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

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

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

4. Context (2) Formulation of Eigenvalue Problem –Discrete - Hiller –Basis Function Expansion - Slaunwhite Ax = x discrete y = f(x) y x y x y x y x + Basis Function Expansion y = G n (x) y = G m (x) f(x) = a*G n (x) + b* G m (x) + … Ax = x

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

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

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 = x 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 For each row For each col Calculate element Compute library Values Trade-off Compute library Values (naïve) … … Naïve smart

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

12. Parallel Design Matrix elements independent Split computation across many processors Ax = x =

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 g++ -03 The program Parallel? Ax = x