survey on additive Schwarz methods applied to the h and p versions of the boundary element method. We consider weakly singular and hypersingular integral equations, namely the single layer potential operator and the normal derivative of the double layer potential operator. That means we have to consider weak formulations of the form

Additive Schwarz Methods for Hyperbolic Equations 5153

Additive Schwarz Methods for Hyperbolic Equations

In recent years there has been gratifying progress in the development of domain decomposition algorithms for symmetric and nonsymmetric elliptic problems and even some inde nite problems Many methods possess the attractive property that the convergence rate is optimal i e independent of the size of the discrete problem and of the number of subdomains or within a polylog factor of optimal There ...

Optimal Left and Right Additive Schwarz Preconditioning for Minimal Residual Methods with Euclidean and Energy Norms

For the solution of non-symmetric or indefinite linear systems arising from discretizations of elliptic problems, two-level additive Schwarz preconditioners are known to be optimal in the sense that convergence bounds for the preconditioned problem are independent of the mesh and the number of subdomains. These bounds are based on some kind of energy norm. However, in practice, iterative method...