Berkeley COMPSCI C267 - Lecture 13: Parallel Matrix Multiply (33 pages)

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Lecture 13: Parallel Matrix Multiply



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Lecture 13: Parallel Matrix Multiply

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Lecture Notes


Pages:
33
School:
University of California, Berkeley
Course:
Compsci C267 - Applications of Parallel Computers
Applications of Parallel Computers Documents

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CS 267 Applications of Parallel Processors Lecture 13 Parallel Matrix Multiply Kathy Yelick http www cs berkeley edu dmartin cs26 7 267 Lecture 13 01 14 19 1 Outline Recap Sources of large dense linear systems BLAS for linear algebra Parallel Matrix multiply 267 Lecture 13 01 14 19 2 Model overview Work depth PRAM Latency Bandwidth model is the 1 time cost per message latency is the per byte cost of communication Use this today LogP model correction gap should be greater than overhead more on this with parallel sorting Topology specific models 267 Lecture 13 01 14 19 3 Dense Linear Algebra in Electromagentics 267 Lecture 13 01 14 19 4 Computational Electromagnetics developed during 1980s driven by defense applications determine the RCS radar cross section of airplane reduce signature of plane stealth technology other applications are antenna design medical equipment two fundamental numerical approaches MOM methods of moments frequency domain and finite differences time domain 267 Lecture 13 01 14 19 5 Computational Electromagnetics discretize surface into triangular facets using standard modeling tools amplitude of currents on surface are unknowns integral equation is discretized into a set of linear equations image NW Univ Comp Electromagnetics Laboratory http nueml ece nwu edu 267 Lecture 13 01 14 19 6 Computational Electromagnetics MOM After discretization the integral equation has the form Z J V where Z is the impedance matrix J is the unknown vector of amplitudes and V is the excitation vector see Cwik Patterson and Scott Electromagnetic Scattering on the Intel Touchstone Delta IEEE Supercomputing 92 pp 538 542 267 Lecture 13 01 14 19 7 Computational Electromagnetics MOM The main steps in the solution process are A computing the matrix elements B factoring the dense matrix C solving for one or more excitations RHS D computing the fields scattered from the object 267 Lecture 13 01 14 19 8 Analysis of MOM for Parallel Implementation Task Speed Fill Work O n 2



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