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Haar wavelets method for solving Pocklington's integral equation

M. Shamsi, Mohsen Razzaghi, J. Nazarzadeh, Masoud Shafiee (2004)

Kybernetika

A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the...

High frequency limit of the Helmholtz equations.

Jean-David Benamou, François Castella, Theodoros Katsaounis, Benoit Perthame (2002)

Revista Matemática Iberoamericana

We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term ( which does not share the...

High order edge elements on simplicial meshes

Francesca Rapetti (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their definition become rather complex. In this paper we propose a simple definition for Whitney edge elements of polynomial degree higher than one. We give a geometrical localization of all degrees of freedom over particular edges and provide a basis for these elements on simplicial meshes. As for Whitney edge elements of degree one, the basis is...

High order transmission conditions for thin conductive sheets in magneto-quasistatics

Kersten Schmidt, Sébastien Tordeux (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...

High order transmission conditions for thin conductive sheets in magneto-quasistatics

Kersten Schmidt, Sébastien Tordeux (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...

High Resolution Tracking of Cell Membrane Dynamics in Moving Cells: an Electrifying Approach

R.A. Tyson, D.B.A. Epstein, K.I. Anderson, T. Bretschneider (2010)

Mathematical Modelling of Natural Phenomena

Cell motility is an integral part of a diverse set of biological processes. The quest for mathematical models of cell motility has prompted the development of automated approaches for gathering quantitative data on cell morphology, and the distribution of molecular players involved in cell motility. Here we review recent approaches for quantifying cell motility, including automated cell segmentation and tracking. Secondly, we present our own novel...

High-frequency limit of the Maxwell-Landau-Lifshitz equations in the diffractive optics regime*

LU Yong (2012)

ESAIM: Proceedings

We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies O(1 / ε) and amplitude O(1), over long time intervals O(1 / ε), in the limit ε → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].

Homogenization of the Maxwell equations: Case I. Linear theory

Niklas Wellander (2001)

Applications of Mathematics

The Maxwell equations in a heterogeneous medium are studied. Nguetseng’s method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.

Homogenization of the Maxwell Equations: Case II. Nonlinear conductivity

Niklas Wellander (2002)

Applications of Mathematics

The Maxwell equations with uniformly monotone nonlinear electric conductivity in a heterogeneous medium, which may be non-periodic, are homogenized by two-scale convergence. We introduce a new set of function spaces appropriate for the nonlinear Maxwell system. New compactness results, of two-scale type, are proved for these function spaces. We prove existence of a unique solution for the heterogeneous system as well as for the homogenized system. We also prove that the solutions of the heterogeneous...

Hybrid Particle Swarm and Neural Network Approach for Streamflow Forecasting

A. Sedki, D. Ouazar (2010)

Mathematical Modelling of Natural Phenomena

In this paper, an artificial neural network (ANN) based on hybrid algorithm combining particle swarm optimization (PSO) with back-propagation (BP) is proposed to forecast the daily streamflows in a catchment located in a semi-arid region in Morocco. The PSO algorithm has a rapid convergence during the initial stages of a global search, while the BP algorithm can achieve faster convergent speed around the global optimum. By combining the PSO with...

Hyperbolic Cauchy problem and Leray's residue formula

Susumu Tanabé (2000)

Annales Polonici Mathematici

We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.

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