This paper presents the software architecture and implementation of the problem solving

We have developed a framework based on relational algebra for compiling efficient sparse matrix code from dense DO-ANY loops and a specification of the representation of the sparse matrix. In this paper, we show how this framework can be used to generate parallel code, and present experimental data that demonstrates that the code generated by our Bernoulli compiler achieves performance competitive with that of hand-written codes for important computational kernels. Keywords: parallelizing compilers, sparse matrix computations 1 Introduction Sparse matrix computations are ubiquitous in computational science. However, the development of high-performance software for sparse matrix computations is a tedious and error-prone task, for two reasons. First, there is no standard way of storing sparse matrices, since a variety of formats are used to avoid storing zeros, and the best choice for the format is dependent on the problem and the architecture. Second, for most algorithms, it takes a lo...

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xiii INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1. MULTI-PARAMETERIZEDSCHWARZ SPLITTING FOR ONE-DIMENSIONAL PROBLEMS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.1 Preliminary : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.1.1 Schwarz Alternating Method (SAM) : : : : : : : : : : : : : : 5 1.1.2 Generalization of SAM : : : : : : : : : : : : : : : : : : : : : : 7 1.1.3 Schwarz Splitting : : : : : : : : : : : : : : : : : : : : : : : : : 10 1.1.4 Generalized Schwarz Splitting : : : : : : : : : : : : : : : : : : 13 1.2 One-Parameter Schwarz Splitting : : : : : : : : : : : : : : : : : : : : 15 1.2.1 Formulation of the Parameterized Schwarz Splitting : : : : : : 17 1.2.2 Convergence Analysis : : : : : : : : : : : : : : : : : : : : : : : 22 1.2.3 Determination of the Optimal Parameter : : : : : : : : : : : : 26 1.3 Multi-Parameter Schwarz...

In this study, we are concerned with the parallelizationof finite element mesh generation and its decomposition, and the parallel solution of sparse algebraic equations which are obtained from the parallel discretization of second order elliptic partial differential equations (PDEs) using finite difference and finite element techniques. For this we use the Parallel ELLPACK (//ELLPACK) problem solving environment (PSE) which supports PDE computations on several MIMD platforms. We have considered the ITPACK library of stationary iterative solvers which we have parallelized and integrated into the //ELLPACK PSE. This Parallel ITPACK package has been implemented using the MPI, PVM, PICL, PARMACS, nCUBE Vertex and Intel NX message passing communication libraries. It performs very efficiently on a variety of hardware and communication platforms. To study the efficiency of three MPI library implementations, the performance of the Parallel ITPACK solvers was measured on several distributed memory architectures and on clusters of workstations for a testbed of elliptic boundary value PDE problems. We present a comparison of these MPI library implementationswith PVM and the native communication libraries, based on their performance on these tests. Moreover we have implemented in MPI, a parallel mesh generator that concurrently produces a semi–optimal partitioning of the mesh to support various domain decomposition solution strategies across the above platforms. The results indicate that the MPI overhead varies among the various implementations without significantly affecting the algorithmic speedup even on clusters of workstations.

In this paper we define a knowledge discovery in databases (KDD) methodology to automatically generate metadata (i.e., knowledge rules) from software/machine pair performance databases. This metadata can be used to characterize the computational behavior of various classes of software or machines. The core and the most computationally intensive part of the KDD methodology is the data mining phase which identifies "interesting" patterns from the performance data. The discovery patterns are expressed in a high level representation to be used to summarize and predict the computational behavior of the targeted software/machine. This paper presents an implementation and evaluation of the proposed KDD process for a class of scientific software together with three data mining algorithms (ID3, HOODG, and CN2). For this case study we have selected a set of software that implements the "mesh/grid partitioning " phase of the domain decomposition approach used for the parallel processing of partial differential equation (PDEs) computations. The raw performance database is generated from a population of elliptic PDEs and PELLPACK [HRW 98] solvers by varying the PDE domain, mesh, and domain partitioning (DP) algorithm. The goal of the KDD process here is to evaluate the performance of PELLPACK, CHACO [HL95c], METIS [KK95c], and PARTY [PD96] algorithms/software. This case study shows that (a) the three data mining algorithms used are qualitatively and quantitatively equally effective, (b) the knowledge discovered for the DP algorithms by this KDD process is quantitatively similar to that deduced by purely experimental observations [VH97], and (c) the KDD process is not limited by the size of the performance data and its dimensionality.

This report summarizes software for sparse matrix computations available at CSRD and gives some information about its usage. The packages described include SPLIB, a collection of basic matrix operations, iterative solvers and preconditioners; RPPACK, a Row Projection methods PACKage; and DNSPCG, a Double precision NonSymmetric Preconditioned Conjugate Gradient package. CSRD, University of Illinois, 305 Talbot, 104 S. Wright, Urbana, IL 61801. This work was supported in part by the U.S. Department of Energy under Grant No. DOE DE-FG02-85ER25001 and the National Science Foundation under Grant No. NSF CCR-8717942. CONTENTS 2 Contents 1 Introduction 4 2 SPLIB 5 2.1 Description : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.2 Usage : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.3 Tools : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.3.1 Basic linear algebra routines : : : : : : : : : : : : : : : : ...

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