Finite element formulation with high-order absorbing boundary conditions for time-dependent waves

2006 ◽  
Vol 195 (29-32) ◽  
pp. 3666-3690 ◽  
Author(s):  
Dan Givoli ◽  
Thomas Hagstrom ◽  
Igor Patlashenko
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Time Dependent ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Absorbing Boundary

LOCAL HIGH-ORDER ABSORBING BOUNDARY CONDITIONS FOR TIME-DEPENDENT WAVES IN GUIDES

2007 ◽  
Vol 15 (01) ◽  
pp. 1-22 ◽  
Author(s):  
THOMAS HAGSTROM ◽  
MANUELA L. DE CASTRO ◽  
DAN GIVOLI ◽  
DINA TZEMACH
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Optimal Choice ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Time Dependent ◽  
Time Varying ◽  
Scalar Wave ◽  
Absorbing Boundary ◽  
Free Parameters

The scalar wave equation in a two-dimensional semi-infinite wave guide is considered. The recently proposed Hagstrom–Warburton (H–W) local high-order absorbing boundary conditions (ABCs), which are based on a modification of the Higdon ABCs, are presented in this context. The P-order ABC involves the free parameters 0 < aj ≤ 1, for j = 0, 1, …, P, which have to be chosen. The choice aj = 1 for all j is shown to be satisfactory, in general, although not necessarily optimal. The optimal choice of the parameters is discussed via both theoretical analysis and numerical experiments. In addition, an adaptive scheme which controls the time-varying values of P and aj is presented and tested.

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