TY - JOUR
T1 - Chebyshev tau meshless method based on the integration-differentiation for Biharmonic-type equations on irregular domain
AU - Shao, Wenting
AU - Wu, Xionghua
AU - Chen, Suqin
N1 - Funding Information:
The support from the National Natural Science Foundation of China under Grants (nos. 10671146 and 50678122 ) is fully acknowledged. The authors are deeply grateful and sincerely obliged to the anonymous reviewers for their very helpful comments made and references recommended, which led to a great improvement of this paper.
PY - 2012/12
Y1 - 2012/12
N2 - This paper reports a new method, Chebyshev tau meshless method based on the integration-differentiation (CTMMID) for numerically solving Biharmonic-type equations on irregularly shaped domains with complex boundary conditions. In general, the direct application of Chebyshev spectral method based on differentiation process to the fourth order equations leads to the corresponding differentiation matrix with large condition numbers. From another aspect, the strategy based on the integral formula of a Chebyshev polynomial could not only create sparsity, but also improve the accuracy, however it requires a lot of computational cost for directly solving high order two-dimensional problems. In this paper, the construction of the Chebyshev approximations is to start from the mix partial derivative uxxyy(x,y) rather than the unknown function u(x,y). The irregular domain is embedded in a domain of rectangle shape and the curve boundary can be efficiently treated by CTMMID. The numerical results show that compared with the existing results, our method yields spectral accuracy, and the main distinguishing feature is reducing the condition number of fourth order equations on rectangle domain from O(N8) to O(N 4). It also appears that CTMMID is effective for the problems on irregular domains.
AB - This paper reports a new method, Chebyshev tau meshless method based on the integration-differentiation (CTMMID) for numerically solving Biharmonic-type equations on irregularly shaped domains with complex boundary conditions. In general, the direct application of Chebyshev spectral method based on differentiation process to the fourth order equations leads to the corresponding differentiation matrix with large condition numbers. From another aspect, the strategy based on the integral formula of a Chebyshev polynomial could not only create sparsity, but also improve the accuracy, however it requires a lot of computational cost for directly solving high order two-dimensional problems. In this paper, the construction of the Chebyshev approximations is to start from the mix partial derivative uxxyy(x,y) rather than the unknown function u(x,y). The irregular domain is embedded in a domain of rectangle shape and the curve boundary can be efficiently treated by CTMMID. The numerical results show that compared with the existing results, our method yields spectral accuracy, and the main distinguishing feature is reducing the condition number of fourth order equations on rectangle domain from O(N8) to O(N 4). It also appears that CTMMID is effective for the problems on irregular domains.
KW - Biharmonic-type equation
KW - Chebyshev tau meshless method
KW - Condition number
KW - Integration-differentiation
KW - Irregular domain
KW - Multiple boundary conditions
UR - http://www.scopus.com/inward/record.url?scp=84864371338&partnerID=8YFLogxK
U2 - 10.1016/j.enganabound.2012.06.005
DO - 10.1016/j.enganabound.2012.06.005
M3 - Article
AN - SCOPUS:84864371338
SN - 0955-7997
VL - 36
SP - 1787
EP - 1798
JO - Engineering Analysis with Boundary Elements
JF - Engineering Analysis with Boundary Elements
IS - 12
ER -