Scalability of high-performance PDE solvers

Performance Modeling of PDE Solvers

In this chapter, we collect actual CPU time measurements of a number of prototypical PDE simulators for solving the Poisson equation, the linear elasticity equation, the heat conduction equation, the equations of nonlinear water waves, the incompressible Navier-Stokes equations, and many more. We show how these measurements can be used to establish performance models of the form: t = C n, which...

Performance of PDE Sparse Solvers on Hypercubes

Code Tiling for Improving the Cache Performance of PDE Solvers

For SOR-like PDE solvers, loop tiling either helps little in improving data locality or hurts their performance. This paper presents a novel compiler technique called code tiling for generating fast tiled codes for these solvers on uniprocessors with a memory hierarchy. Code tiling combines loop tiling with a new array layout transformation called data tiling in such a way that a significant am...

Performance Experiments and Optimizations of PDE Sparse Solvers on Hypercubes,

In this report we present the results of experiments with the parallel sparse matrix solver of the Parallel Ellpack System. 1bree different hypercube parallel machines are used to compare and optimize its performance. After a brief description of the parnIlel sparse matrix solver and a presentation of the machine parameters and features. the measurements of performance of the sparse solver on t...

Performance of PDE solvers on a self-optimizing NUMA architecture

The performance of shared-memory (OpenMP) implementations of three different PDE solver kernels representing finite difference methods, finite volume methods, and spectral methods has been investigated. The experiments have been performed on a self-optimizing NUMA system, the Sun Orange prototype, using different data placement and thread scheduling strategies. The results show that correct dat...