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19
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.
FiniteDifference Computation of Transient Electromagnetic Waves for Cylindrical Geometries in Complex Media
, 2000
"... We present two novel, fully threedimensional (3D) finitedifference timedomain (FDTD) schemes in cylindrical coordinates for transient simulation of electromagnetic wave propagation in complex (inhomogeneous, dispersive, and conductive) and unbounded media. The proposed FDTD schemes incorporate a ..."
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Cited by 15 (2 self)
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We present two novel, fully threedimensional (3D) finitedifference timedomain (FDTD) schemes in cylindrical coordinates for transient simulation of electromagnetic wave propagation in complex (inhomogeneous, dispersive, and conductive) and unbounded media. The proposed FDTD schemes incorporate an extension of the perfectly matched layer (PML) absorbing boundary condition (ABC) to threedimensional (3D) cylindrical coordinates. Dispersion on the media is modeled by using the piecewiselinear recursive convolution (PLRC) algorithm, accounting for multiterm Lorentz and/or Debye models. Splitfield and unsplit (anisotropic medium) formulations of the cylindrical PMLPLRCFDTD schemes are implemented and compared in the time domain. The comparison includes the latetime stability properties of the update schemes. Numerical simulations of susbsurface electromagnetic problems are included. Because the proposed schemes retain the nearestneighbor property of the ordinary FDTD, they are well suited for implementation on massively parallel computers.
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...
HigherOrder Fdtd Methods For Large Problems
 J. Applied Computational Electromagnetics Society
, 1995
"... The FiniteDifference TimeDomain (FDTD) algorithm provides a simple and efficient means of solving Maxwell's equations for a wide variety of problems. In Yee's uniform grid FDTD algorithm the derivatives in Maxwell's curl equations are replaced by central difference approximations. U ..."
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Cited by 7 (2 self)
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The FiniteDifference TimeDomain (FDTD) algorithm provides a simple and efficient means of solving Maxwell's equations for a wide variety of problems. In Yee's uniform grid FDTD algorithm the derivatives in Maxwell's curl equations are replaced by central difference approximations. Unfortunately, numerical dispersion and grid anisotropy are inherent to FDTD methods. For large computational domains, e.g., ones that have at least one dimension forty wavelengths or larger, phase errors from dispersion and grid anisotropy in the Yee algorithm (YA) can be significant unless a small spatial discretization is used. For such problems, the amount of data that must be stored and calculated at each iteration can lead to prohibitive memory requirements and high computational cost. To decrease the expense of FDTD simulations for large scattering problems two higherorder methods have been derived and are reported here. One method is secondorder in time and fourthorder in space (24); the other i...
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) ...
Syms, “Analysis of Folded ErbiumDoped Planar Waveguide Amplifiers by the Method of
 Lines” J. Lighhvave Technology
, 1999
"... Abstract—A numerical model for spiral and folded erbiumdoped planar waveguide amplifiers has been developed, based on a rate equation model of the local complex dielectric constant and beam propagation by the method of lines. A fivelevel system is used to describe the ion–ion interactions that occ ..."
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Cited by 3 (1 self)
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Abstract—A numerical model for spiral and folded erbiumdoped planar waveguide amplifiers has been developed, based on a rate equation model of the local complex dielectric constant and beam propagation by the method of lines. A fivelevel system is used to describe the ion–ion interactions that occur at high erbium concentrations. A suitable form of the method of lines is presented in polar coordinates, and absorbing boundary conditions based on the thirdorder rational series approximation are derived. Using this model, amplification in both straight and curved slab guides can be simulated, and examples of propagation in typical folded amplifier structures are presented. Index Terms — Erbiumdoped planar waveguide amplifier (EDWA), method of lines, modeling, optical amplifier, rate equation. I.
Combining PML and ABC for Finite Element Analysis of Scattering Problems
, 1996
"... A perfectly matched layer (PML) is combined with an absorbing boundary condition (ABC) for mesh truncation in the finite element solution of electromagnetic scattering problems. It is shown by one, two, and threedimensional examples, that the combined PML and ABC has less undesired reflection tha ..."
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Cited by 2 (0 self)
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A perfectly matched layer (PML) is combined with an absorbing boundary condition (ABC) for mesh truncation in the finite element solution of electromagnetic scattering problems. It is shown by one, two, and threedimensional examples, that the combined PML and ABC has less undesired reflection than the PML or ABC alone. I. INTRODUCTION When solving openregion scattering problems using the finite element method (FEM), the infinite region exterior to the scatterer must be truncated with an artificial boundary to limit the number of unknowns. Consequently, a boundary condition must be introduced at this artificial boundary for a unique finite element solution. Such a boundary condition should make the boundary appear as transparent as possible to the scattered field, or in other words, it should minimize the reflection of the scattered field incident upon the boundary. An ideal boundary condition is one that possesses zero reflection for all angles of incidence. However, except for tho...
FDTD Simulations for Ultrasound Propagation in a 2D Breast Model
"... To increase the survival rates of patients with breast cancer, an ultrasound imaging system must detect tumors when they are small, with a diameter of 5 mm or less. This requires an understanding of how propagation of ultrasound energy is affected by the complex structure of the breast. In this pape ..."
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Cited by 2 (0 self)
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To increase the survival rates of patients with breast cancer, an ultrasound imaging system must detect tumors when they are small, with a diameter of 5 mm or less. This requires an understanding of how propagation of ultrasound energy is affected by the complex structure of the breast. In this paper, a FiniteDifference TimeDomain (FDTD) method is developed to simulate ultrasound propagation in a twodimensional model of the human breast. The FDTD simulations make it possible to better understand the behavior of an ultrasound signal in the breast. For example, here the simulations are used to investigate the effect of fat lobes adjacent to the skin layer in a simple breast model. Experimental work performed at the University of Pennsylvania has shown that strong refraction caused by the fat lobes results in nulls in the forward transmitted field. This result was duplicated with the FDTD simulations, and it was shown that the effect of refraction is clearly evident for energy exiting the breast. The existence of strong refraction has a significant impact on ultrasound imaging since it implies that an imaging method based on a weak scattering assumption is unlikely to work well. KEY WORDS: FDTD simulations; higherorder FDTD; ultrasound mammography; ultrasound tomography. q 1996 Academic Press, Inc. 1.
Derivation and Comparison of Radiation Boundary Conditions for the TwoDimensional Helmholtz Equation with NonCircular Artificial Boundaries
, 1995
"... Wave equations in exterior domains typically include a boundary condition at infinity to ensure the wellposedness of the problem. An obstacle to the efficient computation of solutions is the unbounded computational domain; the problem must be reformulated on a bounded domain. The success of this ap ..."
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Wave equations in exterior domains typically include a boundary condition at infinity to ensure the wellposedness of the problem. An obstacle to the efficient computation of solutions is the unbounded computational domain; the problem must be reformulated on a bounded domain. The success of this approach depends critically on the selection of the artificial boundary and on the radiation boundary condition imposed on the artificial boundary. This choice involves a compromise between accuracy of the reformulation and efficiency of solution. Several radiation boundary conditions have been proposed; most are designed to be used on simple boundaries, primarily circles. In scattering problems with a long, thin scatterer a circular artificial boundary results in a relatively large computational domain. Smaller computational domains can be obtained by selecting an artificial boundary which is more conformal with the scatterer. We demonstrate a general method for extending radiation boundary c...
Electromagnetic FDTD Simulation of General Lossy Structures with Nonuniform Grid Spacing.
"... Abstract approved: ..."