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Abstract

No abstract

We make a detailed examination lwas made of the performance achieved by a Krylov space sparse linear system solver that uses incompletely factored matrices for preconditioners. We compared two related mechanisms for parallelizing the computationally critical sparse triangular solves and sparse numeric incomplete factorizations on a range of test problems. From these comparisions we drew several interesting conclusions about methods that can be used to parallelize loops of the type found here. The performance we obtain is brought into perspective hy comparisons with timing results from a Cray X/MP supercomputer. Performance on an Encore Multimax/320 with relatively modest computational capabilities comes within a small factor of the performance on a comparable code run on a Cray X/MP.

In this paper, we extend t h e class of problenis t h a t can be effcrtively m npiled by parallelizing compilers. This is accornplislictl with t h e doconsider coilstruct which would allow these compilers t o paralldizc~ many prohlcnis i n \vliit 11 siil)staiitial loop-lcvel parallelisin is available h i t cattnot bc tlctcctctl hy staiitl;irtl corn pile-t iriie analysis. \Ire describe and espcriincii till IJ analyze mcdia nisni.; II srd to parallclize t h e work required for these types of loops. In each of t hcse met Iiotls.a new loop structure is produced hy modifying t h e loop to be parallclizcd. \\'P also prcscnt t h e rules by wliicli these loop transformations may be autoiiiatcd i n oi t1c.r.that they b e iriclridccl in langiiage conipilers. Tlic i t i a i i i application a1c.n of o u r wscarcli involves problems i n scientific computations aittl engineering. The wot kIo;itl iiscd in our experirnents iitcludcs a mixture of real ~)i~)l)lcins as wc4l as synt 1101 irally gcncratetl inputs. I2rorn our estcwsivc tests oii t l i t 1 I:iicorc hliil t i i t t ; i s / : l~(~, IVV have reaclicd t h e conclusion that for t h e types of \voi liloatls \vv Iiavc. itivfsligat (VI, self-execution almost always perforins better tltitii ~~tc~-sc~liccli~li~ig. b'iirtlier. 1 IIV i r i iprovcment in performance t h a t accriics as a resiil t of global topological sori irig of indices as opposed to the less experisivc local sortiiig. is not very sigiiifirant i r i t IIP case of self-execution.