A methodology for adaptive resolution of numerical problems on heterogeneous hierarchical clusters

Solving a target problem by using a single algorithm or writing portable programs that perform well is not always efficient on any parallel environment due to the increasing diversity of existing computational supports where new characteristics are influencing the execution of parallel applications. The inherent heterogeneity and the diversity of networks of such environments represent a great challenge to efficiently implement parallel applications for high performance computing. Our objective within this work is to propose a generic framework based on adaptive techniques for solving a class of numerical problems on cluster-based heterogeneous hierarchical platforms. Toward this goal, we refer to adaptive approaches to better adapt a given application to a target parallel system. We apply this methodology on a basic numerical problem, namely solving the matrix multiplication problem, while determining an adaptive execution scheme minimizing the overall execution time depending on the problem and architecture parameters.