Partition of Unity Finite Element Method for Short Wave Propagation in Solids
-
摘要: 提出了固体中短波传播数值模拟的单位分解有限元法.有限元空间由形成单位分解的标准等参有限元形函数乘以定义为局部子空间基函数的特殊形函数构成.特殊形函数使试空间中包含了关于波动方程的已有知识,因而在单个单元内能近似地再现高度振荡性质.数值例题显示了所提出单位分解有限元在计算精度和效率上的良好性能.Abstract: A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
-
[1] Deraemaeker A,Babuska I,Bouillard P. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimension[J].Internat J Numer Methods Engrg,1999,46(4):471—499. doi: 10.1002/(SICI)1097-0207(19991010)46:4<471::AID-NME684>3.0.CO;2-6 [2] Zienkiewicz O C.Achievements and some unsolved problems of the finite element method[J].Internat J Numer Methods Engrg,2000,47(1):9—28. doi: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P [3] Melenk J M,Babuska I.The partition of unity finite element method—basic theory and applications[J].Comput Methods Appl Mech Engrg,1996,139(3):289—314. doi: 10.1016/S0045-7825(96)01087-0 [4] Duarte C A M,Oden J T.An hp adaptive method using clouds[J].Comput Methods Appl Mech Engrg,1996,139(3):237—262. doi: 10.1016/S0045-7825(96)01085-7 [5] Ortiz P,Sanchez E.An improved partition of unity finite element model for diffraction problems[J].Internat J Numer Methods Engrg,2001,50(12):2727—2740. doi: 10.1002/nme.161 [6] Laghrouche O,Bettess P,Astley R J.Modelling of short wave diffraction problems using approximating system of plane waves[J].Internat J Numer Methods Engrg,2002,54(10):1501—1533. doi: 10.1002/nme.478 [7] Durate C A,Babuska I,Oden J T.Generalized finite element methods for three-dimensional structural mechanics problems[J].Computers and Structure,2000,77(2):215—232. doi: 10.1016/S0045-7949(99)00211-4 [8] Strouboulis T,Babuska I,Copps K.The design and analysis of the generalized finite element method[J].Comput Methods Appl Mech Engrg,2000,181(1):43—69. doi: 10.1016/S0045-7825(99)00072-9
计量
- 文章访问数: 3029
- HTML全文浏览量: 179
- PDF下载量: 657
- 被引次数: 0