An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales.
An optimal sequential algorithm for the uniform approximation of convex functions on .
An optimum design problem in magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
An Optimum Design Problem in Magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
An optimum iteration for the matrix polar decomposition.
An overlapping additive Schwarz-Richardson method for monotone nonlinear parabolic problems.
An SVD approach to identifying metastable states of Markov chains.
An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination
In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our...
An unconditionally stable finite element scheme for anisotropic curve shortening flow
Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method.
An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of...
An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection
We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical...
An unconditionally stable parallel difference scheme for telegraph equation.
An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations
We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it...
An unusual way of solving linear systems
Mediante integrali multipli agevoli per il calcolo numerico vengono espressi il valore assoluto di un determinante qualsiasi e le formule di Cramer.
An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries.
An up-wind finite element method for a filtration problem
An upwind finite element method for singularly perturbed elliptic problems and local estimates in the -norm
An upwinding mixed finite element method for a mean field model of superconducting vortices
An upwinding mixed finite element method for a mean field model of superconducting vortices
In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.
An XFEM/DG approach for fluid-structure interaction problems with contact
In this work, we address the problem of fluid-structure interaction (FSI) with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it without any constraint on the conformity. Thanks to the Extended Finite Element Method (XFEM), we can treat discontinuities of the fluid solution on...