Pseudospectral solution of linear evolution equations of second order in space and time on unstructured quadrilateral subdomain topologies

Kondaxakis, D; Tsangaris, S

dc.contributor.author	Kondaxakis, D	en
dc.contributor.author	Tsangaris, S	en
dc.date.accessioned	2014-03-01T01:22:59Z
dc.date.available	2014-03-01T01:22:59Z
dc.date.issued	2005	en
dc.identifier.issn	0021-9991	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16752
dc.subject	second-order hyperbolic equations	en
dc.subject	pseudospectral method	en
dc.subject	domain decomposition	en
dc.subject	unstructured topology	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	RADIATION BOUNDARY-CONDITIONS	en
dc.subject.other	WAVE-PROPAGATION PROBLEMS	en
dc.subject.other	NAVIER-STOKES EQUATIONS	en
dc.subject.other	FINITE-ELEMENT SOLUTION	en
dc.subject.other	RUNGE-KUTTA SCHEMES	en
dc.subject.other	SPECTRAL METHODS	en
dc.subject.other	ELASTIC-WAVES	en
dc.subject.other	APPROXIMATION	en
dc.subject.other	CHEBYSHEV	en
dc.subject.other	FLOWS	en
dc.title	Pseudospectral solution of linear evolution equations of second order in space and time on unstructured quadrilateral subdomain topologies	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jcp.2004.07.014	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jcp.2004.07.014	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	A multidomain Legendre pseudospectral method is developed for the solution of linear hyperbolic initial boundary value problems, with mixed boundary conditions, in general two-dimensional and axisymmetric geometries. A weak collocation spectral method is utilized for the spatial approximation of a generic wave evolution equation over multiple nonoverlapping subdomains. The system of ordinary differential equations that stems from the above procedure is integrated in time by implicit as well as explicit high order temporal approximation algorithms. The weak formalism of the influence matrix method is combined with the implicit approximation. so as to efficiently solve the coupled system of linear equations after the full discretization, while a novel technique for avoiding the amplification of roundoff error at high temporal resolution simulations with the implicit temporal integration methods. is also studied. An innovative method for the treatment of Dirichlet boundary conditions is proposed, in order to avoid the order reduction which usually arises with the utilization of the explicit time integrator. Furthermore, appropriate modifications are reported. for dealing with the pole singularity problem faced by the weak formulation of axisymmetric problems. Finally. numerical simulations of a variety of wave problems on curvilinear geometries and unstructured subdomain configuration: are presented in order to assess the capabilities of the proposed methodology in handling efficiently general hyperbolic differential operators. (C) 2004 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	JOURNAL OF COMPUTATIONAL PHYSICS	en
dc.identifier.doi	10.1016/j.jcp.2004.07.014	en
dc.identifier.isi	ISI:000225741800007	en
dc.identifier.volume	202	en
dc.identifier.issue	2	en
dc.identifier.spage	533	en
dc.identifier.epage	576	en