Implicit Space-Time Domain Decomposition Methods for Stochastic Parabolic Partial Differential Equations

Implicit Space-Time Domain Decomposition Methods for Stochastic Parabolic Partial Differential Equations

We introduce and study parallel space-time domain decomposition methods for solving deterministic and stochastic parabolic equations. Traditional parallel algorithms solve parabolic problems time step by time step. The parallelism is restricted to each time step, and the algorithms are purely sequential in time. In this paper, we develop some overlapping Schwarz methods whose subdomains cover b...

Space-time Domain Decomposition for Parabolic Problems Space-time Domain Decomposition for Parabolic Problems

We analyze a space-time domain decomposition iteration, for a model advection diiusion equation in one and two dimensions. The asymptotic convergence rate is superlinear, and it is governed by the diiusion of the error across the overlap between subdomains. Hence, it depends on both the size of this overlap and the diiusion coeecient in the equation. However, it is independent of the number of ...

Postprocessing for Stochastic Parabolic Partial Differential Equations

We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce post-processing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [20] and use an exponential integrator. We prove strong error estimates and discuss the best number of postprocessing terms to ...

Parallel Domain Decomposition Methods for Parabolic Equations

The new implicit finite difference scheme for two-sided space-time fractional partial differential equation

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...