A two-level overlapping Schwarz preconditioner for discontinuous Galerkin methods

• Calvo, Juan G. ^[1] ; Solano, Moisés ^[1]
  1. [1] Universidad de Costa Rica

     Universidad de Costa Rica

     Hospital, Costa Rica

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 32, Nº. 1, 2025 (Ejemplar dedicado a: Revista de Matemática: Teoría y Aplicaciones), págs. 15-33
• Idioma: inglés
• DOI: 10.15517/rmta.v32i1.59472
• Títulos paralelos:
  • Un precondicionador de Schwarz de dos niveles con traslape para métodos discontinuos de Galerkin
• Enlaces
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• Resumen
  • español

    Este artículo presenta un algoritmo aditivo de Schwarz de dos niveles con traslape diseñado para resolver problemas elípticos discretizados con el método Galerkin discontinuo de penalización interior simétrico. El algoritmo propuesto 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 presentan resultados numéricos que validan la pertinencia del método, incluyendo casos donde el coeficiente de la ecuación diferencial es discontinuo, una característica que es relevante en diversas aplicaciones.

  • English

    This article introduces a two-level overlapping additive Schwarz algorithm tailored for solving elliptic problems discretized with the symmetric interior penalty discontinuous Galerkin method. The proposed algorithm allows for the use of irregular subdomains, overcoming limitations of other approaches where the coarse mesh was based on triangular elements. Additionally, we provide a brief description of the numerical implementation of the Galerkin method. We present numerical results validating the relevance of our algorithm, including cases where the coefficient of the differential equation is discontinuous—a feature that is particularly relevant to various practical applications.

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