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

Qiya Hu, Dehao Yu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Koiter shell governed by strongly monotone constitutive equations

Piotr Kalita (2004)

International Journal of Applied Mathematics and Computer Science

In this paper we use the theory of monotone operators to generalize the linear shell model presented in (Blouza and Le Dret, 1999) to a class of physically nonlinear models. We present a family of nonlinear constitutive equations, for which we prove the existence and uniqueness of the solution of the presented nonlinear model, as well as the convergence of the Galerkin method. We also present the physical discussion of the model.

Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping

Gimyong Hong, Hakho Hong (2022)

Applications of Mathematics

We are concerned with a transmission problem for the Kirchhoff plate equation where one small part of the domain is made of a viscoelastic material with the Kelvin-Voigt constitutive relation. We obtain the logarithmic stabilization result (explicit energy decay rate), as well as the wellposedness, for the transmission system. The method is based on a new Carleman estimate to obtain information on the resolvent for high frequency. The main ingredient of the proof is some careful analysis for the...

Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method

Ivo Babuška, Xu Huang, Robert Lipton (2014)

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

A multiscale spectral generalized finite element method (MS-GFEM) is presented for the solution of large two and three dimensional stress analysis problems inside heterogeneous media. It can be employed to solve problems too large to be solved directly with FE techniques and is designed for implementation on massively parallel machines. The method is multiscale in nature and uses an optimal family of spectrally defined local basis functions over a coarse grid. It is proved that the method has an...

Microlocal analysis and seismic imaging

Christiaan Stolk (2003/2004)

Séminaire Équations aux dérivées partielles

We study certain Fourier integral operators arising in the inversion of data from reflection seismology.

Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion

Tetsuya Ishiwata (2015)

Mathematica Bohemica

We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...

Numerical study of acoustic multiperforated plates

Abderrahmane Bendali, M’Barek Fares, Sophie Laurens, Sébastien Tordeux (2012)

ESAIM: Proceedings

It is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic.

On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms

Bui Duc Nam, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long (2022)

Mathematica Bohemica

We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.

On periodic homogenization in perfect elasto-plasticity

Gilles A. Francfort, Alessandro Giacomini (2014)

Journal of the European Mathematical Society

The limit behavior of a periodic assembly of a finite number of elasto-plastic phases is investigated as the period becomes vanishingly small. A limit quasi-static evolution is derived through two-scale convergence techniques. It can be thermodynamically viewed as an elasto-plastic model, albeit with an infinite number of internal variables.

On the change of energy caused by crack propagation in 3-dimensional anisotropic solids

Martin Steigemann, Maria Specovius-Neugebauer (2014)

Mathematica Bohemica

Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a...

On the stability of Bravais lattices and their Cauchy–Born approximations

Thomas Hudson, Christoph Ortner (2012)

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

We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy–Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motivated by recent results in one dimension on the stability of atomistic/continuum coupling methods, we analyze...

On the stability of Bravais lattices and their Cauchy–Born approximations*

Thomas Hudson, Christoph Ortner (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy–Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motivated by recent results in one dimension on the stability of atomistic/continuum coupling methods,...

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