Uppsala University Department of Information Technology

Technical Report 2006-041

Performance Modelling for Parallel PDE Solvers on NUMA-Systems

Markus Nordén

August 2006


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 simplified 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.

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