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 | |