We make a detailed examination 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 comparisons 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 by comparison 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. (KR).

This volume contains the proceedings of the ICASE/LaRC Work shop on the "Algorithmic Trends for Computational Fluid Dynamics (CFD) in the 90's" conducted by the Institute for Computer Applica tions in Science and Engineering (ICASE) and the Fluid Mechanics Division of NASA Langley Research Center during September 15-17, 1991. The purpose of the workshop was to bring together numerical analysts and computational fluid dynamicists i) to assess the state of the art in the areas of numerical analysis particularly relevant to CFD, ii) to identify promising new developments in various areas of numerical analysis that will have impact on CFD, and iii) to establish a long-term perspective focusing on opportunities and needs. This volume consists of five chapters - i) Overviews, ii) Accelera tion Techniques, iii) Spectral and Higher-Order Methods, iv) Multi Resolution/ Subcell Resolution Schemes (including adaptive meth ods), and v) Inherently Multidimensional Schemes. Each chapter covers a session of the Workshop. The chapter on overviews contains the articles by J.L. Steger, H.-O. Kreiss, R.W. MacCormack, O.