Efficient implementation of a 3-dimensional ADI method on the iPSC/860
Rob F. Van der Wijngaart · 1993
A comparison is made between several domain decomposition strategies for the solution of threedimensional partial differential equations on a MIMD distributed memory parallel computer.The grids used are structured, and the numerical algorithm iv ADI.Important implementation issues regarding load balancing, storage requirements, network latency, and overlap of computations and communications are discussed.Results of the solution of the threedimensional heat equation on the Intel iPSC/860 ape presented for the th?'ee most viable methods.It is found that the Bruno-Cappeilo decomposition delivers optimal computational speed through an almost complete elimination of processor idle time, while providing good memory eficiency.plicit methods.Numerical solution of PDE's typically involves more or less the same operations for all the points in a computational grid used to discretize the problem space.Consequently, domain decomposition is the natural way of creating separate tasks for a parallel computer: a roughly equal number of grid points is assigned to each processor.Depending on the type of implicit algorithm chosen, some domain decompositions perform better than others.Efficiency is also affected by hardware parameters (e.g.network latency and bandwidth, and processor memory) and operating model (e.g.MIMD, SIMD).In this paper we compare three viable domain decompositions for the solution of @ 1993 ACM 0-8186-4340-4/93/0011 $1.50 c specific heat, and k the conduction tensor.Assuming k to be a constant scalar, i.e. k = kI, we get Equation (2) is subsequently discretized using central differencing in space and the 0-method in time: (1 -*[(U)2 +(6;)2 + (6:)2])AT = (3) 'k [(6:)2+ (6;)2 + (6:)2]T.p Here &< signifies the central difference operator in the xi-direction, T is the temperature, AT its te"mporal increment, and h is the size of the time step.The Permission to copy wilhout fee all or pan of this material is granted, provided that the copies m not made or ditibuwd for dimcl -ma advantage, the ACM copyright mxice and the title of tk publication and 102 h date appear, and notice is given Ihat copying is by permissmn cl the Association for Compning Machinery.To copy ciherwise, or to mp"blish, requires a fee andfor Spedc fermis$ion.