An approach to optimizing adaptive parabolic PDE solvers for the Grid

The method of lines is a widely used algorithm for solving parabolic partial differential equations that could benefit greatly from implementation on Grid computing environments. This paper outlines the issues involved in executing method-of-lines codes on a Grid and in developing model-driven adaptive control strategies for these codes. We have developed a parameterizable benchmark called MOL that captures a wide range of realistic method-of-lines codes. We are using this benchmark to develop performance models that can be used to achieve specific optimality criteria under the available (and dynamically varying) resources of a Grid environment, and under user-specified goals for solution error and computational rate-of-progress. We are developing a componentization strategy that can enable effective adaptive control of MOL, as well as language and compiler support that can simplify the development of adaptive distributed applications. If successful, this work should yield a much better understanding than we have at present of how an important class of parallel numerical applications can be executed effectively in a dynamic Grid environment.

1. Introduction

Grid computing (or wide-area distributed computing) is attracting increasing attention as a strategy for making large-scale computational resources available to a wide community of users. Certain key aspects of Grid computing are, however, still at a preliminary stage of development. For example, there is relatively little understanding of how to map important classes of parallel applications to a Grid environment and how these applications will perform in this environment. A key technical challenge that requires extensive research is to develop systematic adaptive management techniques for different classes of applications, which are likely to be needed in the dynamic and heterogeneous environment of a Grid.