Resumen

CALVO, Juan G.  y  SOLANO, Moisés. A two-level overlapping Schwarz preconditioner for discontinuous Galerkin methods. Rev. Mat [online]. 2025, vol.32, n.1, pp.14-32. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v32i1.59472.

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.

Palabras clave : Domain decomposition; Discontinuous Galerkin methods; Irregular subdomain boundaries; Overlapping Schwarz algorithms; Nodal elliptic problems..

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