DOMAIN PERTURBATION FOR PARABOLIC EQUATIONS

Parallel Domain Decomposition Methods for Parabolic Equations

Galerkin domain decomposition procedures for parabolic equations on rectangular domain

Galerkin domain decomposition procedures for parabolic equations with three cases of boundary conditions on rectangular domain are discussed. These procedures are non-iterative and non-overlapping ones. They rely on implicit Galerkin method in the sub-domains and integral mean method on the inter-domain boundaries to present explicit flux calculation. Thus, the parallelism can be achieved by th...

Small perturbation of stochastic parabolic equations: a power series analysis

A semi-linear second-order stochastic parabolic equation is considered with coefficients, free terms, and initial condition depending on a parameter. It is shown that under some natural conditions the solution can be written as a power series in the parameter. The equations for the coefficients in the power series expansion are derived and the convergence of the power series is studied. An exam...

Perturbation of Domain: Ordinary Differential Equations

We study a boundary perturbation problem for a one dimensional Schrödinger equation in which the potential has a regular singularity near the perturbed end point. We give the asymptotic behaviour of the eigenvalues under the perturbation. This problem arose out of the author’s studies of singular elliptic operators in higher dimensions and we illustrate this point with an example. The class of ...

An optimization-based domain decomposition method for parabolic equations

An optimization-based, non-overlapping domain decomposition method for the solution of the heat equation is presented. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains. The existence of an optimal solution is proved as is convergence of optimal solutions. A...