Finite Difference Approximations to the Dirichlet Problem for Elliptic Systems.
Finite-difference approximation of energies in fracture mechanics
Finite-difference preconditioners for superconsistent pseudospectral approximations
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
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
Green's function of a centered partial difference equation.
High order accurate two-step approximations for hyperbolic equations
High-order compact implicit difference methods for parabolic equations in geodynamo simulation.
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.
Identifiability for a class of discretized linear partial differential algebraic equations.
Il funzionale di Totale Variazione nel problema dell’eliminazione del rumore da immagini digitali: dal modello al software matematico
Implementing parallel elliptic solver on a Beowulf cluster.
Incremental unknowns method and compact schemes
Incremental unknowns on nonuniform meshes
Inner products in covolume and mimetic methods
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.
Inverse du Laplacien discret dans le problème de Poisson-Dirichlet à deux dimensions sur un rectangle
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.
Iterative schemes for high order compact discretizations to the exterior Helmholtz equation∗
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∗
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...