 
Summary: Parallelizing Implicit Algorithm for
TimeDependent Problems by Parabolic Domain
Decomposition \Lambda
appeared in J. of Scientific Computing, Vol. 8, No. 2, pp. 151166, June 1993
A. Averbuch z , M. Israeli y , L. Vozovoi y
y Faculty of Computer Science, Technion, Haifa 32000, Israel
z School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Abstract
This paper presents a novel parallel highorder algorithm for the solution of parabolic
and elliptic PDE's. The parallelization is achieved by using a domain decomposition
technique. For the spatial discretization the trigonometric Fourier basis is employed
along with a smoothing procedure in order to preserve spectral accuracy. In the time
discretization scheme the diffusive term is treated implicitly. The matching of the
elemental subsolutions which generates the global solution, is performed by using the
boundary Green's functions. To avoid the global coupling and data transfer, inherent
in the implicitness of the timestepping algorithm, the localization properties of the
boundary Green's functions are exploit in an explicit way. In effect, only local commu
nications between neighbouring processors are necessery so that the parallel algorithm
becomes scalable. Another advantage of the present approach is that it allows the
implementation of different resolution in each subdomain, which makes it valuable as
