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Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods

หน่วยงาน Nanyang Technological University, Singapore

รายละเอียด

ชื่อเรื่อง : Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods
นักวิจัย : An, Xinmei , Zhao, Zhiye , Zhang, H. H. , Li, L. X.
คำค้น : -
หน่วยงาน : Nanyang Technological University, Singapore
ผู้ร่วมงาน : -
ปีพิมพ์ : 2555
อ้างอิง : An, X. M., Zhao, Z. Y., Zhang, H. H., & Li, L. X. (2012). Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods. Computer Methods in Applied Mechanics and Engineering, 233-236, 137-151. , 0045-7825 , http://hdl.handle.net/10220/10806 , http://dx.doi.org/10.1016/j.cma.2012.04.010
ที่มา : -
ความเชี่ยวชาญ : -
ความสัมพันธ์ : Computer methods in applied mechanics and engineering.
ขอบเขตของเนื้อหา : -
บทคัดย่อ/คำอธิบาย :

A known problem of partition of unity-based generalized finite element methods is the linear dependence of the approximation space, which leads to singular stiffness matrix. Up to now, the linear dependence problem has not been fully understood and an efficient way to alleviate it is not available. In our previous paper “Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes” [Comput. Methods Appl. Mech. Engrg. 200 (2011) 665–674], the origin of the linear dependence problem was first dissected and then a method was proposed to reliably predict the rank deficiency of the linearly dependent global approximations of two-dimensional partition of unity-based generalized finite element methods. This paper extends the previous work to three-dimensional cases. The linear dependence problem is first investigated at an element level and then extended to the whole mesh. Derivation of general formulations in a three-dimensional setting is undoubtedly more challenging than a two-dimensional setting because of the complicated element topology. The principle of the increase of rank deficiency is once more applied. The methodology of summing up the added rank deficiency of each element as that of the whole mesh is further proved to be valid in three-dimensional cases. This work together with the previous work is regarded as the essential step to successfully and completely solve the linear dependence problem in partition of unity-based finite element methods.

บรรณานุกรม :
An, Xinmei , Zhao, Zhiye , Zhang, H. H. , Li, L. X. . (2555). Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods.
    กรุงเทพมหานคร : Nanyang Technological University, Singapore.
An, Xinmei , Zhao, Zhiye , Zhang, H. H. , Li, L. X. . 2555. "Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods".
    กรุงเทพมหานคร : Nanyang Technological University, Singapore.
An, Xinmei , Zhao, Zhiye , Zhang, H. H. , Li, L. X. . "Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods."
    กรุงเทพมหานคร : Nanyang Technological University, Singapore, 2555. Print.
An, Xinmei , Zhao, Zhiye , Zhang, H. H. , Li, L. X. . Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods. กรุงเทพมหานคร : Nanyang Technological University, Singapore; 2555.