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23
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.
Absorbing Boundary Conditions for the Schrödinger Equation
 SIAM J. Sci. Comput
, 1999
"... A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artif ..."
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Cited by 16 (0 self)
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A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artificial boundary condition which can minimize the size of such subdomains is the absorbing boundary condition. The imposition of absorbing boundary conditions is a technique used to reduce the necessary spatial domain when numerically solving partial differential equations that admit traveling waves. Such absorbing boundary conditions have been extensively studied in the context of hyperbolic wave equations. In this paper, general absorbing boundary conditions will be developed for the Schrödinger equation with one spatial dimension, using group velocity considerations. Previously published absorbing boundary conditions will be shown to reduce to special cases of this absorbing boundary condition. The wellposedness of the initial boundary value problem of the absorbing boundary condition, coupled to the interior Schrödinger equation, will also be discussed. Extension of the general absorbing boundary condition to higher spatial dimensions will be demonstrated. Numerical simulations using initial single Gaussian, double Gaussian, and a narrow Gaussian pulse distributions will be given, with comparision to exact solutions, to demonstrate the reflectivity properties of various orders of the absorbing boundary condition.
Characteristic Evolution and Matching
, 2008
"... I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativ ..."
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Cited by 12 (1 self)
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I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to eliminate the role of this artificial outer boundary via Cauchycharacteristic matching, by which the radiated waveform can be computed at null infinity. Progress in this direction is discussed.
MODELING OF ELASTIC WAVE PROPAGATION IN A FLUIDFILLED BOREHOLE EXCITED BY A PIEZOELECTRIC TRANSDUCER
"... Acoustic logging is an important geophysical method for obtaining relevant information concerning rock properties in formations traversed by boreholes. Typically, the formation parameters that are measured are the compressional, shear, and Stoneley wave slownesses, which are related to important pe ..."
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Cited by 4 (0 self)
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Acoustic logging is an important geophysical method for obtaining relevant information concerning rock properties in formations traversed by boreholes. Typically, the formation parameters that are measured are the compressional, shear, and Stoneley wave slownesses, which are related to important petrophysical parameters such as porosity, permeability, etc. Theoretical waveform modeling has played an important role in helping to understand the complex wave pattern setup in the borehole, and many processing algorithms have come out of this improved understanding. However, in the presence of formation inhomogeneities and borehole irregularities, which are the most common situations found in practice, no satisfactory modeling scheme has yet been presented. Furthermore, source and receivers have been treated as idealized pointwise transducers, with isotropic radiation patterns. As new applications of full waveform acoustic logs arise, such as sonic imaging, crosswell tomography, etc., a better understanding of the wave phenomena including excitation, propagation, scattering, and detection is necessary for inverting the recorded wavefield. In this paper a velocitystress finitedifference
Nonreflecting boundary conditions for waveguides
 Math. Comp
, 1999
"... Abstract. New nonreflecting boundary conditions are introduced for the solution of the Helmholtz equation in a waveguide. These boundary conditions are perfectly transparent for all propagating modes. They do not require the determination of these propagating modes but only their propagation consta ..."
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Cited by 3 (1 self)
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Abstract. New nonreflecting boundary conditions are introduced for the solution of the Helmholtz equation in a waveguide. These boundary conditions are perfectly transparent for all propagating modes. They do not require the determination of these propagating modes but only their propagation constants. A quasilocal form of these boundary conditions is well suited as terminating boundary condition beyond finite element meshes. Related convergence properties to the exact solution and optimal error estimates are established. 1.
Fast Numerical Methods for High Frequency Wave Scattering
, 2012
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Global Particle Simulation Study of Substorm Onset and Particle Acceleration
, 2000
"... Abstract. This paper reports the spatial and temporal development of Bursty Bulk Flows (BBFs) created by the reconnection as well as current disruptions (CDs) in the nearEarth tail using our 3D global EM particle simulation with a southward turning IMF in the context of the substorm onset. Recentl ..."
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Abstract. This paper reports the spatial and temporal development of Bursty Bulk Flows (BBFs) created by the reconnection as well as current disruptions (CDs) in the nearEarth tail using our 3D global EM particle simulation with a southward turning IMF in the context of the substorm onset. Recently, observations show that BBFs are often accompanied by current disruptions for triggering substorms. We have examined the dynamics of BBFs and CDs in order to understand the timing and triggering mechanism of substorms. As the solar wind with the southward IMF advances over the Earth, the nearEarth tail thins and the sheet current intensies. Before the peak of the current density becomes maximum, the reconnection takes place, which ejects particles from the reconnection region. Because of the earthward flows the peak of the current density moves toward the Earth. The characteristics of the earthward flows depend on the ions and electrons. Electrons flow back into the inflow region (the center of reconnection region), which provides current closure. Therefore the structure of electron flows near the reconnection region is rather complicated. In contrast, the ion earthward flows are generated far from the
Highly Accurate Absorbing Boundary Conditions for Wideangle Wave Equations
"... We develop a new class of absorbing boundary conditions (ABCs) to prevent unwanted artifacts and wraparounds associated with aperture truncation in migration / modeling using highorder oneway wave equations. The fundamental approach behind the proposed development is the efficient discretization o ..."
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We develop a new class of absorbing boundary conditions (ABCs) to prevent unwanted artifacts and wraparounds associated with aperture truncation in migration / modeling using highorder oneway wave equations. The fundamental approach behind the proposed development is the efficient discretization of the halfspace using midpointintegrated imaginary finite elements, an idea recently utilized in the development of effective oneway wave equations. The proposed ABCs essentially involve the addition of absorbing layers at the aperture truncation points. We derive the ABCs, analyze their properties, and develop a stable explicit finitedifference scheme to solve the downward continuation problem modified by these boundary conditions. With the help of numerical examples, we conclude that with as few as three absorbing layers, i.e., two additional grid points, the waves can be completely absorbed, thus preventing associated artifacts.