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Software libraries for linear algebra computations on high performance computers
 SIAM REVIEW
, 1995
"... This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed b ..."
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Cited by 73 (17 self)
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This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed by an outline of ScaLAPACK, which is a distributed memory version of LAPACK currently under development. The importance of blockpartitioned algorithms in reducing the frequency of data movement between different levels of hierarchical memory is stressed. The use of such algorithms helps reduce the message startup costs on distributed memory concurrent computers. Other key ideas in our approach are the use of distributed versions of the Level 3 Basic Linear Algebra Subprograms (BLAS) as computational building blocks, and the use of Basic Linear Algebra Communication Subprograms (BLACS) as communication building blocks. Together the distributed BLAS and the BLACS can be used to construct highe...
A Portable Parallel Particle Program
 Computer Physics Communications
, 1995
"... We describe our implementation of the parallel hashed octtree (HOT) code, and in particular its application to neighbor finding in a smoothed particle hydrodynamics (SPH) code. We also review the error bounds on the multipole approximations involved in treecodes, and extend them to include general ..."
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Cited by 56 (7 self)
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We describe our implementation of the parallel hashed octtree (HOT) code, and in particular its application to neighbor finding in a smoothed particle hydrodynamics (SPH) code. We also review the error bounds on the multipole approximations involved in treecodes, and extend them to include general cellcell interactions. Performance of the program on a variety of problems (including gravity, SPH, vortex method and panel method) is measured on several parallel and sequential machines. 1 Introduction There are two strategies that can be applied in the quest for more knowledge from bigger and better particle simulations. One can use the brute force approach; simple algorithms on bigger and faster machines (and bigger and faster now means massively parallel). To compute the gravitational force and potential for a single interaction takes 28 floating point operations (here we count a division as 4 floating point operations and a square root as 4 floating point operations). A typical grav...
Large Dense Numerical Linear Algebra in 1993: The Parallel Computing Influence
 International Journal Supercomputer Applications
, 1994
"... This paper surveys the current state of applications of large dense numerical linear algebra, and the influence of parallel computing. Furthermore, we attempt to crystalize many important ideas that we feel have been sometimes been misunderstood in the rush to write fast programs. 1 Introduction Th ..."
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Cited by 35 (2 self)
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This paper surveys the current state of applications of large dense numerical linear algebra, and the influence of parallel computing. Furthermore, we attempt to crystalize many important ideas that we feel have been sometimes been misunderstood in the rush to write fast programs. 1 Introduction This paper represents my continuing efforts to track the status of large dense linear algebra problems. The goal is to shatter the barriers that separate the various interested communities while commenting on the influence of parallel computing. A secondary goal is to crystalize the most important ideas that have all too often been obscured by the details of machines and algorithms. Parallel supercomputing is in the spotlight. In the race towards the proliferation of papers on person X's experiences with machine Y (and why his algorithm runs faster than person Z's), sometimes we have lost sight of the applications for which these algorithms are meant to be useful. This paper concentrates on la...
The Design of Linear Algebra Libraries for High Performance Computers
, 1993
"... This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followe ..."
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Cited by 16 (1 self)
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This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed by an outline of ScaLAPACK, which is a distributed memory version of LAPACK currently under development. The importance of blockpartitioned algorithms in reducing the frequency of data movementbetween di#erent levels of hierarchical memory is stressed. The use of such algorithms helps reduce the message startup costs on distributed memory concurrent computers. Other key ideas in our approach are the use of distributed versions of the Level 3 Basic Linear Algebra Subgrams #BLAS# as computational building blocks, and the use of Basic Linear Algebra Communication Subprograms #BLACS# as communication building blocks. Together the distributed BLAS and the BLACS can be used to construct ...
The First Annual Large Dense Linear System Survey
 Int. Rept. Univ. California, Berkeley CA
, 1991
"... In the March 24, 1991 issue of NA Digest, I submitted a questionnaire asking who was solving large dense linear systems of equations. Based on the responses, nearly all large dense linear systems today arise from either the benchmarking of supercomputers or applications involving the influence of a ..."
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Cited by 7 (2 self)
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In the March 24, 1991 issue of NA Digest, I submitted a questionnaire asking who was solving large dense linear systems of equations. Based on the responses, nearly all large dense linear systems today arise from either the benchmarking of supercomputers or applications involving the influence of a two dimensional boundary on three dimensional space. Not surprisingly, the area of computational aerodynamics or aeroelectromechanics represents an important commercial application requiring the solution of such systems. The largest unstructured matrix that has been factored using Gaussian Elimination was a complex matrix of size 55,296. The largest dense matrix solved on a Sun using an iterative method was a real matrix of size 20,000. It is unclear at this time whether dense methods are truly needed at all for huge matrices. It is intended to survey users every year with the hope of including more applications as I am made aware of them. 1 Introduction The idea to poll solvers of large d...
The Numerical Solution of Boundary Integral Equations
 THE STATE OF THE ART IN NUMERICAL ANALYSIS, PP.223–259
, 1997
"... Much of the research on the numerical analysis of Fredholm type integral equations during the past ten years has centered on the solution of boundary integral equations (BIE). A great deal of this research has been on the numerical solution of BIE on simple closed boundary curves S for planar region ..."
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Cited by 7 (1 self)
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Much of the research on the numerical analysis of Fredholm type integral equations during the past ten years has centered on the solution of boundary integral equations (BIE). A great deal of this research has been on the numerical solution of BIE on simple closed boundary curves S for planar regions. When a BIE is defined on a smooth curve S, there are many numerical methods for solving the equation. The numerical analysis of most such problems is now wellunderstood, for both BIE of the first and second kind, with many people having contributed to the area. For the case with the BIE defined on a curve S which is only piecewise smooth, new numerical methods have been developed during the past decade. Such methods for BIE of the second kind were developed in the mid to late 80s; and more recently, high order collocation methods have been given and analyzed for BIE of the first kind. The numerical analysis of BIE on surfaces S in R³ has become more active during the past decade, and...
CRPC Research into Linear Algebra Software for High Performance Computers
, 1994
"... In this paper we look at a number of approaches being investigated in the Center for Research on Parallel Computation (CRPC) to develop linear algebra software for highperformance computers. These approaches are exemplified by the LAPACK, templates, and ARPACK projects. LAPACK is a software library ..."
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Cited by 4 (2 self)
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In this paper we look at a number of approaches being investigated in the Center for Research on Parallel Computation (CRPC) to develop linear algebra software for highperformance computers. These approaches are exemplified by the LAPACK, templates, and ARPACK projects. LAPACK is a software library for performing dense and banded linear algebra computations, and was designed to run efficiently on high performance computers. We focus on the design of the distributed memory version of LAPACK, and on an objectoriented interface to LAPACK. The templates project aims at making the task of developing sparse linear algebra software simpler and easier. Reusable software templates are provided that the user can then customize to modify and optimize a particular algorithm, and hence build a more complex applications. ARPACK is a software package for solving large scale eigenvalue problems, and is based on an implicitly restarted variant of the Arnoldi scheme. The paper focuses on issues impact...
Intelligent Automated Grid Generation for Numerical Simulations
 Artificial Intelligence for Engineering Design, Analysis and Manufacturing (AI EDAM
, 1996
"... Numerical simulation of partial differential equations (PDEs) plays a crucial role in predicting the behavior of physical systems and in modern engineering design. However, in order to produce reliable results with a PDE simulator, a human expert must typically expend considerable time and effort in ..."
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Cited by 3 (3 self)
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Numerical simulation of partial differential equations (PDEs) plays a crucial role in predicting the behavior of physical systems and in modern engineering design. However, in order to produce reliable results with a PDE simulator, a human expert must typically expend considerable time and effort in setting up the simulation. Most of this effort is spent in generating the grid, the discretization of the spatial domain which the PDE simulator requires as input. To properly design a grid, the gridder must not only consider the characteristics of the spatial domain, but also the physics of the situation and the peculiarities of the numerical simulator. This paper describes an intelligent gridder that is capable of analyzing the topology of the spatial domain and predicting approximate physical behaviors based on the geometry of the spatial domain to automatically generate grids for computational fluid dynamics simulators. Typically gridding programs are given a partitioning of the spatial...