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dc.contributor.author
Pardo, David
dc.contributor.author
Paszynsk, Maciej
dc.contributor.author
Collier, Nathan
dc.contributor.author
Alvarez, Julien
dc.contributor.author
Dalcin, Lisandro Daniel
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dc.contributor.author
Calo, Victor
dc.date.available
2017-01-09T13:29:16Z
dc.date.issued
2012-01
dc.identifier.citation
Pardo, David; Paszynsk, Maciej; Collier, Nathan; Alvarez, Julien; Dalcin, Lisandro Daniel; et al.; A survey on direct solvers for Galerkin methods; Sociedad Española de Matemática Aplicada; SeMA Journal; 57; 1-2012; 107-134
dc.identifier.issn
1575-9822
dc.identifier.uri
http://hdl.handle.net/11336/10965
dc.description.abstract
In this paper we describe the history, performance, and design concepts of direct solvers for algebraic systems resulting from Galerkin discretizations of partial differential equations. Popular direct solver implementations of Gaussian elimination (also known as LU factorization) are introduced and briefly analyzed. We discuss three of the most relevant aspects influencing the performance of direct solvers on this kind of algebraic systems. First, the ordering of the degrees of freedom of the algebraic system has a significant impact on the solver performance, solution speed and memory requirements. The impact of unknowns ordering for elimination is exemplified and alternative ordering algorithms are described and compared. Second, the effect of round-off error on the simulation results is discussed. We detail this effect for uniform grids where the impact of round-off error on the solution is controlled by the condition number of the matrix in terms of the element size, but is independent of the polynomial order of approximation. Additionally, we discuss the link between unknown ordering and round-off error. Third, we describe the impact of the connectivity pattern (graph) of the basis functions on the performance of direct solvers. Variations in the connectivity structure of the resulting discrete system have severe impact on performance of the solver. That is, the resources needed to factorize the system strongly depend on its connectivity graph. Less connected graphs are cheaper to solve, that is, C0 finite element discretizations are cheaper to solve with direct solvers than Cp-1 discretizations.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Sociedad Española de Matemática Aplicada
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Lu Factorization
dc.subject
Gaussian Elimination
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Frontal Solver
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Multi-Frontal Solver
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Hp-Finite Elements
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Isogeometric Analysis
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Cost of Regularity
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Parallel Direct Solvers
dc.subject.classification
Matemática Aplicada
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
A survey on direct solvers for Galerkin methods
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-01-05T15:01:37Z
dc.journal.volume
57
dc.journal.pagination
107-134
dc.journal.pais
España
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dc.description.fil
Fil: Pardo, David. Universidad del Pais Vasco; España
dc.description.fil
Fil: Paszynsk, Maciej. University of Science and Technology; Polonia
dc.description.fil
Fil: Collier, Nathan. King Abdullah University of Science and Technology; Arabia Saudita
dc.description.fil
Fil: Alvarez, Julien. Universidad del Pais Vasco; España
dc.description.fil
Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
dc.description.fil
Fil: Calo, Victor. King Abdullah University of Science and Technology; Arabia Saudita
dc.journal.title
SeMA Journal
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/BF03322602
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.sema.org.es/ojs/index.php?journal=journal&page=article&op=view&path%5B%5D=616
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