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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 MultiField SpaceTime Finite Element Method for Structural Acoustics. Symposium on Acoustics of Submerged Structures and Transduction Systems
 ASME 15th Biennial Conference on Mechanical Vibration and Noise
, 1995
"... A spacetime nite element method for solution of the exterior structural acoustics problem involving the interaction of vibrating elastic structures submerged in an innite acoustic fluid is formulated. In particular, new timediscontinuous Galerkin and Galerkin LeastSquares (GLS) variational formu ..."
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Cited by 13 (8 self)
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A spacetime nite element method for solution of the exterior structural acoustics problem involving the interaction of vibrating elastic structures submerged in an innite acoustic fluid is formulated. In particular, new timediscontinuous Galerkin and Galerkin LeastSquares (GLS) variational formulations for coupled structural acoustics in unbounded domains are developed and analyzed for stability and convergence. The formulation employs a nite computational fluid domain surrounding the structure and incorporates timedependent nonreflecting boundary conditions on the fluid truncation boundary. Energy estimates are obtained which allow us to prove the unconditional stability of the method for the coupled fluidstructure problem with absorbing boundaries. The methods developed are especially useful for the application of adaptive solution strategies for transient acoustics in which unstructured spacetime meshes are used to track waves propagating along spacetime characteristics. An important feature of the spacetime formulation is the incorporation of temporal jump operators which allow for nite element interpolations that are discontinuous in time. For additional stability, leastsquares operators based on local residuals of the structural acoustics equations including the nonreflecting boundary conditions are incorporated. The energy decay estimates and highorder accuracy predicted by our a priori error estimates are demonstrated numerically in a simple canonical example.
Computation of Far Field Solutions Based on Exact Nonreflecting Boundary Conditions for the TimeDependent Wave Equation
, 1999
"... In this work we show how to combine in the exact nonreflecting boundary conditions (NRBC) first derived by Grote and Keller, the calculation of the exterior (farfield) solution for timedependent radiation and scattering in an unbounded domain. At each discrete time step, radial modes computed on a ..."
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Cited by 6 (4 self)
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In this work we show how to combine in the exact nonreflecting boundary conditions (NRBC) first derived by Grote and Keller, the calculation of the exterior (farfield) solution for timedependent radiation and scattering in an unbounded domain. At each discrete time step, radial modes computed on a spherical artificial boundary which drive the exact NRBC for the nearfield solution, are imposed as Cauchy data for the radial wave equation in the farfield. Similar to the farfield computation scheme used by Wright, the radial modes in the exterior region are computed using an explicit finite difference solver. However, instead of using an `infinite grid', we truncate the exterior radial grid at the farfield point of interest, and for each harmonic, impose the same exact NRBC used for the nearfield truncation boundary, here expressed in modal form. Using this approach, two different methods for extrapolating the nearfield solution to the farfield are possible. In the first, the near fie...
Computation of Transient Radiation in SemiInfinite Regions Based on Exact Nonreflecting Boundary Conditions and Mixed Time Integration
, 1999
"... Transient radiation in a semiinfinite region, bounded by a planar infinite baffle with a local acoustic source is considered. The numerical simulation of the transient radiation problem requires an artificial boundary , here chosen to be a hemisphere, which separates the computational region from t ..."
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Cited by 2 (1 self)
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Transient radiation in a semiinfinite region, bounded by a planar infinite baffle with a local acoustic source is considered. The numerical simulation of the transient radiation problem requires an artificial boundary , here chosen to be a hemisphere, which separates the computational region from the surrounding unbounded acoustic medium. Inside the computational region we use a semidiscrete finite element method. On , we apply the exact nonreflecting boundary condition (NRBC) first derived by Grote and Keller for the freespace problem. Since the problem is symmetric about the infinite planar surface, in order to satisfy the rigid baffle condition it is sufficient to restrict the indices in the spherical harmonic expansion which defines the NRBC and scale the radial harmonics which drive auxiliary equations on the boundary. The Fourier expansion in the circumferential angle appearing in the NRBC may be used to efficiently model axisymmetric problems in twodimensions. A new mixed explicit...
Ecole des Ponts ParisTech,
, 2009
"... boundary conditions for timeharmonic wave problems Denis Duhamel a, ∗ , TienMinh Nguyen a ..."
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boundary conditions for timeharmonic wave problems Denis Duhamel a, ∗ , TienMinh Nguyen a
unknown title
"... bité me rob d e ner s m un stu the ed edia ca ng suc is wel ailable thods roblem in the thods adapted for infinite domains and is described in numerous classical textbooks like [1–5]. It consists in solving an equation on the boundary of the domain only and the radiation conditions are taken into ac ..."
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bité me rob d e ner s m un stu the ed edia ca ng suc is wel ailable thods roblem in the thods adapted for infinite domains and is described in numerous classical textbooks like [1–5]. It consists in solving an equation on the boundary of the domain only and the radiation conditions are taken into account analytically. It also reduces the dimension of the problem to a surface in 3D and to a curve in 2D decreasing thus the size of the linear problem to solve. However, the final problem involves full matrices which are also generally non symmetrical. It and infinite domains. This relation links the variable and its normal derivative on the whole boundary. The DtNmapping is thus non local and every node on the boundary is connected to all other nodes. This gives a full matrix for the nodes of the boundary which partially destroys the sparse matrix of the FEM and increases substantially the computing resources needed to get the solution. The solution has to be found in the exterior domain by analytical or numerical methods. When the analytical solution can be found, it is generally under the form of a series expansion. The number of terms in the expansion must be sufficient for an accurate solution
boundary conditions for the timedependent
, 1999
"... farfield solutions based on exact nonreflecting ..."