Two-level parallel Schwarz methods for singularly perturbed semilinear elliptic problems

Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems

Parallel multi-level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems. Two methods based on the Schwarz alternating procedure are considered: a two-level method with auxiliary "correcting" subproblems as well as a three-level method with auxiliary "predicting" and "correc...

High-order Methods for Semilinear Singularly Perturbed Boundary Value Problems

We considered finite difference methods of higher order for semilinear singularly perturbed boundary value problems, consisted of constructing difference schemes on nonuniform meshes. Construction of schemes is presented and convergence uniform in perturbation parameter for one method is shown on Bakhvalov’s type of mesh. Numerical experiments demonstrated influence of different meshes on devel...

Monotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems

This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...

Heterogeneous Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems

A heterogeneous domain-decomposition method is presented for the numerical solution of singularly perturbed elliptic boundary value problems. The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The subdomains match the domains of validity of the local [ “inner” and “outer”) asymptotic expansions, and cut-off functions are used to match solutions in ...

Parallel Implementation of Some Two - Levelschwarz Methods for Singularly Perturbedsemi - Linear Elliptic Problems