Finite Difference Approximations to the Dirichlet Problem for Elliptic Systems.
Displaying 61 – 80 of 195
Finite-difference approximation of energies in fracture mechanics
Roberto Alicandro, Matteo Focardi, Maria Stella Gelli (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Finite-difference preconditioners for superconsistent pseudospectral approximations
Lorella Fatone, Daniele Funaro, Valentina Scannavini (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems, are presented...
Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation
Weihua Geng, Shan Zhao (2013)
Molecular Based Mathematical Biology
The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator splitting...
Geometric convergence of iterative methods for variational inequalities with -matrices and diagonal monotone operators
Trudy Matematiceskogo Centra Imeni N. I. Lobacevskogo
Green's function of a centered partial difference equation.
Avery, R.I., Anderson, D.R. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
High order accurate two-step approximations for hyperbolic equations
Garth A. Baker, Vassilios A. Dougalis, Steven M. Serbin (1979)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
High-order compact implicit difference methods for parabolic equations in geodynamo simulation.
Liu, Don, Kuang, Weijia, Tangborn, Andrew (2009)
Advances in Mathematical Physics
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.
Serra Capizzano, Stefano, Tablino Possio, Cristina (2000)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Identifiability for a class of discretized linear partial differential algebraic equations.
Cantó, Begoña, Coll, Carmen, Sánchez, Elena (2011)
Mathematical Problems in Engineering
Il funzionale di Totale Variazione nel problema dell’eliminazione del rumore da immagini digitali: dal modello al software matematico
Valentina De Simione (2000)
Bollettino dell'Unione Matematica Italiana
Implementing parallel elliptic solver on a Beowulf cluster.
Paprzycki, Marcin, Petrova, Svetozara, Sanchez, Julian (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Incremental unknowns method and compact schemes
Jean-Paul Chehab (1998)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Incremental unknowns on nonuniform meshes
J.-P. Chehab, A. Miranville (1998)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Inner products in covolume and mimetic methods
Kathryn A. Trapp (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
A class of compatible spatial discretizations for solving partial differential equations is presented. A discrete exact sequence framework is developed to classify these methods which include the mimetic and the covolume methods as well as certain low-order finite element methods. This construction ensures discrete analogs of the differential operators that satisfy the identities and theorems of vector calculus, in particular a Helmholtz decomposition theorem for the discrete function spaces. This...
Interpolation of function spaces and the convergence rate estimates for the finite difference method.
Jovanović, Boško S., Popović, Branislav Z. (1998)
Novi Sad Journal of Mathematics
Inverse du Laplacien discret dans le problème de Poisson-Dirichlet à deux dimensions sur un rectangle
Jean Chanzy (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
Ce travail a pour objet l’étude d’une méthode de « discrétisation » du Laplacien dans le problème de Poisson à deux dimensions sur un rectangle, avec des conditions aux limites de Dirichlet. Nous approchons l’opérateur Laplacien par une matrice de Toeplitz à blocs, eux-mêmes de Toeplitz, et nous établissons une formule donnant les blocs de l’inverse de cette matrice. Nous donnons ensuite un développement asymptotique de la trace de la matrice inverse, et du déterminant de la matrice de Toeplitz....
Iterative methods for operator equations with adjoint factorization.
Konovalov, A.N. (2000)
Siberian Mathematical Journal
Iterative schemes for high order compact discretizations to the exterior Helmholtz equation∗
Yogi Erlangga, Eli Turkel (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges...
Iterative schemes for high order compact discretizations to the exterior Helmholtz equation∗
Yogi Erlangga, Eli Turkel (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges...