On the Schwarz alternating method with more than two subdomains for nonlinear monotone problems
SIAM Journal on Numerical Analysis
Multiplicative Schwarz methods for parabolic problems
SIAM Journal on Scientific Computing
A space-time multigrid method for parabolic partial differential equations
SIAM Journal on Scientific Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Two-grid Discretization Techniques for Linear and Nonlinear PDEs
SIAM Journal on Numerical Analysis
Rate of Convergence of Some Space Decomposition Methods for Linear and Nonlinear Problems
SIAM Journal on Numerical Analysis
Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation
SIAM Journal on Scientific Computing
On Schwarz Alternating Methods for Nonlinear Elliptic PDEs
SIAM Journal on Scientific Computing
Waveform Relaxation with Fast Direct Methods as Preconditioner
SIAM Journal on Scientific Computing
Nonlinearly Preconditioned Inexact Newton Algorithms
SIAM Journal on Scientific Computing
On Schwarz Alternating Methods for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
Global and uniform convergence of subspace correction methods for some convex optimization problems
Mathematics of Computation
A block monotone domain decomposition algorithm for a semilinear convection-diffusion problem
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
The Schwarz Alternating Method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains.In this paper, proofs of convergence of some Schwarz Alternating Methods for nonlinear parabolic problems which are known to have solutions by the monotone method (also known as the method of subsolutions and supersolutions) are given. In particular, an additive Schwarz method for scalar as well some coupled nonlinear PDEs are shown to converge to the solution on finitely many subdomains. In the coupled system case, each subdomain PDE is linear, decoupled and can be solved concurrently with other subdomain PDEs. These results are applicable to several models in population biology. The convergence behavior is illustrated by two numerical examples.