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Multiscale methods for wave problems in heterogenous media

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FE heterogeneous multiscale method for long time wave propagation

Assyr Abdulle

A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our FE-HMM captures long-time dispersive effects of the true solution at a cost similar t ...

Elsevier France-Editions Scientifiques Medicales Elsevier2013

The Adomian Decomposition Method for Nonlinear Partial Differential Equations

Natalie Sauerwald

The goal of this report is to study the method introduced by Adomian known as the Adomian Decomposition Method (ADM), which is used to find an approximate solution to nonlinear partial differential equations (PDEs) as a series expansion involving the recur ...

2013

Solving Wave Equations on Unstructured Geometries

Jan Sickmann Hesthaven

Every wave solver serving the computational study of waves meets a trade-off of two figures of merit—its computational speed and its accuracy. The use of Discontinuous Galerkin (DG) methods on graphical processing units (GPUs) significantly lowers the cost ...

Morgan Kaufmann2012

Explicit methods for stiff stochastic differential equations

Assyr Abdulle

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...

Springer-Verlag Berlin2012

High-Order Discontinuous Galerkin Methods by GPU Metaprogramming

Jan Sickmann Hesthaven

Discontinuous Galerkin (DG) methods for the numerical solution of par- tial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy withou ...

Springer Verlag2012

Finite element heterogeneous multiscale method for the wave equation

Assyr Abdulle

A finite element heterogeneous multiscale method is proposed for the wave equation with highly oscillatory coefficients. It is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coeff ...

2011

Multilevel Schwarz methods for elliptic partial differential equations

Alfio Quarteroni, Giovanni Migliorati

We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method. In our analysis we deal with unstruc ...

Elsevier2011

Multipartite polariton entanglement in semiconductor microcavities

Vincenzo Savona, Timothy Chi Hin Liew

We study the entanglement of multiple polariton modes, which results in continuous variable cluster states suitable for quantum computation. Schemes are based on parametric scattering between spin-polarized lower and upper polariton branches in planar micr ...

2011

Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method

Mehran Khaghani

Nonlinear transient thermal stress and elastic wave propagation analyses are developed for hollow thick temperature-dependent FGM cylinders subjected to dynamic thermomechanical loads. Stress wave propagation, wave shape distortion, and speed variation und ...

Elsevier2010

The radial wave operator in similarity coordinates

Roland Donninger

We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyze linear stability of the fundamental self-similar solution of the wave equation with a focusing power nonlinearity. T ...

American Institute of Physics2010