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The existence of a solution and a numerical method for the Timoshenko nonlinear wave system

Jemal Peradze (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by a version...

The extended adjoint method

Stanislas Larnier, Mohamed Masmoudi (2013)

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

Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore...

The extended adjoint method

Stanislas Larnier, Mohamed Masmoudi (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need...

The far-field modelling of transonic compressible flows

C. A. Coclici, Ivan L. Sofronov, Wolfgang L. Wendland (2001)

Mathematica Bohemica

We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...

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