http:^^www.tc.cornell.edu^sc96^bernoulli^

来自「This data set contains WWW-pages collect」· EDU^SC96^BERNOULLI^ 代码 · 共 59 行

EDU^SC96^BERNOULLI^
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Date: Sun, 01 Dec 1996 20:26:02 GMTServer: NCSA/1.5Content-type: text/htmlLast-modified: Fri, 01 Nov 1996 19:12:16 GMTContent-length: 2473<TITLE> BERNOULLI PROJECT </TITLE><BODY BACKGROUND="./images/bg.gif"><center><!WA0><!WA0><!WA0><!WA0><IMG  WIDTH=550 HEIGHT=410 SRC="http://www.tc.cornell.edu/SC96/Bernoulli/images/bernoulli.gif" alt=""><p></center><p> The Bernoulli project is building tools for constructing problemsolving environments (PSEs) for computational science and engineering.Many of these applications involve the numerical solution of partialdifferential equations like the Navier-Stokes equations and theequations of elasticity. Commonly used solution methods like thefinite element and finite difference methods convert the problem ofsolving differential equations to that of solving systems of algebraicequations, using a process called discretization. The algebraicequations themselves can be solved using numerical techniques likeGaussian elimination, Krylov space methods and Newton's method.  <p><p> The Bernoulli project integrates breakthroughs in three areas:discretization tools,<!WA1><!WA1><!WA1><!WA1><a href="http://www.tc.cornell.edu/SC96/Bernoulli/compiler.html"> restructuring compiler technology </a> and <!WA2><!WA2><!WA2><!WA2><a href="http://www.tc.cornell.edu/SC96/Bernoulli/prema/index.html"> runtime systems </a>. <p> The discretization tools are being implemented by Rich Zippel usinghis Weyl symbolic algebra substrate. Weyl extends the data structuresavailable in Common Lisp to include objects like matrices, vectors,rational functions, rings etc. The discretization toolkit implementsthe weighted residual method which subsumes the finite-element,finite-volume and spectral methods. Finite-difference schemes are alsobeing implemented.<p> The systems of equations produced by discretization can be written inthe form Ax = b where A is a large, sparse matrix, b is a knownvector, and x is a vector of unknowns. Such large systems of equationscan be solved on parallel machines like the IBM SP-2, using solversthat exploit the sparsity of matrix A to reduce computation andcommunication requirements. We are developing restructuring compilertechnology to transform specifications of these solvers (expressed assequential programs operating on dense matrices) to parallel codesthat exploit sparsity. <p> The target of the compiler is a runtime substrate for parallelmachines that conforms to the PORTS specification for portability.The runtime substrate provides low-latency message passing and aglobal address space on distributed-memory platforms like the IBMSP-2. We are experimenting with versions based on MPI and on activemessages. <p><hr><address> Copyright &copy Cornell University </address></BODY>

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