Semi-Automatic Task Graph Construction for $\mathcal{H}$-Matrix Arithmetic

TL;DR

This paper introduces a semi-automatic method for constructing task graphs in -matrix arithmetic, leveraging task information from recursive algorithms to improve efficiency on many-core systems.

Contribution

It presents a novel semi-automatic approach to build task graphs for -matrix operations, extending classical recursive methods for better parallel execution.

Findings

Effective task graph construction for -matrix arithmetic demonstrated

Method simplifies efficient utilization of many-core systems

Applicable to standard and accumulator-based -arithmetic

Abstract

A new method to construct task graphs for \mcH-matrix arithmetic is introduced, which uses the information associated with all tasks of the standard recursive \mcH-matrix algorithms, e.g., the block index set of the matrix blocks involved in the computation. Task refinement, i.e., the replacement of tasks by sub-computations, is then used to proceed in the \mcH-matrix hierarchy until the matrix blocks containing the actual matrix data are reached. This process is a natural extension of the classical, recursive way in which \mcH-matrix arithmetic is defined and thereby simplifies the efficient usage of many-core systems. Examples for standard and accumulator based \mcH-arithmetic are shown for model problems with different block structures.