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dc.contributor.authorBialecki, B.en
dc.contributor.authorKarageorghis, Andreasen
dc.creatorBialecki, B.en
dc.creatorKarageorghis, Andreasen
dc.description.abstractWe 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.sourceJournal of Scientific Computingen
dc.subjectMathematical transformationsen
dc.subjectMatrix algebraen
dc.subjectLinear systemsen
dc.subjectConvergence propertiesen
dc.subjectFinite difference methoden
dc.subjectBoundary conditionsen
dc.subjectFast Fourier transformsen
dc.subjectMatrix decompositionen
dc.subjectMatrix decomposition algorithmen
dc.subjectPreconditioned conjugate gradient methoden
dc.subjectCauchy–Navier equationsen
dc.subjectConjugate gradient methoden
dc.subjectDirichlet boundary conditionen
dc.subjectDirichlet-neumann boundary conditionen
dc.subjectFinite difference schemeen
dc.subjectNavier equationsen
dc.subjectNeumann boundary conditionen
dc.titleFinite Difference Schemes for the Cauchy–Navier Equations of Elasticity with Variable Coefficientsen
dc.description.endingpage121Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied SciencesΤμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics
dc.contributor.orcidKarageorghis, Andreas [0000-0002-8399-6880]

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