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Finite subdomain radial basis collocation method

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Abstract

Radial basis collocation method has easy implementation and exponential convergence. However, generally, the resultant collocation matrix is full and ill-conditioned and it’s hard to represent the local properties in solutions. Therefore, a finite subdomain collocation method with radial basis approximation is proposed. The approximation in subdomain is established within the subdomain and continuity conditions are imposed on all the interfaces in strong form. Consequently, the original full matrix can be transformed into a sparse matrix. Variant shape parameters can be used in different subdomains considering the need of solution representation in each subdomain. It can not only well alleviate the ill-condition and improve the solution accuracy, but also possess exponential convergence. Furthermore, CPU time can be markedly reduced. Error analysis and proper domain decomposition are also investigated. Numerical results show that this method has good performance for problems with high-gradient and singular problems which are prominent for their local characteristics.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (Project No. 11202150), Fundamental Research Funds for the Central Universities and Shanghai Leading Academic Discipline Project (Project No. B302).

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, People’s Republic of China

    Fuyun Chu, Lihua Wang & Zheng Zhong

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  1. Fuyun Chu
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  2. Lihua Wang
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  3. Zheng Zhong
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Correspondence to Lihua Wang.

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Chu, F., Wang, L. & Zhong, Z. Finite subdomain radial basis collocation method. Comput Mech 54, 235–254 (2014). https://doi.org/10.1007/s00466-014-0981-9

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