Benchmarking Solvers for the One Dimensional Cubic Nonlinear Klein Gordon Equation on a Single Core

Abstract

Many parallel computing benchmarks specify a specific algorithm that should be used to solve a specific problem, with much effort focused on machine specific optimization of a reference implementation. Since the solution of linear systems of equations, is often the most time consuming part for many problems in high performance scientific computing, a number of recent benchmarks for high performance computers suggest the use of an iterative method for solving sparse linear systems of equations to rank computer performance. Particular methods used include multigrid and conjugate gradients, though other methods such as the fast Fourier transform are also applicable in some cases. The best choice of method may vary with the problem chosen and the hardware the implemented software solution is executed on. Furthermore in solving a scientific computing problem, the level of accuracy can also be important, with some numerical methods being efficient for low accuracy simulations, but others more efficient for high accuracy simulations. Some of these tradeoffs are examined in the numerical solution of the one dimensional Klein Gordon equation on a single core of an x86-64 CPU and a single core of a NEC SX-ACE vector processor.

A Comparison of Parallel Profiling Tools for Programs utilizing the FFT

“…The effects of job placement and communication interference on result reproducibility will also be studied, an area for which there are still challenges [22]. Finally, there are other numerical methods that can be used to solve the Klein Gordon equation [34], it would be interesting to use these other methods to aid in performance prediction and optimal matching of algorithm to hardware architecture.…”