Treatment of Dirichlet-type boundary conditions in the spline-based wavelet Galerkin method employing multiple point constraints

Sannomaru Shogo

Tanaka Satoyuki

Yoshida Ken-ichiro

Bui Tinh Quoc

Okazawa Shigenobu

Hagihara Seiya

Applied Mathematical Modelling

The wavelet methods have been extensively adopted and integrated in various numerical methods to solve partial differential equations. The wavelet functions, however, do not satisfy the Kronecker delta function properties, special treatment methods for imposing the Dirichlet-type boundary conditions are thus required. It motivates us to present in this paper a novel treatment technique for the essential boundary conditions (BCs) in the spline-based wavelet Galerkin method (WGM), taking the advantages of the multiple point constraints (MPCs) and adaptivity. The linear B-spline scaling function and multilevel wavelet functions are employed as basis functions. The effectiveness of the present method is addressed, and in particular the applicability of the MPCs is also investigated. In the proposed technique, MPC equations based on the tying relations of the wavelet basis functions along the essential BCs are developed. The stiffness matrix is degenerated based on the MPC equations to impose the BCs. The numerical implementation is simple, and no additional degrees of freedom are needed in the system of linear equations. The accuracy of the present formulation in treating the BCs in the WGM is high, which is illustrated through a number of representative numerical examples including an adaptive analysis.

Wavelet Galerkin method

Meshfree method

Multiple point constraints

Adaptive analysis

eng

Elsevier

© <2016>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

This is not the published version. Please cite only the published version.

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[DOI] https://doi.org/10.1016/j.apm.2016.11.018 isVersionOf

日本学術振興会

Japan Society for the Promotion of Science

[Crossref Funder] https://doi.org/10.13039/501100001691

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