Iterative radiation boundary conditions for finite element solutions of the scalar wave equation

Safjan, A.

doi:10.1016/s0045-7825(01)00238-9

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…Iterative boundary operators are introduced as follows [16]. First, the exact boundary condition on Γ ∞ , eqn (65), is replaced with…”

Section: Iterative Boundary Operatorsmentioning

confidence: 99%

“…J , can be practically limited to the truncated boundary Γ ∞ [16]. As a consequence, iterative boundary operators should be easy to implement into a standard finite element code.…”

Section: Iterative Boundary Operatorsmentioning

confidence: 99%

“…Finally, by appending appropriate corner conditions, the formulation can be extended to rectangular computational domains [3,16].…”

Section: Iterative Boundary Operatorsmentioning

confidence: 99%

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Safjan

2002

Z angew Math Phys

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The structural acoustics problem is formulated as a hyperbolic system of conservation laws which leads to an abstract Cauchy problem in common Hilbert space settings. The Cauchy problem is approximated by using high-order, multi-stage Taylor-Galerkin methods which provide high-order temporal accuracy and unconditional stability on arbitrary (unstructured) finite element grids. The formulation is extended to problems posed on unbounded domains by introduction of iterative radiation boundary conditions. The proposed approaches are shown to produce very good results for the test cases considered. Mathematics Subject Classification (2000). 35L05, 65M60, 65M99.

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“…Iterative boundary operators are introduced as follows [16]. First, the exact boundary condition on Γ ∞ , eqn (65), is replaced with…”

Section: Iterative Boundary Operatorsmentioning

confidence: 99%

“…J , can be practically limited to the truncated boundary Γ ∞ [16]. As a consequence, iterative boundary operators should be easy to implement into a standard finite element code.…”

Section: Iterative Boundary Operatorsmentioning

confidence: 99%

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Safjan

2002

Z angew Math Phys

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A non‐reflecting layer method for non‐linear wave‐type equations on unbounded domains with applications to shape memory alloy rods

Newman

Safjan

Popov

et al. 2005

Numerical Meth Engineering

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In this paper a new technique is introduced and applied in solving one‐dimensional linear and non‐linear wave‐type equations on an unbounded spatial domain. This new technique referred to as the non‐reflecting layer method (NRLM) extends the computational domain with an artificial layer on which a one‐way wave equation is solved. The method will be applied to compute stress waves in long rods consisting of NiTi shape memory alloy material subjected to impact loading and undergoing detwinning and pseudo‐elastic material responses. The NRLM has been tested on model problems and it has been found that the computed solutions agree well with the exact solutions, i.e. normalized error levels are in ranges acceptable for engineering computations. Copyright © 2005 John Wiley & Sons, Ltd.

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A computational model for seismically induced liquefaction

Struckmeier¹

2007

Braunschweiger Schriften Zur Mechanik

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Iterative radiation boundary conditions for finite element solutions of the scalar wave equation

Cited by 3 publications

References 15 publications

Untitled

Untitled

A non‐reflecting layer method for non‐linear wave‐type equations on unbounded domains with applications to shape memory alloy rods

A computational model for seismically induced liquefaction

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