{"ID":5675144,"CreatedAt":"2026-07-03T01:40:09.565152011Z","UpdatedAt":"2026-07-05T05:45:35.603470622Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.01735","arxiv_id":"2607.01735","title":"Exploiting Task-Based Parallelism for the Red-Black Gauss-Seidel Method on 2D Grids","abstract":"Gauss-Seidel is a well-established iterative method for the solution of linear systems, and multicoloring has been widely used to increase parallelism in iterative solution techniques. Implementing multi-color Gauss-Seidel with conventional divide-and-conquer parallelization strategies, however, may be inefficient due to global synchronization requirements and load imbalances. Task-based programming models can mitigate these issues by enabling fine-grained parallelism, removing global barriers and allowing updates of different colors to partially overlap in time. In this work, we implement the red-black Gauss-Seidel method using two task-based programming models and compare them with a classical divide-and-conquer parallel implementation to evaluate the impact of fine-grained parallelism on execution efficiency. The red-black scheme serves as a representative example, as task-based approaches naturally extend to more general multi-color schemes arising from unstructured grids and wider stencils. Using the solve of the 2D Poisson equation as benchmark, our results show that task-based implementations can achieve performance comparable to conventional divide-and-conquer parallelization while providing greater resilience to hardware-level asynchronicity.","short_abstract":"Gauss-Seidel is a well-established iterative method for the solution of linear systems, and multicoloring has been widely used to increase parallelism in iterative solution techniques. Implementing multi-color Gauss-Seidel with conventional divide-and-conquer parallelization strategies, however, may be inefficient due...","url_abs":"https://arxiv.org/abs/2607.01735","url_pdf":"https://arxiv.org/pdf/2607.01735v1","authors":"[\"Shiting Long\",\"Gustavo Ramirez-Hidalgo\",\"Andreas Frommer\",\"Dirk Pleiter\"]","published":"2026-07-02T05:45:18Z","proceeding":"cs.DC","tasks":"[\"cs.DC\",\"math.NA\"]","methods":"[]","has_code":false}