New Algorithm Speeds Lattice QCD Equations

By Will Parker on October 2, 2007 in News

Writing in the physics journal Nuclear Physics B, two Baylor University researchers explain the development of a new mathematical algorithm that quickly solves Lattice Quantum Chromodynamics (Lattice QCD) linear equations. It marks the first time an effective method has been developed to overcome a significant bottleneck experienced by all Lattice QCD researchers.

Lattice QCD is a theory of quarks and gluons formulated and solved on a finite space-time lattice of points; however, the process of solving millions of linear equations is slowed thanks to small eigenvalues in the matrix. Eigenvalues help determine energy levels of atoms, but they also determine how fast solution methods for linear equations converge. The algorithms created by Dr. Ron Morgan, professor of mathematics at Baylor, and Dr. Walter Wilcox, professor of physics at Baylor, essentially “throw out” the small eigenvalues, thus speeding up the process considerably.

“I knew these algorithms had potential, but it was very nice to find that they could work well for an important application such as Lattice QCD,” Morgan said. “Our new methods work at computing eigenvalues at the same time that the linear equations are solved and using them to speed up the convergence. The methods are particularly effective when systems with multiple right-hand sides need to be solved as is the case in Lattice QCD.”

“It seems the bigger the problem, the better it works,” Wilcox said. “These methods are the culmination of a remarkable collaboration between mathematics and physics researchers and we are very pleased with the result. This will allow researchers in my field to do more, at a faster pace.”