Exploiting Generic Tiled Algorithms Toward Scalable H-Matrices Factorizations on Top of Runtime Systems

International audienceHierarchical matrices (H-matrices) have become important in applications where accuracy can be reduced to decrease to a logarithmic order both the execution time and memory consumption. It happens for instance when solving Boundary Element Methods (BEM) problems. However the natural hierarchical structure of the H-Matrices makes it more difficult to efficiently parallelize with modern programming paradigm such as task-based implementations. We discuss in this presentation how we can combine, Chameleon, a tiled dense linear algebra software relying on sequential task-based algorithms and runtime systems such as StarPU, and Hmat-oss, a library focused on providing a set of sequential algorithms for H-algebra operations. We will discuss the limitations in terms of H-matrices structure and memory compression that are imposed by the use of a tiled algorithm, and we will show the performance that can be brought by such a generic solution with respect to more advanced implementation fully exploiting the hierarchical data structure