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Finite-volume level set method and its adaptive version in completing subjective contours

Zuzana Krivá (2007)

Kybernetika

In this paper we deal with a problem of segmentation (including missing boundary completion) and subjective contour creation. For the corresponding models we apply the semi-implicit finite volume numerical schemes leading to methods which are robust, efficient and stable without any restriction to a time step. The finite volume discretization enables to use the spatial adaptivity and thus improve significantly the computational time. The computational results related to image segmentation with partly...

Finite-volume solvers for a multilayer Saint-Venant system

Emmanuel Audusse, Marie-Odile Bristeau (2007)

International Journal of Applied Mathematics and Computer Science

We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to D hydrostatic Navier-Stokes equations.

Fluid–particle shear flows

Bertrand Maury (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction,...

Fluid–particle shear flows

Bertrand Maury (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction,...

Forced anisotropic mean curvature flow of graphs in relative geometry

Dieu Hung Hoang, Michal Beneš (2014)

Mathematica Bohemica

The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.

Fractional-order Bessel functions with various applications

Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi (2019)

Applications of Mathematics

We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error estimate between...

Free-energy-dissipative schemes for the Oldroyd-B model

Sébastien Boyaval, Tony Lelièvre, Claude Mangoubi (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman in [J. Non-Newtonian...

Frequency analysis of preconditioned waveform relaxation iterations

Andrzej Augustynowicz, Zdzisław Jackiewicz (1999)

Applicationes Mathematicae

The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...

Full discretization of some reaction diffusion equation with blow up

Geneviève Barro, Benjamin Mampassi, Longin Some, Jean Ntaganda, Ousséni So (2006)

Open Mathematics

This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension

Raimund Bürger, Ricardo Ruiz, Kai Schneider, Mauricio Sepúlveda (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume discretization using the Engquist-Osher numerical flux and explicit time stepping. An adaptive multiresolution scheme based on cell averages is then used to speed up the CPU time and the memory requirements of the underlying finite volume scheme, whose first-order...

Fully discrete error estimation by the method of lines for a nonlinear parabolic problem

Tomáš Vejchodský (2003)

Applications of Mathematics

A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven.

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...

Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise

Georgios T. Kossioris, Georgios E. Zouraris (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method...

Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples

Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a numerical analysis of proper orthogonal decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and – whereas a general uniform continuity bound seems out...

Currently displaying 601 – 620 of 1396