Direct Solvers for the Biharmonic Eigenvalue Problems Using Legendre Polynomials
We propose an efficient algorithm based on the Legendre–Galerkin approximations for the direct solution of the biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn–Hilliard type. The key point to the efficiency of our algorithm is...
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| Veröffentlicht in: | Journal of scientific computing 2017-03, Vol.70 (3), p.1030-1041 |
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| creator | Chen, Lizhen An, Jing Zhuang, Qingqu |
| description | We propose an efficient algorithm based on the Legendre–Galerkin approximations for the direct solution of the biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn–Hilliard type. The key point to the efficiency of our algorithm is to construct appropriate basis functions which satisfying the corresponding boundary condition automatically and leading to linear systems with sparse matrices for the discrete variational formulations. In addition, the error estimate was driven by the minimax principle. Finally, the numerical results demonstrate the accuracy and the efficiency of this method. |
| doi_str_mv | 10.1007/s10915-016-0277-7 |
| format | Article |
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The key point to the efficiency of our algorithm is to construct appropriate basis functions which satisfying the corresponding boundary condition automatically and leading to linear systems with sparse matrices for the discrete variational formulations. In addition, the error estimate was driven by the minimax principle. 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The key point to the efficiency of our algorithm is to construct appropriate basis functions which satisfying the corresponding boundary condition automatically and leading to linear systems with sparse matrices for the discrete variational formulations. In addition, the error estimate was driven by the minimax principle. Finally, the numerical results demonstrate the accuracy and the efficiency of this method.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Basis functions</subject><subject>Boundary conditions</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Eigenvalues</subject><subject>Linear systems</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Minimax technique</subject><subject>Partial differential equations</subject><subject>Polynomials</subject><subject>Sparse matrices</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kF9LwzAUxYMoOKcfwLeAz9GbJmnSR53zDwwc6J5D2qZbRtvMpBvs25tRwSefDpx7zrnwQ-iWwj0FkA-RQkEFAZoTyKQk8gxNqJCMyLyg52gCSgkiueSX6CrGLQAUqsgmaPnsgq0G_Onbgw0RNz7gYWPxk9uY0PneVXju1rY_mHZv8TL4srVdxKvo-jVe2HSpQ_J9e-x950wbr9FFk8Te_OoUrV7mX7M3svh4fZ89LkjFaD4Qa5SqOAgqLRjOK8pZboxkosypKiUwMMrUjAloeFkLDk0pQFkroFYqU4pN0d24uwv-e2_joLd-H_r0UmcFVYxmBWMpRcdUFXyMwTZ6F1xnwlFT0CdwegSnEzh9Aqdl6mRjJ6Zsv7bhb_n_0g-M9W_O</recordid><startdate>20170301</startdate><enddate>20170301</enddate><creator>Chen, Lizhen</creator><creator>An, Jing</creator><creator>Zhuang, Qingqu</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>20170301</creationdate><title>Direct Solvers for the Biharmonic Eigenvalue Problems Using Legendre Polynomials</title><author>Chen, Lizhen ; 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| subjects | Algorithms Approximation Basis functions Boundary conditions Computational Mathematics and Numerical Analysis Eigenvalues Linear systems Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Minimax technique Partial differential equations Polynomials Sparse matrices Theoretical |
| title | Direct Solvers for the Biharmonic Eigenvalue Problems Using Legendre Polynomials |
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