1996
DOI: 10.1007/s004660050110
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Some studies on dual reciprocity BEM for elastodynamic analysis

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Cited by 26 publications
(52 citation statements)
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“…For a model problem, the Dirichlet problem for Poisson's equation in the plane, we show that the error has two components: (1) that due to approximating the particular solution (which generally depends on the error in approximating the source term) and (2) error due to the choice of boundary element method. Using this we argue that traditional BEMs using low order piecewise polynomial approximations that the dominant part of the computational error may be due to BEM error ± not the interpolation error ± so that all commonly used rbfs tend to have similar overall behavior ± in accord with the observed numerical results in Agnantiaris, Polyzos and Beskos (1996); while if higher order solvers are used the dominant error may now be the interpolation error and the effects of the choice of rbfs is evident. To verify this computationally, we present the results of a 3 Â 3 experiment solving the boundary value problem in Section 4 using three different algorithms to solve the boundary integral equations: a standard piecewise quadratic BEM (Partridge, Brebbia and Wrobel (1992); a sophisticated adaptive method due to Jeon and Atkinson (1993) based on the Nystro Èm method and the Method of Fundamental Solutions (MFS) (Golberg, Chen and Karur (1996)) and three basis functions, 1 r, TPS and MQs.…”
Section: Introductionsupporting
confidence: 66%
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“…For a model problem, the Dirichlet problem for Poisson's equation in the plane, we show that the error has two components: (1) that due to approximating the particular solution (which generally depends on the error in approximating the source term) and (2) error due to the choice of boundary element method. Using this we argue that traditional BEMs using low order piecewise polynomial approximations that the dominant part of the computational error may be due to BEM error ± not the interpolation error ± so that all commonly used rbfs tend to have similar overall behavior ± in accord with the observed numerical results in Agnantiaris, Polyzos and Beskos (1996); while if higher order solvers are used the dominant error may now be the interpolation error and the effects of the choice of rbfs is evident. To verify this computationally, we present the results of a 3 Â 3 experiment solving the boundary value problem in Section 4 using three different algorithms to solve the boundary integral equations: a standard piecewise quadratic BEM (Partridge, Brebbia and Wrobel (1992); a sophisticated adaptive method due to Jeon and Atkinson (1993) based on the Nystro Èm method and the Method of Fundamental Solutions (MFS) (Golberg, Chen and Karur (1996)) and three basis functions, 1 r, TPS and MQs.…”
Section: Introductionsupporting
confidence: 66%
“…In Section 2 we discuss the appropriate implementation of TPS indicating that the failure to include the linear terms may have biased the results in Agnantiaris, Polyzos and Beskos (1996). Similar observations have been made by Karur and Ramachandran (1995).…”
Section: Introductionsupporting
confidence: 55%
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