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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 ..."
Abstract

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.
An Alternative Derivation of the Exact DtNMap on a Circle
, 1998
"... The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of timeharmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the b ..."
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Cited by 3 (1 self)
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The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of timeharmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the boundary of a disc or sphere. The solution of the exterior domain problem is obtained via Laplace transformation techniques, where the asymptotic Sommerfeld radiation condition is reformulated accordingly.
Error bounds for the finiteelement approximation of the exterior . . .
, 2003
"... In this paper we design highorder (non)local artificial boundary conditions (ABCs) which are different from those proposed by Han, H. & Bao, W. (1997 Numer. Math., 77, 347–363) for incompressible materials, and present error bounds for the finiteelement approximation of the exterior Stokes equ ..."
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In this paper we design highorder (non)local artificial boundary conditions (ABCs) which are different from those proposed by Han, H. & Bao, W. (1997 Numer. Math., 77, 347–363) for incompressible materials, and present error bounds for the finiteelement approximation of the exterior Stokes equations in two dimensions. The finiteelement approximation (especially its corresponding stiff matrix) becomes much simpler (sparser) when it is formulated in a bounded computational domain using the new (non)local approximate ABCs. Our error bounds indicate how the errors of the finiteelement approximations depend on the mesh size, terms used in the approximate ABCs and the location of the artificial boundary. Numerical examples of the exterior Stokes equations outside a circle in the plane are presented. Numerical results demonstrate the performance of our error bounds.