The generalized finite element method for Helmholtz equation. II: Effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment. (English) Zbl 1169.76397
Summary: In Part I [T. Strouboulis, I. Babuška, R. Hidajat, Comput. Methods Appl. Mech. Eng. 195, No. 37–40, 4711–4731 (2006; Zbl 1120.76044)] we introduced the \(q\)-version of the generalized finite element method (GFEM) for the Helmholtz equation and we addressed its: (a) pollution error due to the wave number; (b) exponential \(q\)-convergence; (c) robustness to perturbations of the mesh, the roundoff and numerical quadrature errors; and (d) a-posteriori error estimation. Here we continue the development of the GFEM for Helmholtz and we address the effects of: (a) alternative handbook functions and mesh types; (b) the error due to the artificial truncation boundary conditions and its assessment. The conclusions are: (1) the employment of plane-wave, wave-band, and Vekua handbook functions lead to equivalent results; and (2) for high \(q\), the most significant component of error may be the one due to the artificial truncation boundary conditions. A rather straightforward approach for assessing this error is proposed.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76Q05 | Hydro- and aero-acoustics |
Keywords:
generalized finite element method (GFEM); Helmholtz equation; handbook functions; plane-wave versus wave-band functions; error due to artificial truncation boundary condition; multiple scatterersCitations:
Zbl 1120.76044References:
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