Parallel domain decomposition algorithms for parabolic problems

This work deals with domain decomposition difference schemes oriented to approximate solution of transient problems on parallel computers. The emphasis is on the decomposition of initial domain onto a large number of subdomains. Two classes of difference schemes are investigated: component-wise splitting schemes (operator analogs of ordinary locally-onedimensional schemes) and additively-averaged schemes, which provide more efficient use of specific peculiarities of parallel computers. The principal issue is studying accuracy of these domain decomposition schemes. Dependence of approximate solution accuracy on the method of decomposition is investigated. In particular, estimates of the convergence rate are obtained for problems with various weights and different methods of decomposition.