Performance Evaluation and Design of Hardware-Aware PDE Solvers: An Introduction

Abstract

In an ideal situation, all performance optimization of computationally intensive software would take place automatically, allowing the researchers to concentrate on the development of more efficient algorithms (in terms of computational complexity) rather than having to worry about performance. However, for the time being, optimizing compilers are unable to synthesize long chains of complicated code transformations to optimize program execution. As a consequence, the need to identify and to remove the performance bottlenecks of computationally intensive codes remains.

As an example of a class of computationally intensive problems, this minisymposium concentrated on the numerical solution of partial differential equations (PDEs). As with every computer program, the run times of PDE solvers depend both on the algorithms and on the data structures used in the implementations. In the context of numerical PDEs, algorithms with optimal asymptotic complexity are known for certain types of problems; e.g., multigrid methods for elliptic problems. In those cases where the optimal algorithms are applicable, only the data structures and the implementation details offer scope for improvement.