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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 ..."
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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.
A Posteriori Finite Element Error Bounds for Nonlinear Outputs of the Helmholtz Equation
, 1999
"... We present a Neumannsubproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, constantfree upper and lower bounds for nonlinear outputs of the Helmholtz equation in twodimensional exterior domains. We first formulate the bound procedure, with particu ..."
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Cited by 10 (1 self)
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We present a Neumannsubproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, constantfree upper and lower bounds for nonlinear outputs of the Helmholtz equation in twodimensional exterior domains. We first formulate the bound procedure, with particular emphasis on appropriate extension to complexvalued equations; we then provide illustrative numerical examples for outputs such as the intensity of the scattered wave over a small segment of the domain boundary.
Fast Numerical Solution Of Exterior Helmholtz Problems With Radiation Boundary Condition By Imbedding
, 1994
"... The development of efficient solution algorithms for Poisson's equation on domains allowing for separation of variables prompted research towards extending these algorithms to domains of general shape. The resulting numerical techniques are known as imbedding methods or capacitance matrix metho ..."
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Cited by 8 (2 self)
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The development of efficient solution algorithms for Poisson's equation on domains allowing for separation of variables prompted research towards extending these algorithms to domains of general shape. The resulting numerical techniques are known as imbedding methods or capacitance matrix methods. In this dissertation, we develop capacitance matrix methods for exterior boundary value problems for the Helmholtz equation, a secondorder elliptic PDE which governs timeharmonic wave propagation. Solutions of exterior Helmholtz problems must satisfy an asymptotic boundary condition at infinity in order to be uniquely determined. We incorporate this boundary condition into the discretization by posing the DirichlettoNeumann (DtN) condition, an exact nonlocal boundary condition, on a circular artificial boundary. A fast Helmholtz solver of complexity O(nm log n) can then be obtained for the resulting discrete problem on an m \Theta n grid when the underlying computational domain is an an...