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A multilevel preconditioner for the mortar method for nonconforming P1 finite element

Talal Rahman, Xuejun Xu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming P1 finite element or the lowest order Crouzeix-Raviart finite element on nonmatching grids. It is shown that the proposed preconditioner is quasi-optimal in the sense that the condition number of the preconditioned system is independent of the mesh size, and depends only quadratically on the number of refinement levels. Some numerical results confirming...

A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction

Roland Ernst, Bernd Flemisch, Barbara Wohlmuth (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.

A multiscale correction method for local singular perturbations of the boundary

Marc Dambrine, Grégory Vial (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uE of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uE based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We...

A Multiscale Enrichment Procedure for Nonlinear Monotone Operators

Y. Efendiev, J. Galvis, M. Presho, J. Zhou (2014)

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

In this paper, multiscale finite element methods (MsFEMs) and domain decomposition techniques are developed for a class of nonlinear elliptic problems with high-contrast coefficients. In the process, existing work on linear problems [Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media. Submitted.; Y. Efendiev, J. Galvis and X. Wu, J. Comput. Phys. 230 (2011) 937–955; J. Galvis and...

A Multiscale Model Reduction Method for Partial Differential Equations

Maolin Ci, Thomas Y. Hou, Zuoqiang Shi (2014)

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

We propose a multiscale model reduction method for partial differential equations. The main purpose of this method is to derive an effective equation for multiscale problems without scale separation. An essential ingredient of our method is to decompose the harmonic coordinates into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Such a decomposition plays a key role in our construction of the effective equation. We show...

A multiscale mortar multipoint flux mixed finite element method

Mary Fanett Wheeler, Guangri Xue, Ivan Yotov (2012)

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

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid...

A multiscale mortar multipoint flux mixed finite element method

Mary Fanett Wheeler, Guangri Xue, Ivan Yotov (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid...

A multiscale mortar multipoint flux mixed finite element method

Mary Fanett Wheeler, Guangri Xue, Ivan Yotov (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid...

A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case

Jacques Baranger, Ahmed Machmoum (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the numerical approximation of a first order stationary hyperbolic equation by the method of characteristics with pseudo time step k using discontinuous finite elements on a mesh 𝒯 h . For this method, we exhibit a “natural” norm || ||h,k for which we show that the discrete variational problem P h k is well posed and we obtain an error estimate. We show that when k goes to zero problem ( P h k ) (resp. the || ||h,k norm) has as a limit problem (Ph) (resp. the || ||h norm) associated to the...

A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices

Günter Mayer, Lars Pieper (1993)

Applications of Mathematics

A necessary and sufficient to guarantee feasibility of the interval Gaussian algorithms for a class of matrices. We apply the interval Gaussian algorithm to an n × n interval matrix [ A ] the comparison matrix [ A ] of which is irreducible and diagonally dominant. We derive a new necessary and sufficient criterion for the feasibility of this method extending a recently given sufficient criterion.

A New Algorithm for Monte Carlo for American Options

Mallier, Roland, Alobaidi, Ghada (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 91B28, 65C05.We consider the valuation of American options using Monte Carlo simulation, and propose a new technique which involves approximating the optimal exercise boundary. Our method involves splitting the boundary into a linear term and a Fourier series and using stochastic optimization in the form of a relaxation method to calculate the coefficients in the series. The cost function used is the expected value of the option using the the current estimate...

Currently displaying 501 – 520 of 9149