dc.contributor.author Bialecki, B. en dc.contributor.author Karageorghis, Andreas en dc.creator Bialecki, B. en dc.creator Karageorghis, Andreas en dc.date.accessioned 2019-12-02T10:34:00Z dc.date.available 2019-12-02T10:34:00Z dc.date.issued 2015 dc.identifier.uri http://gnosis.library.ucy.ac.cy/handle/7/56528 dc.description.abstract We solve the variable coefficient Cauchy–Navier equations of elasticity in the unit square, for Dirichlet and Dirichlet-Neumann boundary conditions, using second order finite difference schemes. The resulting linear systems are solved by the preconditioned conjugate gradient (PCG) method with preconditioners corresponding to to the Laplace operator. The multiplication of a vector by the matrices of the resulting systems and the solution of systems with the preconditioners are performed at optimal and nearly optimal costs, respectively. For the case of Dirichlet boundary conditions, we prove the second order accuracy of the scheme in the discrete (Formula presented.) norm, symmetry of the resulting matrix and its spectral equivalence to the preconditioner. For the case of Dirichlet–Neumann boundary conditions, we prove symmetry of the resulting matrix. Numerical tests demonstrating the convergence properties of the schemes and PCG are presented. © 2014, Springer Science+Business Media New York. en dc.source Journal of Scientific Computing en dc.source.uri https://www.scopus.com/inward/record.uri?eid=2-s2.0-84958012497&doi=10.1007%2fs10915-014-9847-8&partnerID=40&md5=4f17fdb0d4b48757612df0f64ac529fb dc.subject Mathematical transformations en dc.subject Matrix algebra en dc.subject Linear systems en dc.subject Convergence properties en dc.subject Finite difference method en dc.subject Boundary conditions en dc.subject Elasticity en dc.subject Fast Fourier transforms en dc.subject Matrix decomposition en dc.subject Matrix decomposition algorithm en dc.subject Preconditioned conjugate gradient method en dc.subject Cauchy–Navier equations en dc.subject Conjugate gradient method en dc.subject Dirichlet boundary condition en dc.subject Dirichlet-neumann boundary condition en dc.subject Finite difference scheme en dc.subject Navier equations en dc.subject Neumann boundary condition en dc.title Finite Difference Schemes for the Cauchy–Navier Equations of Elasticity with Variable Coefficients en dc.type info:eu-repo/semantics/article dc.identifier.doi 10.1007/s10915-014-9847-8 dc.description.volume 62 dc.description.issue 1 dc.description.startingpage 78 dc.description.endingpage 121 dc.author.faculty Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences dc.author.department Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics dc.type.uhtype Article en dc.source.abbreviation J.Sci.Comput. en dc.contributor.orcid Karageorghis, Andreas [0000-0002-8399-6880] dc.gnosis.orcid 0000-0002-8399-6880
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