Performance Modelling for Parallel PDE Solvers on NUMA-Systems

A detailed model of the memory performance of a PDE solver running on a NUMA-system is set up. Due to the complexity of modern computers, such a detailed model inevitably is very complicated. Therefore, approximations are introduced that simplify the model and allows NUMA-systems and PDE solvers to be described conveniently. Using the simpli ed model, it is shown that PDE solvers using ordered local methods can be made very unsensitive to high NUMA-ratios, allowing them to scale well on virtually any NUMA-system. PDE solvers using unordered local methods, semiglobal methods or global methods are more sensitive to high NUMA-ratios and require special techniques in order to scale well beyond a single locality group. Nevertheless, the potential performance gain of improving the data distribution on a NUMA-system can be considerable for all kinds of PDE solvers studied.