Search results for "Modeling and simulation"
showing 10 items of 1561 documents
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
2012
Abstract We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations
2021
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed.
Scheduled Relaxation Jacobi method: improvements and applications
2016
Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficien…
A 1D coupled Schrödinger drift-diffusion model including collisions
2005
We consider a one-dimensional coupled stationary Schroedinger drift-diffusion model for quantum semiconductor device simulations. The device domain is decomposed into a part with large quantum effects (quantum zone) and a part where quantum effects are negligible (classical zone). We give boundary conditions at the classic-quantum interface which are current preserving. Collisions within the quantum zone are introduced via a Pauli master equation. To illustrate the validity we apply the model to three resonant tunneling diodes.
A partially reflecting random walk on spheres algorithm for electrical impedance tomography
2015
In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias…
Collision orbits in the oblate planet problem
1984
Some of the properties of the oblate planet problem are derived. We use the technique of blowing up the singularity to study the collision orbits. We define some families of them in terms of their asymptotic behavior.
Classes of orbits in the main problem of satellite theory
1986
We consider the main problem in satellite theory restricted to the polar plane. For suitable values of the energy the system has two unstable periodic orbits. We classify the trajectories in terms of their ultimate behavior with respect these periodic orbits in: oscillating, asymptotic and capture orbits. We study the energy level set and the existence and properties of the mentioned types of motion.
Dipole soliton solution for the homogeneous high-order nonlinear Schrödinger equation with cubic–quintic–septic non-Kerr terms
2015
Abstract We consider a high-order nonlinear Schrodinger equation with third- and fourth-order dispersions, cubic–quintic–septic nonlinearities, self-steepening, and instantaneous Raman response. This equation models describes ultra-short optical pulse propagation in highly-nonlinear media. The ansatz solution of Choudhuri and Porsezian (in Ref. [16]) is adapted to investigate solutions composed of the product of bright and dark solitary waves. Parametric conditions for the existence of the derived soliton solutions are given and their stabilities are numerically discussed. These exact solutions provide insight into balance mechanisms between several high-order nonlinearities of different na…
On the effect of damping on dispersion curves in plates
2013
AbstractThis paper presents a study on quantitative prediction and understanding of time-harmonic wave characteristics in damped plates. Material dissipation is modelled by using complex-valued velocities of free dilatation and shear waves in an unbounded volume. As a numerical example, solution of the classical Rayleigh–Lamb problem for a viscoelastic plate is presented to illustrate and discuss the role of dissipation in the cut-off phenomenon and in the phenomenon of veering for dispersion curves. These phenomena are explained in more detail considering a simple model, which allows accurate asymptotic analysis of the perturbation of dispersion curves in the regions of cut-off and veering.
ON FRACTIONAL RELAXATION
2003
Generalized fractional relaxation equations based on generalized Riemann-Liouville derivatives are combined with a simple short time regularization and solved exactly. The solution involves generalized Mittag-Leffler functions. The associated frequency dependent susceptibilities are related to symmetrically broadened Cole-Cole susceptibilities occurring as Johari Goldstein β-relaxation in many glass formers. The generalized susceptibilities exhibit a high frequency wing and strong minimum enhancement.