ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Recently Published Articles
- Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm
Peter Benner, Patrick Kürschner, Zoran Tomljanović and Ninoslav Truhar
Article first published online: 3 MAY 2015 | DOI: 10.1002/zamm.201400158
We consider the problem of determining an optimal semi-active damping of vibrating systems. For this damping optimization we use a minimization criterion based on the impulse response energy of the system. The optimization approach yields a large number of Lyapunov equations which have to be solved. In this work, we propose an optimization approach that works with reduced systems which are generated using the parametric dominant pole algorithm. This optimization process is accelerated with a modal approach while the initial parameters for the parametric dominant pole algorithm are chosen in advance using residual bounds. Our approach calculates a satisfactory approximation of the impulse response energy while providing a significant acceleration of the optimization process. Numerical results illustrate the effectiveness of the proposed algorithm.
- A positive scheme for diffusion problems on deformed meshes
Xavier Blanc and Emmanuel Labourasse
Article first published online: 3 MAY 2015 | DOI: 10.1002/zamm.201400234
We present in this article a positive finite volume method for diffusion equation on deformed meshes. This method is mainly inspired from , and uses auxiliary unknowns at the nodes of the mesh. The flux is computed so as to be a two-point nonlinear flux, giving rise to a matrix which is the transpose of an M-matrix, which ensures that the scheme is positive. A particular attention is given to the computation of the auxiliary unknowns. We propose a new strategy, which aims at providing a scheme easy to implement in a parallel domain decomposition setting. An analysis of the scheme is provided: existence of a solution for the nonlinear system is proved, and the convergence of a fixed-point strategy is studied.
- Blowup criterion of smooth solutions for the incompressible chemotaxis-Euler equations
Article first published online: 29 APR 2015 | DOI: 10.1002/zamm.201500040
In this paper, we establish the blowup criterion of smooth solutions for the incompressible chemotaxis-Euler equations in with by and .
- Remark on the pointwise stabilization of an elastic string equation
Article first published online: 29 APR 2015 | DOI: 10.1002/zamm.201400260
We consider an initial and boundary value problem the one dimensional wave equation with damping concentrated at an interior point. We prove a result of a logarithmic decay of the energy of a system with homogeneous Dirichlet boundary conditions. The method used is based on the resolvent estimate approach which derives from the Carleman estimate technique. Under an algebraic assumption describing the right location of the actuator, we prove a logarithmic decay of the energy of solution. We show that this assumption is lower than the one given by and which depends on the diophantine approximations properties of the actuator's location.
- On a free boundary problem arising in snow avalanche dynamics
Benedetta Calusi, Lorenzo Fusi and Angiolo Farina
Article first published online: 29 APR 2015 | DOI: 10.1002/zamm.201400250
In this paper we prove a local result of existence and uniqueness for a free boundary problem for snow avalanche arising from a new model proposed in . The mathematical problem consists of a parabolic free boundary problem with non-standard free boundary conditions (erosion dynamics). The proof is essentially based on a fixed point argument.