Linear algebra on lattices : Simit language extensions with applications to lattice QCD

Abstract

This thesis presents language extensions to Simit, a language for linear algebra on graphs. Currently, Simit doesn't efficiently handle lattice graphs (regular grids). This thesis defines a stencil assembly construct to capture linear algebra on these graphs. A prototype compiler with a Halide backend demonstrates that these extensions capture the full structure of linear algebra applications operating on lattices, are easily schedulable, and achieve comparable performance to existing methods. Many physical simulations take the form of linear algebra on lattices. This thesis reviews Lattice QCD as a representative example of such a class of applications and identifies the structure of the linear algebra involved. In this application, iterative inversion of the Dirac matrix dominates the runtime, and time-intensive hand-optimization of inverters for specific forms of the matrix limit further research. This thesis implements this computation using the language extensions, while demonstrating competitive performance to existing methods.