2,523 research outputs found
Absorbing boundary conditions for the Westervelt equation
The focus of this work is on the construction of a family of nonlinear
absorbing boundary conditions for the Westervelt equation in one and two space
dimensions. The principal ingredient used in the design of such conditions is
pseudo-differential calculus. This approach enables to develop high order
boundary conditions in a consistent way which are typically more accurate than
their low order analogs. Under the hypothesis of small initial data, we
establish local well-posedness for the Westervelt equation with the absorbing
boundary conditions. The performed numerical experiments illustrate the
efficiency of the proposed boundary conditions for different regimes of wave
propagation
A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains
We study some convergence issues for a recent approach to the problem of
transparent boundary conditions for the Helmholtz equation in unbounded
domains. The approach is based on the minimization on an integral functional
which arises from an integral formulation of the radiation condition at
infinity. In this Letter, we implement a Fourier-Chebyschev collocation method
and show that this approach reduce the computational cost significantly. As a
consequence, we give numerical evidence of some convergence estimates available
in literature and we study the robustness of the algorithm at low and mid-high
frequencies
Adaptive Finite Element Method for Simulation of Optical Nano Structures
We discuss realization, properties and performance of the adaptive finite
element approach to the design of nano-photonic components. Central issues are
the construction of vectorial finite elements and the embedding of bounded
components into the unbounded and possibly heterogeneous exterior. We apply the
finite element method to the optimization of the design of a hollow core
photonic crystal fiber. Thereby we look at the convergence of the method and
discuss automatic and adaptive grid refinement and the performance of higher
order elements
A Rigorous Finite-Element Domain Decomposition Method for Electromagnetic Near Field Simulations
Rigorous computer simulations of propagating electromagnetic fields have
become an important tool for optical metrology and design of nanostructured
optical components. A vectorial finite element method (FEM) is a good choice
for an accurate modeling of complicated geometrical features. However, from a
numerical point of view solving the arising system of linear equations is very
demanding even for medium sized 3D domains. In numerics, a domain decomposition
method is a commonly used strategy to overcome this problem. Within this
approach the overall computational domain is split up into smaller domains and
interface conditions are used to assure continuity of the electromagnetic
field. Unfortunately, standard implementations of the domain decomposition
method as developed for electrostatic problems are not appropriate for wave
propagation problems. In an earlier paper we therefore proposed a domain
decomposition method adapted to electromagnetic field wave propagation
problems. In this paper we apply this method to 3D mask simulation.Comment: 9 pages, 7 figures, SPIE conference Advanced Lithography / Optical
Microlithography XXI (2008
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
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
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