Page 1 Next

Displaying 1 – 20 of 156

Showing per page

2D-1D dimensional reduction in a toy model for magnetoelastic interactions

Mouhcine Tilioua (2011)

Applications of Mathematics

The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

A numerical minimization scheme for the complex Helmholtz equation

Russell B. Richins, David C. Dobson (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...

A numerical minimization scheme for the complex Helmholtz equation

Russell B. Richins, David C. Dobson (2012)

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

We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...

A remark on the local Lipschitz continuity of vector hysteresis operators

Pavel Krejčí (2001)

Applications of Mathematics

It is known that the vector stop operator with a convex closed characteristic Z of class C 1 is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping n is Lipschitz continuous on the boundary Z of Z . We prove that in the regular case, this condition is also necessary.

A stability analysis for finite volume schemes applied to the Maxwell system

Sophie Depeyre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present in this paper a stability study concerning finite volume schemes applied to the two-dimensional Maxwell system, using rectangular or triangular meshes. A stability condition is proved for the first-order upwind scheme on a rectangular mesh. Stability comparisons between the Yee scheme and the finite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.

Currently displaying 1 – 20 of 156

Page 1 Next