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Particle Dynamics Modelling of Cell Populations

N. Bessonov, P. Kurbatova, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

Evolution of cell populations can be described with dissipative particle dynamics, where each cell moves according to the balance of forces acting on it, or with partial differential equations, where cell population is considered as a continuous medium. We compare these two approaches for some model examples

Partition of unity method for Helmholtz equation: q -convergence for plane-wave and wave-band local bases

Theofanis Strouboulis, Realino Hidajat (2006)

Applications of Mathematics

In this paper we study the q -version of the Partition of Unity Method for the Helmholtz equation. The method is obtained by employing the standard bilinear finite element basis on a mesh of quadrilaterals discretizing the domain as the Partition of Unity used to paste together local bases of special wave-functions employed at the mesh vertices. The main topic of the paper is the comparison of the performance of the method for two choices of local basis functions, namely a) plane-waves, and b) wave-bands....

Plane wave discontinuous Galerkin methods: Analysis of the h-version

Claude J. Gittelson, Ralf Hiptmair, Ilaria Perugia (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We are concerned with a finite element approximation for time-harmonic wave propagation governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along with numerical dispersion, render standard finite element methods grossly inefficient already in medium-frequency regimes. As an alternative, methods that incorporate information about the solution in the form of plane waves have been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that ...

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Castro, L.P., Kapanadze, D. (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness of the problem...

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