Application of Multiquadric Radial Basis Function method for Helmholtz equation in seismic wave analysis for reservoir of rigid dams

Document Type : Research Article

Authors

1 University of Qom

2 University of Tehran

Abstract

 The high costs of mesh generation in mesh-dependent solution, weakness in capturing 
singularities, the need of modeling all over the domain, the need of problem dependent fundamental 
solutions, etc. are some of weaknesses in the common numerical mesh-dependent methods for solving 
continuum mechanics boundary value problems. In this study, aiming for eliminating some of these 
shortcomings, one of the well-known Radial Basis Functions (RBF) methods, Multiquadric (MQ), is 
developed for dynamic analysis of 2D reservoirs of rigid dams in frequency-domain. To this end, the 
Helmholtz equation and the governing complex boundary conditions are reproduced using MQ function 
in the frequency domain. The results show that with the use of real and complex forms of the MQ 
function, the computational time will be respectively optimized for frequencies smaller and larger than 
the natural frequency of the reservoir. Also, to determine the most important factors affecting both the 
accuracy and convergence of MQ method, first the inefficiency of some of the previously introduced 
methods is proved, and then a new high-speed algorithm is presented. It is shown that the optimal 
shape parameter for MQ method can be formulated in terms of the frequencies of seismic records. 
This advantage simplifies the application of MQ method in this particular problem and reduces the 
computational time, considerably. The high accuracy of the present method is shown in two different 
examples, where the effects of sediment absorption may either be considered or not. The high accuracy 
compared to the exact solutions achieved in this paper is due to a continuous estimation function defined 
all over the domain and also due to the simple algorithm used for finding the optimal shape parameter.

Keywords

Main Subjects

References

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Amirkabir Journal of Civil Engineering
Volume 52, Issue 12
March 2021
Pages 3015-3030

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