# Exploiting nested task-parallelism in the $\mathcal{H}-LU$ factorization

## TL;DR

This paper presents a novel approach to parallelizing $\\mathcal{H}$-matrix LU factorization using task-parallelism in OmpSs, effectively managing data dependencies and exploiting nested parallelism for boundary element methods.

## Contribution

It introduces a dependency analysis decoupled from data structures and leverages OmpSs-2 features to enhance nested task-parallel execution of hierarchical matrix factorizations.

## Key findings

- Achieved efficient parallel LU factorization of $\\mathcal{H}$-matrices.
- Demonstrated improved performance with nested task-parallelism.
- Validated approach on boundary element method applications.

## Abstract

We address the parallelization of the LU factorization of hierarchical matrices ($\mathcal{H}$-matrices) arising from boundary element methods. Our approach exploits task-parallelism via the OmpSs programming model and runtime, which discovers the data-flow parallelism intrinsic to the operation at execution time, via the analysis of data dependencies based on the memory addresses of the tasks' operands. This is especially challenging for $\mathcal{H}$-matrices, as the structures containing the data vary in dimension during the execution. We tackle this issue by decoupling the data structure from that used to detect dependencies. Furthermore, we leverage the support for weak operands and early release of dependencies, recently introduced in OmpSs-2, to accelerate the execution of parallel codes with nested task-parallelism and fine-grain tasks.