Parallel Domain Decomposition Procedures Of D-D Type For Linearparabolic Integro-Dierential Equations

This thesis contributes to the development of numerical methods for solving linear parabolic integro-differential equations that enable the use of different time steps in the subdomains. In this work, we study the application of the domain decomposition methods of D-D type algorithm to decompose a large or complicated domain into several small or regular overlapping or non-overlapping sub-domains. The equation is first discretized in time by the Galerkin method with piecewise constant or piecewise linear approximating functions considering the combination of finite element discretization in space. The approximate normal derivatives along the interfaces are calculated in an accurate and stable manner without iterations on the subdomains and interfaces and no overlapping in the subdomains, which exhibits a constraint involving an interface discretization parameter and the time step. The procedures are conservative both in the subdomains and across the inter-domain boundaries. Error estimates and convergence results are then given.