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A two level overlapping Schwarz preconditioner for discontinuous Galerkin methods [Preprint]

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Calvo Alpízar, Juan Gabriel
Solano Córdoba, Moisés Eduardo

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This article presents a two-level overlapping additive Schwarz algorithm designed to solve an elliptic problem discretized with the symmetric discontinuous Galerkin method. The algorithm allows for the use of irregular subdomains, overcoming limitations of other approaches where the coarse mesh was based on triangular elements. Additionally, a brief description of the numerical implementation of the Galerkin method is included. Numerical results validating the relevance of our algorithm are also presented, including cases where the coefficient of the differential equation is discontinuous, which is relevant in different applications.
Este artículo presenta un algoritmo aditivo de Schwarz de dos niveles con traslape diseñado para resolver un problema elíptico discretizado con el método discontinuo de Galerkin simétrico. El algoritmo permite utilizar subdominios irregulares, superando limitaciones de otros enfoques donde la malla gruesa se basaba en elementos triangulares. Se incluye además una breve descripción de la implementación numérica del método de Galerkin. Se presenta además resultados numéricos que validan la pertinencia del método, incluyendo casos donde el coeficiente de la ecuación diferencial es discontinuo, lo cual es relevante en diversas aplicaciones.

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Domain decomposition, Discontinuous Galerkin methods, Irregular subdomain boundaries, Overlapping Schwarz algorithms, Nodal elliptic problems

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