PARALLEL IMPLEMENTATION OF NONLINEAR EVOLUTION PROBLEMS USING PARABOLIC DOMAIN DECOMPOSITION

We present implementation of parallel algorithms for the numerical sol ution of nonlinear time-dependent partial differential equations of pa rabolic type arising from complex large scale problems. The paralleliz ation is achieved by using domain decomposition (DD) techniques. The e ssential feature of this algorithm is that the spatial discretization in each subdomain is performed by using spectral method with the Local Fourier Basis (LFB) [1]. Our solutions are based on a special project ion technique that employed to localize functions in a smooth way on t he extended subdomain. The current paper continue the flow of our prev ious results [1,4,12,13] on spectral multidomain algorithm. The applic ation of the Parabolic Domain Decomposition (PDD) approach along with the LFB is shown to be very efficient when applied to a 2-dimensional domain splitted into strips and rectangular cells. In this case, all m atching relations become completely uncoupled (at the price of some ov erlapping of subdomains required by the LFB implementation). Thus, all communication is reduced to interactions between neighbouring element s and thus fits to scalable message-passing multiprocessor. The contin uity of a global solution is attained by using a direct point-wise mat ching of the local subsolutions on the interfaces. The implementation of the LFB technique enables us to trade a 2-D problem with the overal l coupling of the interface unknown into a set of uncoupled 1-D differ ential equations with simple matching relations. 2-D Navier-Stokes typ e modeling equation is implemented on the Meiko message-passing type s calable MIMD multiprocessor.