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Scalable Computational Methods in Quantum Field Theory

Scalable Computational Methods in Quantum Field Theory. Jason Slaunwhite Computer Science and Physics Senior Project. Advisors: Hemmendinger, Reich, Hiller (UMD). Outline. Context / Background Design Optimization Compiler Data Structures Parallel Summary. Context (1).

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Scalable Computational Methods in Quantum Field Theory

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  1. Scalable Computational Methods in Quantum Field Theory Jason Slaunwhite Computer Science and Physics Senior Project Advisors: Hemmendinger, Reich, Hiller (UMD)

  2. Outline • Context / Background • Design • Optimization • Compiler • Data Structures • Parallel • Summary

  3. Context (1) QED picture not QCD, particle exchange • Physical Model • Strong Force • Yukawa Theory • Quantum field thoery • Interactions = particle exchanges • Gauge Bosons • Eigenvalue Problem • Common ex: rotation • Form: Z Eigenvector Rotation About z Ax = lx xy-plane Matrix Vector Scalar

  4. Context (2) • Formulation of Eigenvalue Problem • Discrete - Hiller • Basis Function Expansion - Slaunwhite y y = f(x) x Basis Function Expansion y y y = Gn (x) y = Gm (x) + discrete y Ax = lx x x f(x) = a*Gn (x) + b* Gm (x) + … x Ax = lx

  5. Context (3) • Is BFE a good method for solving the eigenvalue problem? • Is it scalable? • Convergence of eigenvalues as w/ increasing # of functions • Time dependence of computational methods convergence

  6. Design (1) Calc Matrix Solve (Diagonalize) Input • What does the program do? • Input Parameters • Calculate each independent matrix elements • Solve (Diagonalize the matrix) • Structure Reflects Mathematics libraries easy

  7. Design (2) Level 1 Calc Matrix Diagonalize (solve) Input Level 2 Integrate Integrate Integrate Level 3 Kernel Kernel Kernel

  8. Review • Quantum Field Theory Model of the strong force • Eigenvalue problem • Programming work: calculate the matrix elements. • How did I optimize it? • Can it run in parallel? Ax = lx Matrix Vector Scalar The program

  9. Optimization - Compiler • g++ -03 • Simple • Adds compile time • Very Effective! - Unoptimized - Optimized

  10. Optimization – Data Structures … • Naïve approach • Storage vs. Time • Precompute values outside of element iteration • Need organized way to index the values Compute library Values Trade-off smart For each row For each col Calculate element Compute library Values (naïve) Naïve …

  11. Optimization Results Key: --naïve --data structure --data structure + compiler Slopes: red/yellow = 2.56 Slopes: yellow/green = 2.28 Slopes: red/green = 5.84

  12. Parallel Design • Matrix elements independent • Split computation across many processors Ax = lx = l

  13. Work in progress - Paralellization • OpenMP libraries • IBM SP – MSI • Slower processors, but more of them and more memory • Work in progress From http://www.ibm.com The IBM SP consists of 96 shared-memory nodes with a total of 376 processors and 616 GB of memory

  14. Summary Parallel? Ax = lx g++ -03 The program

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