A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation - Keyes, David E.; Gropp, William 1955- (1985)
Several preconditioned conjugate gradient (PCG)-based domain decomposition techniques for self-adjoint elliptic partial differential equations in two dimensions are compared against each other and against conventional PCG iterative techniques in serial and parallel contexts. The authors consider preconditioners that make use of fast Poisson solvers on the subdomain interiors. Several preconditioners for the interfacial equations are tested on a set of model problems involving two or four subdomains, which are prototype of the stripwise and boxwise decompositions of a two-dimensional region. Selected methods have been implemented on the Intel Hypercube by assigning one processor to each subdomain, making use of up to 64 processors. The choice of a 'best' method for a given problem depends in general upon: (a) the domain geometry, (b) the variability of the operator, and (c) machine characteristics such as the number of processors available and their interconnection scheme, the memory available per processor, and communication and computation rates. Emphasized is the importance of the third category, which has not been as extensively explored as the first two in the domain decomposition literature to date. (Author).
Keywords: Domain decomposition; Computations; Decomposition; Ellipses; Gradients; Interfaces; Iterations; Partial differential equations; Processing equipment; Rates; Theoretical Mathematics