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Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

François Alouges (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the...

Convergence of a method for solving the magnetostatic field in nonlinear media

Jozef Kačur, Jindřich Nečas, Josef Polák, Jiří Souček (1968)

Aplikace matematiky

For solving the boundary-value problem for potential of a stationary magnetic field in two dimensions in ferromagnetics it is possible to use a linearization based on the succesive approximations. In this paper the convergence of this method is proved under some conditions.

Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics

Alexandru Oană, Mircea Neagu (2012)

Communications in Mathematics

In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.

Electrowetting of a 3D drop: numerical modelling with electrostatic vector fields

Patrick Ciarlet Jr., Claire Scheid (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The electrowetting process is commonly used to handle very small amounts of liquid on a solid surface. This process can be modelled mathematically with the help of the shape optimization theory. However, solving numerically the resulting shape optimization problem is a very complex issue, even for reduced models that occur in simplified geometries. Recently, the second author obtained convincing results in the 2D axisymmetric case. In this paper, we propose and analyze a method that is suitable...

Graphical Processing Unit accelerated Poisson equation solver and its application for calculation of single ion potential in ion-channels

Nikolay A. Simakov, Maria G. Kurnikova (2013)

Molecular Based Mathematical Biology

Poisson and Poisson-Boltzmann equations (PE and PBE) are widely used in molecular modeling to estimate the electrostatic contribution to the free energy of a system. In such applications, PE often needs to be solved multiple times for a large number of system configurations. This can rapidly become a highly demanding computational task. To accelerate such calculations we implemented a graphical processing unit (GPU) PE solver described in this work. The GPU solver performance is compared to that...

Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition

Dana Říhová-Škabrahová (2001)

Applications of Mathematics

The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part Γ 1 of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and the right-hand...

On a certain two-sided symmetric condition in magnetic field analysis and computations

František Melkes, Alexander Ženíšek (1997)

Applications of Mathematics

A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity...

On a quasi-variational inequality arising in semiconductor theory.

José-Francisco Rodrigues (1992)

Revista Matemática de la Universidad Complutense de Madrid

Some new mathematical results of existence and uniqueness of solutions are obtained for a class of quasi-variational inequalities modeling the free boundary problem for the determination of the depletion zone in reverse biased semiconductor diodes. The corresponding one (or two) obstacle implicit problems are solved by direct methods with weak regularity estimates for mixed boundary value elliptic problems of second order.

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