4,726 research outputs found
Preconditioning harmonic unsteady potential flow calculations
This paper considers finite element discretisations of the Helmholtz equation and its generalisation arising from harmonic acoustics perturbations to a non-uniform steady potential flow. A novel elliptic, positive definite preconditioner, with a multigrid implementation, is used to accelerate the iterative convergence of Krylov subspace solvers. Both theory and numerical results show that for a model 1D Helmholtz test problem the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. For the 2D Helmholtz equation, grid independent convergence is achieved using a QMR Krylov solver, significantly outperforming the popular SSOR preconditioner. Impressive results are also presented on more complex domains, including an axisymmetric aircraft engine inlet with non-stagnant mean flow and modal boundary conditions
Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures
We present a domain decomposition approach for the computation of the
electromagnetic field within periodic structures. We use a Schwarz method with
transparent boundary conditions at the interfaces of the domains. Transparent
boundary conditions are approximated by the perfectly matched layer method
(PML). To cope with Wood anomalies appearing in periodic structures an adaptive
strategy to determine optimal PML parameters is developed. We focus on the
application to typical EUV lithography line masks. Light propagation within the
multi-layer stack of the EUV mask is treated analytically. This results in a
drastic reduction of the computational costs and allows for the simulation of
next generation lithography masks on a standard personal computer.Comment: 24 page
Lorenz-Mie theory for 2D scattering and resonance calculations
This PhD tutorial is concerned with a description of the two-dimensional
generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method
used to compute the interaction of light with arrays of cylindrical scatterers.
This theory is based on the method of separation of variables and the
application of an addition theorem for cylindrical functions. The purpose of
this tutorial is to assemble the practical tools necessary to implement the
2D-GLMT method for the computation of scattering by passive scatterers or of
resonances in optically active media. The first part contains a derivation of
the vector and scalar Helmholtz equations for 2D geometries, starting from
Maxwell's equations. Optically active media are included in 2D-GLMT using a
recent stationary formulation of the Maxwell-Bloch equations called
steady-state ab initio laser theory (SALT), which introduces new classes of
solutions useful for resonance computations. Following these preliminaries, a
detailed description of 2D-GLMT is presented. The emphasis is placed on the
derivation of beam-shape coefficients for scattering computations, as well as
the computation of resonant modes using a combination of 2D-GLMT and SALT. The
final section contains several numerical examples illustrating the full
potential of 2D-GLMT for scattering and resonance computations. These examples,
drawn from the literature, include the design of integrated polarization
filters and the computation of optical modes of photonic crystal cavities and
random lasers.Comment: This is an author-created, un-copyedited version of an article
published in Journal of Optics. IOP Publishing Ltd is not responsible for any
errors or omissions in this version of the manuscript or any version derived
from i
Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions
In this paper, we consider the boundary integral equation (BIE) method for
solving the exterior Neumann boundary value problems of elastic and
thermoelastic waves in three dimensions based on the Fredholm integral
equations of the first kind. The innovative contribution of this work lies in
the proposal of the new regularized formulations for the hyper-singular
boundary integral operators (BIO) associated with the time-harmonic elastic and
thermoelastic wave equations. With the help of the new regularized
formulations, we only need to compute the integrals with weak singularities at
most in the corresponding variational forms of the boundary integral equations.
The accuracy of the regularized formulations is demonstrated through numerical
examples using the Galerkin boundary element method (BEM).Comment: 24 pages, 6 figure
Structure of Defective Crystals at Finite Temperatures: A Quasi-Harmonic Lattice Dynamics Approach
In this paper we extend the classical method of lattice dynamics to defective
crystals with partial symmetries. We start by a nominal defect configuration
and first relax it statically. Having the static equilibrium configuration, we
use a quasiharmonic lattice dynamics approach to approximate the free energy.
Finally, the defect structure at a finite temperature is obtained by minimizing
the approximate Helmholtz free energy. For higher temperatures we take the
relaxed configuration at a lower temperature as the reference configuration.
This method can be used to semi-analytically study the structure of defects at
low but non-zero temperatures, where molecular dynamics cannot be used. As an
example, we obtain the finite temperature structure of two 180^o domain walls
in a 2-D lattice of interacting dipoles. We dynamically relax both the position
and polarization vectors. In particular, we show that increasing temperature
the domain wall thicknesses increase
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