A non-overlapping Schwarz algorithm for the HDG method
Issei Oikawa
TL;DR
This paper introduces two non-overlapping Schwarz algorithms tailored for the HDG method, enhancing domain decomposition techniques with numerical validation for improved computational efficiency.
Contribution
The paper develops two novel non-overlapping Schwarz algorithms specifically designed for the HDG method, including a Neumann-Neumann based approach and an iterative method utilizing interface unknowns.
Findings
Algorithms are validated through numerical experiments.
The methods improve computational efficiency for HDG problems.
The approaches are effective for domain decomposition in HDG.
Abstract
In this paper, we present two non-overlapping Schwarz algorithms for the hybridizable discontinuous Galerkin (HDG) method. The first algorithm is based on the Neumann-Neumann method. The second one is an iterative algorithm uses both trace and flux interface unknowns on interfaces between subdomains. Numerical results are provided to verify the validity of our algorithms.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Computational Fluid Dynamics and Aerodynamics · Fluid Dynamics and Turbulent Flows