Solving the Klein-Gordon equation using Fourier spectral methods: A benchmark test for computer performance
Provides a practical benchmark for evaluating parallel FFT performance across diverse computer architectures, useful for researchers and system designers.
The study uses Fourier spectral methods with the 2DECOMP&FFT library to solve the cubic Klein-Gordon equation, demonstrating strong scaling on 13 different machines for a 512^3 problem size. The results provide a benchmark for assessing performance of parallel FFT-based PDE solvers.
The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of the code is examined on thirteen different machines for a problem size of 512^3. The results are useful in assessing likely performance of other parallel fast Fourier transform based programs for solving partial differential equations. The problem is chosen to be large enough to solve on a workstation, yet also of interest to solve quickly on a supercomputer, in particular for parametric studies. Unlike other high performance computing benchmarks, for this problem size, the time to solution will not be improved by simply building a bigger supercomputer.