Displaying similar documents to “A numerical minimization scheme for the complex Helmholtz equation”

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

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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...

Numerical analysis and simulations of quasistatic frictionless contact problems

José Fernández García, Weimin Han, Meir Shillor, Mircea Sofonea (2001)

International Journal of Applied Mathematics and Computer Science

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A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.

Iteratively solving a kind of signorini transmission problem in a unbounded domain

Qiya Hu, Dehao Yu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...

Application of relaxation scheme to degenerate variational inequalities

Jela Babušíková (2001)

Applications of Mathematics

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In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.