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12
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.
Numerical Solution Of Problems On Unbounded Domains. A Review
 A review, Appl. Numer. Math
, 1998
"... While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many ..."
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Cited by 126 (19 self)
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While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems represent a wide class of important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms and interpretation of the results. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computa...
Revisiting open boundary conditions from the point of view of characteristic variables
 OCEAN MODELLING (2005)
, 2005
"... ..."
Multigrid Methods For Differential Equations With Highly Oscillatory Coefficients
 In Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods
, 1993
"... this paper we analyse the convergence of multigrid methods for equation (1) by introducing new coarse grid operators, based on local or global homogenized form of the equation. We consider only two level multigrid methods. For full multigrid or with more general coefficients the homogenized operator ..."
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Cited by 13 (3 self)
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this paper we analyse the convergence of multigrid methods for equation (1) by introducing new coarse grid operators, based on local or global homogenized form of the equation. We consider only two level multigrid methods. For full multigrid or with more general coefficients the homogenized operator can be numerically calculated from the finer grids based on local solution of the so called cell problem [2]. In a number of numerical tests we compare the convergence rate for different choices of parameter and coarse grid operators applied to a two dimensional elliptic model problem. The convergence rate is also analyzed theoretically for a one dimensional problem. If, for example, the oscillatory coefficient is replaced by its average, the direct estimate for multigrid convergence rate is not asymptotically better than just using the damped Jacobi smoothing operator. The homogenized coefficient reduces the number of smoothing operation from O(h
An Application of the Difference Potentials Method to Solving External Problems in CFD
 Problems in CFD, NASA Technical Memorandum No. 110338, Langley Research Center
, 1997
"... Numerical solution of infinitedomain boundaryvalue problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the origi ..."
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Cited by 7 (2 self)
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Numerical solution of infinitedomain boundaryvalue problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinitedomain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABCs) at the newly formed external boundary. The role of the ABCs is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinitedoma...
Artificial Boundary Conditions Based On The Difference Potentials Method
 IN PROCEEDINGS OF THE SIXTH INTERNATIONAL SYMPOSIUM ON COMPUTATIONAL FLUID DYNAMICS, IV
, 1996
"... While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant i ..."
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Cited by 6 (3 self)
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While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensiv...
An analysis of higher order boundary conditions for the wave equation
, 2005
"... Thanks to the use of the Cagniard–De Hoop method, we derive an analytic solution in the time domain for the halfspace problem associated with the wave equation with Engquist– Majda higher order boundary conditions. This permits us to derive new convergence results when the order of the boundary con ..."
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Cited by 4 (1 self)
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Thanks to the use of the Cagniard–De Hoop method, we derive an analytic solution in the time domain for the halfspace problem associated with the wave equation with Engquist– Majda higher order boundary conditions. This permits us to derive new convergence results when the order of the boundary condition tends to +∞, as well as error estimates. The theory is illustrated by numerical results.
NESTING OCEAN MODELS
, 2000
"... This note is focused on the problem of providing boundary conditions for regional ocean models. It is shown that usual methods generally do not address the correct problem, but more or less approaching ones. A tentative classification of these methods is proposed. Then their theoretical foundations ..."
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Cited by 2 (1 self)
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This note is focused on the problem of providing boundary conditions for regional ocean models. It is shown that usual methods generally do not address the correct problem, but more or less approaching ones. A tentative classification of these methods is proposed. Then their theoretical foundations are discussed, and recommendations are given.
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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Cited by 1 (0 self)
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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...
The NASA STI Program Office provides
, 2001
"... Since its founding, NASA has been dedicated to the advancement of aeronautics and space ..."
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Since its founding, NASA has been dedicated to the advancement of aeronautics and space