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Two of the most basic problems encountered in numerical optimization are least-squares problems and systems of nonlinear equations. The use of more and more complex simulation tools on high performance computers requires solving problems involving an incre ...
We consider the system of a quantum well embedded in a planar semiconductor microcavity with a shallow circular mesa patterned on top of the cavity spacer. For this system we develop the linear coupling theory of polaritons. We then compute polariton eigen ...
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This paper presents the development of spectral element methods to simulate unsteady flows of viscoelastic fluids using a closed-form differential constitutive equation. The generation and decay Poiseuille planar flows are considered as benchmark problems ...
The last twenty years have seen enormous progress in the design of algorithms, but little of it has been put into practice. Because many recently developed algorithms are hard to characterize theoretically and have large running_time coefficients, the gap ...
In this thesis we will show that unsteady, incompressible fluid-flow problems, as described by the three-dimensional Navier-Stokes equations, can efficiently be simulated by a parallel computer code based on a spectral element discretization. This efficien ...
The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the memory f ...
In this work, we are interested in elaborating models and numerical methods in order to study some phenomena which arise in the solidification of binary alloys. We propose two distinct models based on the mass and energy conservation laws as well as on cla ...
We present a high-order particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas dynamics. The core of the algorithm utilizes an unstructured grid discontinuous Galerkin Maxwell field solver combining high-order accuracy with geometric flexib ...
*This book provides a full, general purpose and application independent exposition of the moiré phenomenon. * Based on the Fourier theory it leads the reader through the various phenomena which occur in the superposition of repetitive layers, both in the i ...
A computational method for multiscale modeling of plasticity is presented wherein each dislocation is treated as either an atomistic or continuum entity within a single computational framework. The method divides space into atomistic and continuum regions ...
