A. Averbuch et al., PARALLEL IMPLEMENTATION OF NONLINEAR EVOLUTION PROBLEMS USING PARABOLIC DOMAIN DECOMPOSITION, Parallel computing, 21(7), 1995, pp. 1151-1183
Citations number
14
Categorie Soggetti
Computer Sciences","Computer Science Theory & Methods
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.