Scheduled Relaxation Jacobi method: Improvements and applications
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Scheduled Relaxation Jacobi method: Improvements and applications

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Scheduled Relaxation Jacobi method: Improvements and applications

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dc.contributor.author Adsuara, J.E.
dc.contributor.author Cordero Carrión, Isabel
dc.contributor.author Cerdá Durán, Pablo
dc.contributor.author Aloy Toras, Miguel Angel
dc.date.accessioned 2016-07-27T15:58:33Z
dc.date.available 2016-07-27T15:58:33Z
dc.date.issued 2016
dc.identifier.uri http://hdl.handle.net/10550/54811
dc.description.abstract Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non- linear) algebraic-differential system of equations from which they result becomes notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 2^15 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Most of the success in finding SRJ optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.
dc.language.iso eng
dc.relation.ispartof Journal of Computational Physics, 2016, vol. 321, p. 369-413
dc.rights.uri info:eu-repo/semantics/openAccess
dc.source Adsuara, J.E. Cordero Carrión, Isabel Cerdá Durán, Pablo Aloy Toras, Miguel Angel 2016 Scheduled Relaxation Jacobi method: Improvements and applications Journal of Computational Physics 321 369 413
dc.subject Equacions diferencials parcials
dc.subject Algorismes
dc.title Scheduled Relaxation Jacobi method: Improvements and applications
dc.type info:eu-repo/semantics/article
dc.date.updated 2016-07-27T15:58:33Z
dc.identifier.doi http://dx.doi.org/10.1016/j.jcp.2016.05.053
dc.identifier.idgrec 113517

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