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On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Comparison Of TwoDimensional Conformal Local Radiation Boundary Conditions
 Electromagnetics
, 1996
"... Numerical solutions for openregion electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation Boundary Conditions (RBCs) for general boundary shapes have been proposed during the past decade. Many are generalizatio ..."
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Cited by 8 (4 self)
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Numerical solutions for openregion electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation Boundary Conditions (RBCs) for general boundary shapes have been proposed during the past decade. Many are generalizations of the BaylissTurkel RBC for circular truncation boundaries. This paper reviews several twodimensional RBCs for general truncation boundaries. The RBCs are evaluated on the basis of their performance on two separate numerical tests: the annihilation of terms in the Hankel series and the comparison of nearfield and radar cross sections for finite element solutions to scattering problems. These tests suggest that the simpler RBCs can be very competitive with RBCs based on more sophisticated derivations. 1. INTRODUCTION Despite the rapid growth of computer resources over the last few years, the main concern in solving realistic open region electromagnetic problems is to reduce the size of...
Fast Numerical Solution Of Exterior Helmholtz Problems With Radiation Boundary Condition By Imbedding
, 1994
"... The development of efficient solution algorithms for Poisson's equation on domains allowing for separation of variables prompted research towards extending these algorithms to domains of general shape. The resulting numerical techniques are known as imbedding methods or capacitance matrix metho ..."
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Cited by 8 (2 self)
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The development of efficient solution algorithms for Poisson's equation on domains allowing for separation of variables prompted research towards extending these algorithms to domains of general shape. The resulting numerical techniques are known as imbedding methods or capacitance matrix methods. In this dissertation, we develop capacitance matrix methods for exterior boundary value problems for the Helmholtz equation, a secondorder elliptic PDE which governs timeharmonic wave propagation. Solutions of exterior Helmholtz problems must satisfy an asymptotic boundary condition at infinity in order to be uniquely determined. We incorporate this boundary condition into the discretization by posing the DirichlettoNeumann (DtN) condition, an exact nonlocal boundary condition, on a circular artificial boundary. A fast Helmholtz solver of complexity O(nm log n) can then be obtained for the resulting discrete problem on an m \Theta n grid when the underlying computational domain is an an...
Comparison of Local Radiation Boundary Conditions for the Scalar Helmholtz Equation with General Boundary Shapes
 IEEE Trans. Antennas Propagat
, 1995
"... The relative accuracy of several local radiation boundary conditions based on the secondorder BaylissTurkel condition are evaluated. These boundary conditions permit the approximate solution of the scalar Helmholtz equation in an infinite domain using traditional finite element and finite differe ..."
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Cited by 5 (4 self)
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The relative accuracy of several local radiation boundary conditions based on the secondorder BaylissTurkel condition are evaluated. These boundary conditions permit the approximate solution of the scalar Helmholtz equation in an infinite domain using traditional finite element and finite difference techniques. Unlike the standard BaylissTurkel condition, the generalizations considered here are applicable to noncircular solution domains. The accuracy of these conditions are investigated for elliptical and linear/circular boundaries. I. Introduction When solving the scalar Helmholtz equation in unbounded regions, a radiation boundary condition (RBC) must be imposed to obtain a unique solution. Efficient numerical solution procedures for scattering problems necessitate the imposition of an RBC as close as possible to the scatterer. In order to maintain the desirable sparse characteristics of a differential equation formulation, a local RBC is often employed. Bayliss and Turkel (BT) ...
Stability estimates for an inverse scattering problem at high frequencies
 J. Math. Anal. Appl
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The unified transform for the modified Helmholtz equation in the exterior of a square, to appear
 in Unified Transform for Boundary Value Problems: Applications and Advances
, 2014
"... Abstract. The Unified Transform provides a novel method for analyzing boundary value problems for linear and for integrable nonlinear PDEs. The numerical implementation of this method to linear elliptic PDEs formulated in the interior of a polygon has been investigated by several authors (see the a ..."
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Cited by 2 (0 self)
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Abstract. The Unified Transform provides a novel method for analyzing boundary value problems for linear and for integrable nonlinear PDEs. The numerical implementation of this method to linear elliptic PDEs formulated in the interior of a polygon has been investigated by several authors (see the article by Iserles, Smitheman, and one of the authors in this book). Here, we show that the Unified Transform also yields a novel numerical technique for computing the solution of linear elliptic PDEs in the exterior of a polygon. One of the advantages of this new technique is that it actually yields directly the scattering amplitude. Details are presented for the modified Helmholtz equation in the exterior of a square.
Vector absorbing boundary conditions for nodal or mixed finite elements
 IEEE Trans. Magn
, 1996
"... finite elements ..."
(www.interscience.wiley.com) DOI: 10.1002/jae.1091 LAND OF ADDICTS? AN EMPIRICAL INVESTIGATION OF HABITBASED ASSET PRICING MODELS
"... This paper studies the ability of a general class of habitbased asset pricing models to match the conditional moment restrictions implied by asset pricing theory. We treat the functional form of the habit as unknown, and estimate it along with the rest of the model’s finite dimensional parameters. ..."
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This paper studies the ability of a general class of habitbased asset pricing models to match the conditional moment restrictions implied by asset pricing theory. We treat the functional form of the habit as unknown, and estimate it along with the rest of the model’s finite dimensional parameters. Using quarterly data on consumption growth, assets returns and instruments, our empirical results indicate that the estimated habit function is nonlinear, that habit formation is better described as internal rather than external, and the estimated timepreference parameter and the power utility parameter are sensible. In addition, the estimated habit function generates a positive stochastic discount factor (SDF) proxy and performs well in explaining crosssectional stock return data. We find that an internal habit SDF proxy can explain a crosssection of size and bookmarket sorted portfolio equity returns better than (i) the Fama and French (1993) threefactor model, (ii) the Lettau and Ludvigson (2001b) scaled consumption CAPM model, (iii) an external habit SDF proxy,
Numerical Implementation of a Conformable TwoDimensional Radiation Boundary Condition
, 1995
"... In open region differential equation problems it is common to limit the computational domain by introducing an artificial boundary. The artifical boundary condition must be chosen to produce as little reflection as possible. Numerous ideas have been employed in the search of accurate and efficient r ..."
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In open region differential equation problems it is common to limit the computational domain by introducing an artificial boundary. The artifical boundary condition must be chosen to produce as little reflection as possible. Numerous ideas have been employed in the search of accurate and efficient radiation boundary conditions (RBCs). A finite element method (FEM) formulation that encompasses many different RBCs is presented. The computational domain can be a general convex twodimensional domain containing the scatterer. The resulting system of linear equations is sparse and, in general, nonHermitian. Examples using a generalization of the second order Bayliss Turkel RBC with both circular and noncircular artificial boundaries are also discussed. The results from these tests both validate the present computational system and illustrate some of the computational savings (time and memory) that can be obtained by selecting an artificial boundary conformal with the scatterer.
Acquisitions and Acquisitions et Biblbgraphic Services services bibliographiques
, 1997
"... a thesis submitted to the ..."