Nonoverlapping discretization methods for partial differential equations

Autor:	Luis M. de la Cruz, Ismael Herrera, Alberto Rosas-Medina
Rok vydání:	2014
Předmět:	Numerical Analysis Partial differential equation Discretization Interface (Java) Applied Mathematics Domain decomposition methods Type (model theory) Computational Mathematics Partial derivative Applied mathematics Node (circuits) Algorithm Analysis Mortar methods Mathematics
Zdroj:	Numerical Methods for Partial Differential Equations. 30:1427-1454
ISSN:	1098-2426 0749-159X
DOI:	10.1002/num.21852
Popis:	Ideally, domain decomposition methods (DDMs) seek what we call the DDM-paradigm: “constructing the ‘global’ solution by solving ‘local’ problems, exclusively”. To achieve it, it is essential to disconnect the subdomain problems. This explains in part the success of nonoverlapping DDMs. However, in this kind of methods, different subdomains are linked by interface nodes that are shared by several subdomains. Discretization procedures for partial differential equations of a new kind, in which each node belongs to one and only one coarse-mesh subdomain, are here introduced and analyzed. A discretization method of this type was very successfully used to develop the derived vector-space-framework. Using it, it is possible to develop algorithms that satisfy the DDM-paradigm. Other enhanced numerical and computational properties of them are also discussed. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 000: 000–000, 2014
Databáze:	OpenAIRE
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