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87
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.
Inverse medium scattering for the Helmholtz equation at fixed frequency
 INVERSE PROBLEMS
, 2005
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Differential Forms, Galerkin Duality, and Sparse Inverse Approximations in Finite Element Solutions of Maxwell Equations
, 2007
"... We identify primal and dual formulations in the finite element method (FEM) solution of the vector wave equation using a geometric discretization based on differential forms. These two formulations entail a mathematical duality denoted as Galerkin duality. Galerkindual FEM formulations yield identi ..."
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Cited by 10 (2 self)
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We identify primal and dual formulations in the finite element method (FEM) solution of the vector wave equation using a geometric discretization based on differential forms. These two formulations entail a mathematical duality denoted as Galerkin duality. Galerkindual FEM formulations yield identical nonzero (dynamical) eigenvalues (up to machine precision), but have static (zero eigenvalue) solution spaces of different dimensions. Algebraic relationships among the degrees of freedom of primal and dual formulations are explained using a deeprooted connection between the Hodge–Helmholtz decomposition of differential forms and Descartes–Euler polyhedral formula, and verified numerically. In order to tackle the fullness of dual formulation, algebraic and topological thresholdings are proposed to approximate inverse mass matrices by sparse matrices.
Mixed finiteelement timedomain method for transient Maxwell equations in doubly dispersive media
 IEEE TRANS. MICROW. THEORY TECH
, 2008
"... We describe a mixed finiteelement timedomain algorithm to solve transient Maxwell equations in inhomogeneous and doubly dispersive linear media where both the permittivity and permeability are functions of frequency. The mixed finiteelement timedomain algorithm is based on the simultaneous use o ..."
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Cited by 6 (3 self)
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We describe a mixed finiteelement timedomain algorithm to solve transient Maxwell equations in inhomogeneous and doubly dispersive linear media where both the permittivity and permeability are functions of frequency. The mixed finiteelement timedomain algorithm is based on the simultaneous use of both electric and magnetic field as state variables with a mix of edge (Whitney 1form) and face (Whitney 2form) elements for discretization of the coupled firstorder Maxwell curl equations. The constitutive relations are decoupled from the curl equations and cast in terms of (auxiliary) ordinary differential equations involving time derivatives. Permittivity and permeability dispersion models considered here are quite general and recover Lorentz, Debye, and Drude models as special cases. The present finiteelement timedomain algorithm also incorporates the perfectly matched layer absorbing boundary conditions in a natural way.
Finiteelement time–domain algorithms for modeling linear Debye and Lorentz dielectric dispersions at low frequencies
 IEEE Trans. Biomed. Eng
"... Abstract—We present what we believe to be the first algorithms that use a simple scalarpotential formulation to model linear Debye and Lorentz dielectric dispersions at low frequencies in the context of finiteelement timedomain (FETD) numerical solutions of electric potential. The new algorithms, ..."
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Cited by 5 (1 self)
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Abstract—We present what we believe to be the first algorithms that use a simple scalarpotential formulation to model linear Debye and Lorentz dielectric dispersions at low frequencies in the context of finiteelement timedomain (FETD) numerical solutions of electric potential. The new algorithms, which permit treatment of multiplepole dielectric relaxations, are based on the auxiliary differential equation method and are unconditionally stable. We validate the algorithms by comparison with the results of a previously reported method based on the Fourier transform. The new algorithms should be useful in calculating the transient response of biological materials subject to impulsive excitation. Potential applications include FETD modeling of electromyography, functional electrical stimulation, defibrillation, and effects of lightning and impulsive electric shock. Index Terms—Finite element methods, transient analysis. I.
Dispersion relation on the Kerr constant of a polymerstabilized optically isotropic liquid crystal
 University of Central
, 2011
"... The dispersion relation on the Kerr constant (K) of a polymerstabilized isotropic phase (PSIP) liquidcrystal (LC) composite is investigated. Our experimental results show that K decreases as the wavelength (λ) increases. The singleband birefringence dispersion model is used to fit the λK values ..."
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Cited by 5 (4 self)
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The dispersion relation on the Kerr constant (K) of a polymerstabilized isotropic phase (PSIP) liquidcrystal (LC) composite is investigated. Our experimental results show that K decreases as the wavelength (λ) increases. The singleband birefringence dispersion model is used to fit the λK values of the PSIP LC composite. Very good agreement between the experiment and physical model is obtained.
A Hybrid Finite ElementLaplace Transform Method for the Analysis of Transient Electromagnetic Scattering by anOverFilledCavity in theGround Plane
, 2008
"... Abstract. A hybrid finite elementLaplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2D overfilled cavity embedded in the infinite ground plane. The algorithm divides the whole scattering domain into two, interior and exterior, subdomains. I ..."
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Cited by 5 (2 self)
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Abstract. A hybrid finite elementLaplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2D overfilled cavity embedded in the infinite ground plane. The algorithm divides the whole scattering domain into two, interior and exterior, subdomains. In the interior subdomain which covers the cavity, the problem is solved via the finite element method. The problem is solved analytically in the exterior subdomain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane. The use of the Laplace transform leads to an analytical link condition between the overlapping subdomains. The analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz iteration. This dramatically improves the efficiency for solving transient scattering problems. Numerical solutions are tested favorably against analytical ones for a canonical geometry. The perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method. An error analysis is also performed.
Toeplitztype approximations to the Hadamard integral operator and their applications to electromagnetic cavity problems
, 2008
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AModified WaveletMeshless Method for Lossy Magnetic Dielectrics at Microwave Frequencies
"... In this work, the use of existing multiresolution analysis (MRA) in meshless method is studied to analyze some dielectrics for which the permeability and permittivity are complex at microwave frequencies. It will be shown that the existing MRA has some disadvantages and non meaningful aspects when i ..."
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Cited by 3 (3 self)
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In this work, the use of existing multiresolution analysis (MRA) in meshless method is studied to analyze some dielectrics for which the permeability and permittivity are complex at microwave frequencies. It will be shown that the existing MRA has some disadvantages and non meaningful aspects when is used in above dielectric simulation. In general, this type of MRA belongs to other areas of study such as image processing. Specifying these aspects and proposing some modifications to overcome the disadvantages of existing MRA for reaching a strict method of using wavelets in area of high frequency dielectrics, is the aim of this paper. We have selected the meshless method that is one of the newest and most powerful existing numerical methods as an area of using the modified MRA called computational MRA (CMRA). The use of CMRA in meshless methods, not only leaves most of the disadvantages, but also is faster and more accurate in comparison with the most other numerical methods. Index Terms—Complex dielectrics, Daubechies ’ wavelets, meshless method, multiresolution analysis (MRA), partition of unity, scaling functions, shape functions, Shepard’s method. I.