All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 52 Next

Displaying 1021 – 1040 of 2162

Showing per page

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 Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi (2016)

Mathematics of Climate and Weather Forecasting

Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...

On the choice of iteration parameters in the Stone incomplete factorization

Karel Segeth (1983)

Aplikace matematiky

The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values...

On the circle criterion for boundary control systems in factor form : Lyapunov stability and Lur’e equations

Piotr Grabowski, Frank M. Callier (2006)

ESAIM: Control, Optimisation and Calculus of Variations

A Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur’e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on results...

On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations

Piotr Grabowski, Frank M. Callier (2005)

ESAIM: Control, Optimisation and Calculus of Variations

A Lur'e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur'e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on...

On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients

Pulin K. Bhattacharyya, Neela Nataraj (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Error estimates for the mixed finite element solution of 4th order elliptic problems with variable coefficients, which, in the particular case of aniso-/ortho-/isotropic plate bending problems, gives a direct, simultaneous approximation to bending moment tensor field Ψ = ( ψ i j ) 1 ≤ i , j ≤ 2 and displacement field 'u', have been developed considering the combined effect of boundary approximation and numerical integration.

On the computation of roll waves

Shi Jin, Yong Jung Kim (2001)

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

The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation u t + u u x = u , u ( x , 0 ) = u 0 ( x ) , which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the numerical solution and yields false...

Currently displaying 1021 – 1040 of 2162