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Time splitting for wave equations in random media

Guillaume Bal, Lenya Ryzhik (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the...

Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations

Markus Stammberger, Heinrich Voss (2014)

Applications of Mathematics

Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.

Vibrational properties of nanographene

Sandeep Kumar Singh, F.M. Peeters (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

The eigenmodes and the vibrational density of states of the ground state configuration of graphene clusters are calculated using atomistic simulations. The modified Brenner potential is used to describe the carbon-carbon interaction and carbon-hydrogen interaction in case of H-passivated edges. For a given configuration of the C-atoms the eigenvectors and eigenfrequencies of the normal modes are obtained after diagonalisation of the dynamical matrix whose elements are the second derivative of the...

Currently displaying 381 – 400 of 449