Developing a Parallelisable Eigensolver

Sengupta, Sreyam (2018) Developing a Parallelisable Eigensolver. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Sreyam Sengupta (13MS121)) 13MS121.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

The goal of this project was to develop a parallelisable algorithm to calculate the lowlying eigenspectrum of a large, sparse, positive-definite Hermitian matrix. The parallelised eigensolver will then be applied to some problems in lattice QCD. This report offers a very brief introduction to QCD as an SU(3) gauge theory, before motivating and introducing lattice QCD. The introduction is followed by a section describing a method used to resolve the fermion doubling problem on the lattice, and two subsequent sections on eigensolver algorithms. The first is the Lanczos method, the traditional algorithm which nevertheless suffers from a few flaws. The Kalkreuter-Simma (KS) algorithm is then introduced as a more viable alternative. The KS algorithm is alternated with Jacobi diagonalisations to further refine the eigenspectrum estimates. A program that implements the above algorithm is written and parallelised for the GPU using the OpenACC paradigm. Timing studies are performed on the program with two pre-generated lattices of different sizes as input. The results obtained so far are outlined, along with a brief discussion of further prospects.

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