波传播的单位分解有限元法
|
摘要
弹性波传播问题的研究在许多科学和技术领域都有着广泛的应用。例如:通过研究弹性波传播中的衍射现象来解释和研究结构中的动应力集中问题:通过研究真实或人工地震产生的波动以了解地球的内部结构;通过研究地下间断的反射波可以大概地知道可能含油的地层;对材料和结构进行无损探伤;在土木工程领域对地基和地下建筑进行强度和结构分析;在医学上对人体物理信息探测所使用的最普遍的B超和CT等等都与弹性波传播理论有着密切的关系。
有限单元法是求解波传播问题的主要数值方法之一。虽然它有很多优点,并成功地模拟了很多波传播问题,但同样存在许多不足之处。事实上,Zienkiewicz把短波问题的数值模拟视为有限元法尚未解决的两个主要问题之一。例如,为使结果达到可接受的程度,一般说来低阶的有限单元每个波长需要至少布置10个节点。由此导致计算时需要的内存较大,耗时较多,计算效率低下。并且,低阶的有限单元有比较严重的频散特性,高阶的有限单元则可能产生虚假的波动。单位分解有限元法(PUFEM)是近十年来发展起来的数值方法,它使得有限元插值空间中可以包含所求问题解的已知解析信息。因此它可以胜任许多传统有限元方法不能处理得很好或者需要非常大计算量的问题。
本文首先回顾了PUFEM的理论基础和现有工作,然后针对传统有限元法模拟短波传播问题的严重局限性,利用PUFEM插值空间中可包含所求问题解的已知信息的特点,主要进行了以下工作:1.首次发展了一种用于瞬态弹性波传播数值模拟的单位分解有限元模型,有限元空间由形成单位分解的标准有限单元形函数乘以定义为局部子空间基函数的简谐振荡形函数构成。2.针对PUFEM单元矩阵中的被积函数具有强烈的振荡特性,应用直角坐标下的标准有限元形函数和单元内的波动方向知识提出了一种新的单元矩阵解析积分方案。3.将PUFEM应用于反平面剪切波的传播和散射问题中。对已知波传播方向时单位分解有限元如何选择局部子空间中的波数k给出了建议。4.在Zienkiewicz和Shiomi的用于高速动力过程分析的饱和多孔介质广义Biot理论u-U公式的基础上,推导和建立了基于PUFEM的饱和多孔介质动力问题的离散方程。5.在大型通用有限元分析程序LAGAMINE的框架下,编制了用于二维波传播数值模拟的PUFEM程序。数值例题显示在相同精度下,PUFEM的计算效率明显高于传统的有限元法。解析积分在计算效率上也比高斯—勒让德数值积分有大幅度的提高。各章的内容安排如下:
第一章首先对有限差分法、伪谱法、有限元法、无限元法、边界元法、谱单元法和格子法等各种用于波传播的数值方法做了简单的回顾,接下来着重介绍了以单位分
The theory of elastic wave propagation can be applied to a variety of fields of science and technology, such as dynamic stress concentration in the structure, earthquake in seismology, oil exploration in geophysics, nondestructive evaluation of materials, strength and structure analysis in civil engineering, CT in medicine etc.The finite element method is one of the most effective numerical methods to simulate wave propagation problems. But there still have some unsolved problems. Indeed Zienkiewicz regarded the numerical simulation of the short wave problem as one of the two main unsolved problems of FEM. It is known that the choice of around 10 nodal points per wavelength is usually recommended to obtain an acceptable level of accuracy in order to solve the elastic wave equation. Consequently, this issue presents a severe limitation on the application of the FE procedure to the numerical simulation of the short wave problems in practice since the computational time needed is prohibitively expensive. In addition, it was reported that low-order finite elements exhibit poor dispersion properties, while higher-order finite elements raise some troublesome problems like the occurrence of spurious waves.Partition of unity finite element method (PUFEM), which was developed and studied in last decade, has the ability to include a priori knowledge about the local behavior of the solution in the finite element space. It enables us to construct finite element spaces that perform very well in cases where the classical finite element methods fail or are prohibitively expensive.In the dissertation, the mathematical foundation and recent work of PUFEM are reviewed firstly. Then, PUFEM was used to study the numerical simulation of elastic wave propagation as follows. (1) A PUFEM model is developed for the numerical simulation of transient elastic wave propagation. The finite element spaces are constructed by multiplying the standard finite element shape functions, which form a partition of unity, with the harmonic shape functions defined as the bases of the subspaces, which consist of a set of plane waves traveling in prescribed directions. (2) A special integration scheme, which is analytic for the elements with straight edges and semi-analytic for the elements with curved edges, for computing element matrices with the oscillatory nature of the integrands is developed. (3) The PUFEM model was used to simulate the wave propagation and scattering problem of anti-plane wave. The proper choice of the wave number k in the subspace of discretization approximation is discussed when the directions of wave propagation are
known. (4) A PUFEM model in the frame of generalized Biot u-U formulations proposed by Zienkiewicz and Shiomi is developed to simulate the problem of wave propagation in the saturated porous media when the fluid is compressible. (5) A program of PUFEM was developed to simulate the wave propagation in two dimensions in the framework of LAGAMINE, which is a general FEM code. The results of numerical examples exhibit that PUFEM is more efficient than FEM and the derived analytic integration scheme used for PUFEM saves a great deal of computational time as compared with standard Gauss-Legendre integration scheme. The present dissertation is outlined with the following chapters.In chapter 1, the numerical methods for simulating wave propagation are surveyed, such as finite difference method, pseudo-spectral method, finite element method, infinite element method, boundary element method, spectral element method and grid method etc. The PUFEM and its recent developments are discussed. Some existing work used to simulate wave propagation in the saturated porous media is also briefly reviewed. At the last of the chapter, the contents of the dissertation are outlined.In chapter 2, the theory and application of PUFEM are surveyed briefly. The concept of PUFEM is introduced after the discussion on the property of FEM approximation. The mathematical foundation of PUFEM and the relation of PUFEM to other numerical methods are presented. The applications of PUFEM to both Crack and the wave propagation problems are introduced in detail.In chapter 3, the PUFEM model for simulating transient elastic wave propagation is investigated. It is remarked that the existing work on PUFEM for simulations of wave propagations are only limited to steady-state scalar problems. The Shape function spaces of PUFEM for transient analysis are constructed, that makes the model able to directly handle the essential boundary conditions as it does in FEM. In each local shape function subspace, the wave direction and the wave number can be specified individually for a nodal point. The ill-conditioning problem of the effective stiffness matrix is also discussed in this chapter.In chapter 4, an analytic integration scheme for the element matrix in PUFEM is studied. The integrand of the matrix has highly oscillatory property; few existing integration schemes are successful in view of both accuracy and efficiency in computation. Here, a special integration scheme for computing the oscillatory function is developed. The integration scheme is analytic for the elements with straight edges and semi-analytic for the elements with curved edges. Therefore, the computational efficiency of the PUFEM is further enhanced as compared with the PUFEM using standard Gauss-Legendre integration scheme.
In chapter 5, PUFEM is used to simulate the propagation and scattering problem of anti-plane wave, and the choice of the wave numbers k in the harmonic subspaces is suggested when the directions of wave propagation are known. When the directions of the wave propagation are known, the harmonic shape function subspaces of PUFEM can be enriched by taking different values of the wave number in the given few directions to obtain the numerical results superior to those obtained by the standard FEM in accuracy and efficiency, while the ill-conditioning of the effective stiffness matrix can be alleviated and even avoided. It is noted that the PUFEM can not only well simulate the propagation of a single harmonic wave but also simulate that of the complex wave composed of a number of harmonic waves.In chapter 6, the PUFEM is used to simulate the wave propagation problem in the saturated porous media. A PUFEM model in the frame of generalized Biot u-U formulations proposed by Zienkiewicz and Shiomi is developed to simulate the problem of wave propagation in the saturated porous media when the fluid is compressible. The PUFEM model is used to simulate the elastic wave propagation problems in drained and undrained saturated porous media.In chapter 7, the PUFEM program and data structures of the PUFEM code for simulating the wave propagation in two dimensions are described. The program was developed in the framework of the general FEM code LAGAMINE. Particularly, the functions of main subroutines, the flow charts of the PUFEM analysis, and the format of the data flow are explained and presented.The main contributions of the dissertation are summarized and the further work is suggested in the chapter 8.The work carried out in the dissertation is supported by National Key Basic Research and Development Program (973 Program, No. 2002CB412709) and the National Natural Science Foundation of China (No. 19832010).
有限单元法是求解波传播问题的主要数值方法之一。虽然它有很多优点,并成功地模拟了很多波传播问题,但同样存在许多不足之处。事实上,Zienkiewicz把短波问题的数值模拟视为有限元法尚未解决的两个主要问题之一。例如,为使结果达到可接受的程度,一般说来低阶的有限单元每个波长需要至少布置10个节点。由此导致计算时需要的内存较大,耗时较多,计算效率低下。并且,低阶的有限单元有比较严重的频散特性,高阶的有限单元则可能产生虚假的波动。单位分解有限元法(PUFEM)是近十年来发展起来的数值方法,它使得有限元插值空间中可以包含所求问题解的已知解析信息。因此它可以胜任许多传统有限元方法不能处理得很好或者需要非常大计算量的问题。
本文首先回顾了PUFEM的理论基础和现有工作,然后针对传统有限元法模拟短波传播问题的严重局限性,利用PUFEM插值空间中可包含所求问题解的已知信息的特点,主要进行了以下工作:1.首次发展了一种用于瞬态弹性波传播数值模拟的单位分解有限元模型,有限元空间由形成单位分解的标准有限单元形函数乘以定义为局部子空间基函数的简谐振荡形函数构成。2.针对PUFEM单元矩阵中的被积函数具有强烈的振荡特性,应用直角坐标下的标准有限元形函数和单元内的波动方向知识提出了一种新的单元矩阵解析积分方案。3.将PUFEM应用于反平面剪切波的传播和散射问题中。对已知波传播方向时单位分解有限元如何选择局部子空间中的波数k给出了建议。4.在Zienkiewicz和Shiomi的用于高速动力过程分析的饱和多孔介质广义Biot理论u-U公式的基础上,推导和建立了基于PUFEM的饱和多孔介质动力问题的离散方程。5.在大型通用有限元分析程序LAGAMINE的框架下,编制了用于二维波传播数值模拟的PUFEM程序。数值例题显示在相同精度下,PUFEM的计算效率明显高于传统的有限元法。解析积分在计算效率上也比高斯—勒让德数值积分有大幅度的提高。各章的内容安排如下:
第一章首先对有限差分法、伪谱法、有限元法、无限元法、边界元法、谱单元法和格子法等各种用于波传播的数值方法做了简单的回顾,接下来着重介绍了以单位分
The theory of elastic wave propagation can be applied to a variety of fields of science and technology, such as dynamic stress concentration in the structure, earthquake in seismology, oil exploration in geophysics, nondestructive evaluation of materials, strength and structure analysis in civil engineering, CT in medicine etc.The finite element method is one of the most effective numerical methods to simulate wave propagation problems. But there still have some unsolved problems. Indeed Zienkiewicz regarded the numerical simulation of the short wave problem as one of the two main unsolved problems of FEM. It is known that the choice of around 10 nodal points per wavelength is usually recommended to obtain an acceptable level of accuracy in order to solve the elastic wave equation. Consequently, this issue presents a severe limitation on the application of the FE procedure to the numerical simulation of the short wave problems in practice since the computational time needed is prohibitively expensive. In addition, it was reported that low-order finite elements exhibit poor dispersion properties, while higher-order finite elements raise some troublesome problems like the occurrence of spurious waves.Partition of unity finite element method (PUFEM), which was developed and studied in last decade, has the ability to include a priori knowledge about the local behavior of the solution in the finite element space. It enables us to construct finite element spaces that perform very well in cases where the classical finite element methods fail or are prohibitively expensive.In the dissertation, the mathematical foundation and recent work of PUFEM are reviewed firstly. Then, PUFEM was used to study the numerical simulation of elastic wave propagation as follows. (1) A PUFEM model is developed for the numerical simulation of transient elastic wave propagation. The finite element spaces are constructed by multiplying the standard finite element shape functions, which form a partition of unity, with the harmonic shape functions defined as the bases of the subspaces, which consist of a set of plane waves traveling in prescribed directions. (2) A special integration scheme, which is analytic for the elements with straight edges and semi-analytic for the elements with curved edges, for computing element matrices with the oscillatory nature of the integrands is developed. (3) The PUFEM model was used to simulate the wave propagation and scattering problem of anti-plane wave. The proper choice of the wave number k in the subspace of discretization approximation is discussed when the directions of wave propagation are
known. (4) A PUFEM model in the frame of generalized Biot u-U formulations proposed by Zienkiewicz and Shiomi is developed to simulate the problem of wave propagation in the saturated porous media when the fluid is compressible. (5) A program of PUFEM was developed to simulate the wave propagation in two dimensions in the framework of LAGAMINE, which is a general FEM code. The results of numerical examples exhibit that PUFEM is more efficient than FEM and the derived analytic integration scheme used for PUFEM saves a great deal of computational time as compared with standard Gauss-Legendre integration scheme. The present dissertation is outlined with the following chapters.In chapter 1, the numerical methods for simulating wave propagation are surveyed, such as finite difference method, pseudo-spectral method, finite element method, infinite element method, boundary element method, spectral element method and grid method etc. The PUFEM and its recent developments are discussed. Some existing work used to simulate wave propagation in the saturated porous media is also briefly reviewed. At the last of the chapter, the contents of the dissertation are outlined.In chapter 2, the theory and application of PUFEM are surveyed briefly. The concept of PUFEM is introduced after the discussion on the property of FEM approximation. The mathematical foundation of PUFEM and the relation of PUFEM to other numerical methods are presented. The applications of PUFEM to both Crack and the wave propagation problems are introduced in detail.In chapter 3, the PUFEM model for simulating transient elastic wave propagation is investigated. It is remarked that the existing work on PUFEM for simulations of wave propagations are only limited to steady-state scalar problems. The Shape function spaces of PUFEM for transient analysis are constructed, that makes the model able to directly handle the essential boundary conditions as it does in FEM. In each local shape function subspace, the wave direction and the wave number can be specified individually for a nodal point. The ill-conditioning problem of the effective stiffness matrix is also discussed in this chapter.In chapter 4, an analytic integration scheme for the element matrix in PUFEM is studied. The integrand of the matrix has highly oscillatory property; few existing integration schemes are successful in view of both accuracy and efficiency in computation. Here, a special integration scheme for computing the oscillatory function is developed. The integration scheme is analytic for the elements with straight edges and semi-analytic for the elements with curved edges. Therefore, the computational efficiency of the PUFEM is further enhanced as compared with the PUFEM using standard Gauss-Legendre integration scheme.
In chapter 5, PUFEM is used to simulate the propagation and scattering problem of anti-plane wave, and the choice of the wave numbers k in the harmonic subspaces is suggested when the directions of wave propagation are known. When the directions of the wave propagation are known, the harmonic shape function subspaces of PUFEM can be enriched by taking different values of the wave number in the given few directions to obtain the numerical results superior to those obtained by the standard FEM in accuracy and efficiency, while the ill-conditioning of the effective stiffness matrix can be alleviated and even avoided. It is noted that the PUFEM can not only well simulate the propagation of a single harmonic wave but also simulate that of the complex wave composed of a number of harmonic waves.In chapter 6, the PUFEM is used to simulate the wave propagation problem in the saturated porous media. A PUFEM model in the frame of generalized Biot u-U formulations proposed by Zienkiewicz and Shiomi is developed to simulate the problem of wave propagation in the saturated porous media when the fluid is compressible. The PUFEM model is used to simulate the elastic wave propagation problems in drained and undrained saturated porous media.In chapter 7, the PUFEM program and data structures of the PUFEM code for simulating the wave propagation in two dimensions are described. The program was developed in the framework of the general FEM code LAGAMINE. Particularly, the functions of main subroutines, the flow charts of the PUFEM analysis, and the format of the data flow are explained and presented.The main contributions of the dissertation are summarized and the further work is suggested in the chapter 8.The work carried out in the dissertation is supported by National Key Basic Research and Development Program (973 Program, No. 2002CB412709) and the National Natural Science Foundation of China (No. 19832010).
引文
1.黎在良,刘殿魁。固体中的波。第1版,北京,科学出版社,1995,28
2. Karl F. Graff. Wave motion in elastic solids. First edition, American, Ohio state university press, 1975, 3-8
3.杨桂通,张善元。弹性动力学。第1版,中国铁道出版社,1988,3-5
4. Julius Miklowitz. Elastic waves and waveguides. First edition, Amsterdam, North-holland publishing company, 1978, 2-12
5. Z. Alterman, F. C. Karal. Propagation of elastic waves in layered media by finite difference methods. Bull. Seism. Soc. Am, 1968, 58: 367-398
6. Z. Alterman, D. Loewenthal. Seismic wave in a quarter and three quarter plane. Geophys. J. Roy. Astr. Soc., 1970, 20: 101-126
7. D. M. Boore. Finite-difference methods for seismic wave propagation in heterogeneous materials. in Methods in Computational physics. 1972, 11. B. A. Bolt, ed., Academic Press, Inc.
8. R. M. Alford, K. Kelly, D. Boore. Accuracy of finite difference modeling of the acoustic wave equation. Geophysics, 1974, 39: 834-842
9. J. Virieux. SH-wave propagation in heterogeneous media: Velocity-stress finite difference method. Geophysics, 1984, 49: 1933-1957
10. J. Virieux. P-SV wave propagation in heterogeneous media: Velocity-stress finite difference method. Geophysics, 1986, 51: 889-901
11. A. R. Levander. Fourth-order finite difference P-SV Seismograms. Geophysics, 1988, 53: 1425-1436
12. E. Crase. High-order(space and time) finite-difference modeling of elastic wave equation. Expand Abstract of 60th SEG Mth, 1990, 987-991
13. R. W. Graves. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bull. Seism. Soci. Am., 1996, 86(4): 1091-1106
14. S. A. Magnier, R Mora, Tarantola. Finite difference on minimal grids. Geophysics, 1994, 59: 1435-1443
15.周家纪,贺振华。模拟地震波传播的大网格快速差分算法。地球物理学报,1994,37:450-454
16.周家纪,王铎。用最佳差分方法计算P-SV波。哈尔滨工业大学学报,1994,26(1):85-89
17. Jianfeng Zhang. Quadrangle-grid velocity-stress finite-difference method for elastic-wave-propagation simulation. Geophys. J. Int., 1997, 131: 127-134
18.张剑锋。弹性波数值模拟的非规则网格差分法。地球物理学报,1998,41:357-366
19.孙卫涛,杨慧珠。双相各向异性介质弹性波场有限差分正演模拟。固体力学学报,2004,25(1):21-28
20.孙卫涛,杨慧珠,舒继武。非均匀介质弹性波动方程的不规则网格有限差分方法。计算力学学报,21(2):135-142
21.田小波,吴庆举,曾融生。弹性波场数值模拟的隐式差分多重网格算法。地球物理学报,47(1):81-87
22.王秀明,张海澜。用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法。中国科学,G辑,2004,34(5):481-493
23.裴正林。任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟。石油地球物理勘探,39(6):629-635
24. H. Kreiss, J. Oliger. Comparison of accurate methods for the integration of hyperbolic equations. Tellus, 1972, 24: 199-215
25. S. A. Orszag. Comparison of pseudospectral and spectral approximation. Stud. Appl. Math., 1972, 51: 253-259
26. J. Gazdag. Modeling of the acoustic wave equation with transform method. Geophysics, 1981, 46(6): 854-859
27. D. Kosloff, E. Baysal. Forward modeling by a fourier method. Geophysics, 1982, 47: 1402-1412
28. B. Fornberg. The pseudospectral method: Comparisons with finite differences for the elastic wave equation. Geophysics, 1987, 52: 483-501
29. E. Tessmer, D. Kosloff. A. Behle. Elastic wave propagation simulation in the presence of surface topography. Geophys. J. Int., 1992, 108: 621-632
30. E. Tessmer, D. Kosloff. 3-D elastic modeling with surfacee topography by a Chebychev spectral method. Geophysics, 1994, 59: 464-473
31.侯安宁,何樵登.各向异性介质中弹性波传播特征的伪谱法模拟研究.石油物探,1993,34(2):36-45
32.石玉梅。流体饱和多孔介质中弹性波运动方程的解—伪谱法,西南石油学院学报,1995,17(1):34-37
33.傅旦丹,何樵登。正交各向异性介质地震弹性波场的伪谱法正演模拟。石油物探。2001,40(3):8-14
34.马永旺,詹正彬,顾汉明。伪谱法地震波传播数值模拟。石油物探,2001,40(2):42-48
35.张光莹。含分布裂缝岩石的本构及波传播特性研究。工学博士论文,国防科技大学,2003
36.张光莹,曾新吾。伪谱法模拟各向异性/非均质介质中弹性波的传播。国防科技大学学报,2002,24:18-22
37.马德堂,朱光明。有限元法与伪谱法混合求解弹性波动方程。地球科学与环境学报,2004,26(1):61-64
38.寇哲君,程建钢,黄文彬,姚振汉。结构动力分析显隐式混合积分并行算法及实现。清华大学学报,1999,39(4):21-24
39. T. Belytschko and T. J. R. Hughes. Computational methods in mechanics. First Edition, Elsevier, Amsterdam, 1983
40. Claes Johnson. Discontinuous Galerkin finite element methods for second order hyperbolic problems. Computer Methods in Applied Mechanics and Engineering. 1993, 107: 117-129
41. Torbjorn Ekevid and Nils-Erik Wiberg, Wave propagation-explicit code for parallel computing, European congress on computational methods in applied sciences and engineering, Barcelona, 11-14 September 2000
42. T. J. R. Hughes, G. M. Hulbert. Space-time finite element methods for elastodynamics: Formulations and error estimates. Comput. Methods Appl. Mech. Engrg., 1988, 66: 339-363
43. G. M. Hulbert, T. J. R. Hughes. Space-time finite element methods for second-order hyperbolic equations. Comput. Methods Appl. Mech. Engrg., 1990, 84: 327-348
44. G. M. Hulbert. Time finite element methods for structural dynamics. Int. J. Numer. Methods Eng., 1992, 33: 307-331
45. G. M. Hulbert. Space-time finite element methods for second order hyperbolic equations. Comput. Ph. D. Thesis, Department of Mechanical Engineering, Stanford University, Stanford, 1989
46. Wiberg NE, Li XD. Adaptive finite element procedures for linear and non-linear dynamics. Int. J. Numer. Methods Eng., 1999, 46: 1781-1802
47. Li XD, Wiberg NE. Structural dynamic analysis by a time-discontinuous Galerkin finite element method. Int. J. Numer. Methods Eng., 1996, 39: 2131-2152
48. Li XD, Wiberg NE. Implementation and adaptivity of a space-time finite element method for structural dynamics. Comput. Methods Appl. Mech. Eng., 1998, 156: 211-229
49. Xikui Li, Dongmei Yao, R. W. Lewis. A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media. Int. J. Numer. Methods Eng. 2003, 57: 1775-1800
50.李锡夔,姚冬梅。弹塑性结构动力学和波传播问题的间断Galerkin有限元法。固体力学学报,2003,24(4):399-409
51.廖振鹏,杨光。稳态SH波动的有限元模拟。地震学报,1994,16(1):96-105
52.李小军,廖振鹏,关慧敏。粘弹性场地地形对地震动影响分析的显式有限元—有限差分方法。地震学报,1995,17(3):362-369
53.景立平,廖振鹏。波动方程的应力-速度有限元解耦交叠格式。地震工程与工程振动,2000,20(4):1-7
54.廖振鹏。透射边界与无穷远辐射条件。中国科学E辑,2001,31(3):254-262
55.廖振鹏。工程波动导论。第2版,北京,科学出版社,2002
56.廖振鹏。近场波动的数值模拟。力学进展,1997,27(2):193-212
57.张剑锋。一种高精度有限元弹性波场正演方法。石油地球物理勘探,1994,29(1):29-36
58.杨光,刘增武。地下隧道工程地震动分析的有限元—人工透射边界方法。工程力学,1994,11(4):122-130
59. Lei Jiang, J. B. Haddow. A finite element solution of plane wave propagation in inhomogeneous linear viscoelastic solids. Journal of Sound and Vibration, 1995, 184(3): 429-438
60. G. W. Ma, H. Hao, Y. X. Zhou, Modeling of wave propagation induced by underground explosion. Computers and Geotechnics, 1998, 22(3/4): 283-303
61. J. A. Smirnova, L. V. Zhigilei, B. J. Garrison. A combined molecular dynamics and finite element method technique applied to laser induced pressure wave propagation. Compute Physics Communications, 1999, 118: 11-16
62. J. F. Semblat, J. J. Brioist. Efficiency of higher order finite elements for the analysis of seismic wave propagation. Journal of Sound and Vibration, 2000, 231(2): 460-467
63.刘天云,刘光廷,刘颖黎。无限域波动问题的有限元模型。工程力学,2002,19(2):22-25
64. A. Zerwer, M. A. Polak, J. C. Santamarina. Rayleigh wave propagation for the Detection of Near Surface Discontinuities: finite element Modeling. Journal of Nondestructive Evaluation, 2003, 22(2): 39-52
65. K. Morgan, O. Hassan, J. Peraire. A time domain unstructured grid approach to simulation of electromagnatic scattering in piecewise homogeneous media. Computer Methods in Applied Mechanics and Engineering, 1996, 134: 17-36
66. K. Morgan, P. J. Brookes, O. Hassan and N. P. Weatherill. Parallel processing for the simulation of problems involving scattering of electromagnetic waves, Compt. Meth. Appl. Mech. Eng., 1998, 152: 157-174
67. K. J. Marfurt. Accuracy of finite-difference and finite-element modeling of the scalar wave equations. Geophysics, 1984, 49: 533-549
68. K. J. Marfurt. Analysis of higher order finite-element methods. Numerical Modeling of Seismic Wave Propagation, Society of Exploration Geophysicists, K. R. Kelly, K. J. Marfurt (Eds.), 1990, 516-520.
69. W. A. Mulder. Spurious modes in finite-element discretizations of the wave equation may not be all that bad. Appl. Numer. Math., 1999, 30: 425-445
70. M. N. Guddati and B. Yue. Modified integration rules for reducing dispersion error in finite element methods. Comp. Methods Appl. Mech. Eng., 2004, 193: 275-287
71. A. Deraemaeker, I. Babuska, P. Bouillard. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimension. Int. J. Numerical Methods Eng. 1999, 46(4): 471-499
72. F. Ihlenburg, I. Babuska. Finite element solution to the Helmholtz equation with high wavenumber part Ⅰ: the h-version of the FEM. Computers Math. Applic. 1995, 30: 9-37
73. F. Ihlenburg, I. Babuska. Finite element solution of the Helmholtz equation with high wave number part Ⅱ: the h-p version of the FEM. SIAM J. Numer. Anal. 1997, 34: 315-358
74. O. C. Zienkiewicz. Achievements and some unsolved problems of the finite element method. Int. J. Numerical Methods Eng. 2000, 47: 9-28
75.应隆安。无限元方法。第1版,北京,北京大学出版社,1992
76. P. Bettess, O. C. Zienkiewicz. Diffraction and refraction of surface waves using finite and infinite elements. International Journal for Numerical Methods in Engineering. 1977, 11: 1271-1290
77. P. Bettess. Infinite Elements. First edition, Penshaw Press, Sunderland, U. K., 1992.
78. R. J. Astley, W. Eversman. Finite element formulations for acoustical radiation. Journal of Sound and Vibration, 1983, 88: 47-64
79. R. J. Astley. Wave envelope and infinite elements for acoustical radiation. International Journal for Numerical Methods in Fluids, 1983, 3: 507-526
80. R. J. Astley. Finite element, wave envelope formulation for acoustical radiation in moving flows. Journal of Sound and Vibration, 1985, 13: 471-485
81. A. V. Parrett, W. Eversman. Wave envelope and finite element approximations for turbofan noise radiation in flight. AIAA Journal, 1986, 24: 753-760
82. O. C. Zienkiewicz, K. Bando, P. Bettess, C. Emson, T. C. Chiam. Mapped infinite elements for exterior wave problems. International Journal for Numerical Methods in Engineering, 1985, 21: 1229-1252
83. J. Gorranson, C. Davidsson. Three dimensional infinite elements for wave propagation. Journal of Sound and Vibration, 1987, 115: 556-559.
84. E. T. Moyer. Performance of mapped infinite elements for exterior wave scattering applications. Communications in Applied Numerical Methods, 1992, 8: 27-39
85. D. S. Burnett. Three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. Journal of The Acoustical Society of America, 1994, 96: 2798-2816
86. R. J. Astley. Mapped spheroidal elements for unbounded wave problems. International Journal for Numerical Methods in Engineering, 1998, 41: 1235-1254
87. L. G. Olson, K-J Bathe. Infinite element for transient fluid-structure interactions. Engineering Computation 1985, 2: 319-329
88. T. L. Geers. Doubly asymptotic approximations for transient motions of submerged structures. Journal of The Acoustical Society of America, 1978, 64: 1500-1508
89. R. J. Astley. A transient infinite element for Multi-dimensional acoustic radiation. DE Vol. 84-2, Design Engineering Technical Conference, Vol. 3 Part B, ASME, 1995; 97-111
90. R. J. Astley. Transient wave envelope elements for wave problems. Journal of Sound and Vibration, 1996, 192: 245-261
91. R. J. Astley, J-P. Coyette, L. Cremers. Three dimensional wave-envelope elements of variable order for acoustic radiation and scattering. Part 2. Formulation in the time domain. Journal of The Acoustical Society of America, 1998, 103: 64-72
92. R. J. Astley. Transient spheroidal elements for unbounded wave problems. Computer Methods in Applied Mechanics and Engineering, 1998; 164(1-2): 3-15
93. R. J. Astley. Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. Int. J. Numer. Meth. Engng, 2000, 49: 951-976
94. C. A. Brebbia. Recent advances in boundary elements. First edition, London, Pentech Press, 1978
95.杜庆华等。我国工程中边界元方法研究的十年。力学与实践,1989,11(1):3-6
96.C.A.Brabbia,王嘉新译。对边界元若干基本概念和重要文献的综述。力学进展,1993,23(1):121-134
97. N. Atalla, R. J. Bernhard. Review of numerical solutions for low-frequency structural-acoustic problems. Applied Acoustics, 1994, 43: 271-294
98. D. E. Bescos. Boundary element methods in dynamic analysis. Applied Mechanics Reviews, 1987, 40: 1-23
99. D. E. Bescos. Boundary element methods in dynamic analysis part Ⅱ(1986-1996). Applied Mechanics Reviews, 1997, 50: 149-197
100.刘恩儒,J.H.Queen,张中杰,陈东。裂缝诱导的多次散射波边界元法模拟。中国科学(E辑),2000,30(5):395-402
101. M. Schanz. Application of 3D time domain boundary element formulation to wave propagation in poroelastic solids. Engineering analysis with boundary elements, 2001, 25: 363-376
102.张楚汉,刘海笑。层状与各向异性介质波动问题的时域边界元法及工程应用。重庆建筑大学学报,2000,22(6):100-104
103.刘海笑,张楚汉。层状介质波动问题的时域边界元模型及实验。清华大学学报(自然科学版),2002,42(2):34-37
104.冯仰德,汪越胜,章梓茂。单侧摩擦约束夹杂物的瞬态弹性波散射的时域边界元分析-反平面情况。固体力学学报,2002,23(3):301-305
105. Y. D. Feng, Y. S. Wang, Z. M. Zhang. Transient scattering of SH waves from an inclusion with a unilateral frictional contact interface-a 2D time domain boundary element analysis. Communications in Numerical Methods in Engineering, 2003, 19(1): 25-36
106.曹志远,曾三平。爆炸波作用下地下防护结构与围岩的非线性动力相互作用分析。爆炸与冲击,2003,23(5):385-390
107.曹志远,曾三平。含地下孔洞层状半空间中瞬态波的传播。同济大学学报,2004,32(2):202-207
108. J. A. M. Carrer, W. J. Mansur. Time-dependent fundamental solution generated by a not impulsive source in the boundary element method analysis of the 2D scalar wave equation. Commun. Numer. Meth. Engng., 2002, 18: 277-285
109. C. D. Wang, M. H. Meylan. A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate. Journal of Fluids and Structures, 2004, 19: 557-572
110. A. T. Patera. A spectral element method for fluid dynamics: laminar flow in a channel expansion. Journal of Computational Physics, 1984, 54: 468-488
111. Y. Maday, A. T. Patera. Spectral element methods for the incompressible Naview-Stokes equations. In State of the Art Survey in Computational Mechanics. Noor AK, Oden JT(eds), 1989: 71-143
112. Geza Seriani. 3-D large-scale wave propagation modeling by spectral element method on Cray T3E multiprocessor. Comput. Methods. Appl. Mech. Engrg., 1998, 164: 235-247
113. R. Al-Khoury, A. Scarpas, C. Kasbergen, J. Blaauwendraad. Spectral element technique for efficient parameter identification of layered media. Part Ⅰ. Forward calculation. International Journal of Solids and Structures, 2001, 38: 1605-1623.
114. R. Al-Khoury, C. Kasbergen, A. Scarpas, J. Blaauwendraad. Spectral element technique for efficient parameter identification of layered media. Part Ⅱ. Inverse calculation. International Journal of Solids and Structures, 2001, 38: 8753-8772.
115. R. Al-Khoury, C. Kasbergen, A. Scarpas, J. Blaauwendraad. Poroelastic spectral element for wave propagation and parameter identification in multi-layer systems. International Journal of Solids and Structures, 2002, 39: 4073-4091
116. A. Chakraborty, S. Gopalakrishnan. A spectrally formulated finite element for wave propagation analysis in layered composite media. International Journal of Solids and Structures, 2004, 41: 5155-5183
117. D. Komatitsch, J. P. Vilotte, R. Vai, J. Castillo-Covarrubias, F. Sanchez-Sesma. The spectral element method for elastic wave equations-Application to 2-D and 3-D seismic problems. Int. J. Numer. Meth. Engng., 1999, 45: 1139-1164
118. Dimitri Komatitsch and Jeroen Tromp. Spectral-element simulations of global seismic wave propagation, Part Ⅰ: Validation. Geophysical Journal International, 2002, 149: 390-412
119. Dimitri Komatitsch and Jeroen Tromp. Spectral-element simulations of global seismic wave propagation, Part Ⅱ: 3-D models, oceans, rotation, and gravity. Geophysical Journal International, 2002, 150: 303-318
120. J. Zhang, T. Liu. P-SV wave propagation in heterogeneous media: grid method. Geophys. J. Int., 1999, 136: 431-438.
121.张剑锋,刘铁林。三维非均匀介质中弹性波传播的数值模拟。固体力学学报,2001,22(4):356-360
122. T. Liu, K. Liu and J. Zhang, Unstructured grid method for stress wave propagation in elastic media. Comp. Methods Appl. Mech. Eng., 2004, 193: 2427-2452
123. J. H. Lin, W. S. Zhang and F. W. Williams, Pseudo-excitation algorithm for non-stationary random seismic responses, Engineering Structures, 1994, 16(4): 270-276
124. J. H. Lin, Y. Zhao and Y. H. Zhang. Accurate and highly efficient algorithms for structural stationary/ non-stationary Random responses. Computer Method in Applied Mechanics and Engineering, 2001, 191(1-2): 103～111
125.林家浩,张亚辉。随机振动的虚拟激励法。第一版,北京,科学出版社,2004
126. W. X. Zhong, J. H. Lin, Q. Gao. The Precise Computation for Random Wave Propagation in Stratified Materials. World Conference of Computational Mechanics-5(WCCM-V), Vienna 2002
127.钟万勰,纪峥。理性有限元。计算结构力学及其应用,1996,13(1):1-8
128.钟万勰,纪峥。平面理性元的收敛性证明。计算力学学报,1997,29(6):676-685
129. J. M. Melenk. On generalized finite element methods. Ph. D dissertation, University of Maryland, College Park, MD, 1995
130. J. M. Melenk and I. Babuska. The partition of unity finite element method: Basic theory and applications. Comp. Methods Appl. Mech. Eng. 1996, 139: 289-314
131. J. M. Melenk and I. Babuska. The partition of unity finite element method. Int. J. Numerical Methods Eng. 1997, 40: 727-758
132. C. A. M. Duarte. The hp cloud method. Ph. D. dissertation, University of Texas at Austin, TX, 1996
133. C. A. M. Duarte and J. T. Oden. An hp adaptive method using clouds. Comp. Methods Appl. Mech. Eng. 1996, 139: 237-262
134. J. T. Oden, C. A. M. Duarte and O. C. Zienkiewicz. A new cloud-based hp finite element method. Comp. Methods Appl. Mech. Eng. 1998, 153: 117-126
135.梁国平,何江衡。广义有限元法——类新的逼近空间。力学进展,1995,25(4):562-565
136. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45: 601-620
137. Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46: 131-150
138.栾茂田,田荣,杨庆。广义节点有限元法。计算力学学报。2000,17(2):192-200
139.栾茂田.田荣,杨庆。平面广义四节点等参单元GQ4及其性能探讨。力学学报,2002,34(4):578-585
140. T. strouboulis, K. Copps and I. Babuska. The generalized finite element method: an example of its implementation and illustration of its performance. Int. J. numer. Methods engrg., 2000, 47: 1401-1417.
141. C. A. Duarte, I. Babuska, J. T. Oden. Generalized finite element methods for three-dimensional structural mechanics problems. Computers and Structures, 2000, 77(2): 215-232.
142. T. Strouboulis, I. Babuska and K. Copps. The design and analysis of the Generalized Finite Element Method, Comput. Methods Appl. Mech. Engrg., 2000, 181: 43-69
143.刘欣,朱德懋。基于单位分解的新型有限元方法研究。计算力学学报,2000,17(4):422-427
144.彭自强,王水林,葛修润。单位分解法、无网格法、数值流形方法之形函数的内在联系。岩石力学与工程学报,2002,21(增2):2429-2431
145.彭自强,李小凯,葛修润。广义有限元法对动态裂纹扩展的数值模拟。岩石力学与工程学报,2004,23(18):3132-3137
146. C. A. Duarte, O. N. Hamzeh, T. J. Liszka, W. W. Tworzydlo. A Generalized Finite Element Method for the Simulation of Three-Dimensional Crack Propagation. Comput. Methods Appl. Mech. Engrg., 2001, 190: 2227-2262
147. T. Strouboulis, K. Copps, I. Babuska. The generalized finite element method. Comput. Methods Appl. Mech. Engrg., 2001, 190: 4081-4193
148. T. Strouboulis, L. Zhang, I. Babuska. Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids. Comput. Methods Appl. Mech. Engrg., 2003, 192: 3109-3161
149. I. Babuska, U. Banerjee, J. E. Osborn. On principles for the selection of shape functions for the Generalized Finite Element Method. Comput. Methods Appl. Mech. Engrg., 2002, 191: 5595-5629
150. C. A. Duarte, I. Babuska. Mesh-independent p-orthotropic enrichment using the generalized finite element method. Int. J. Numer. Meth. Engng., 2002, 55: 1477-1492
151. F. B. Barros, S. P. B. Proen, C. S. de Barcellos. On error estimator and p-adaptivity in the generalized finite element method. Int. J. Numer. Meth. Engng., 2004, 60: 2373-2398
152.邵国建,王卫国,苏静波。地下工程开挖计算的广义有限元法。岩石力学与工程学报,2004,23(10):1694-1699
153. T. Strouboulis, L. Zhang and I. Babuska. p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems. Int. J. Numer. Meth. Engng, 2004, 60: 1639-1672
154. J. Fish and Z. Yuan. Multiscale enrichment based on partition of unity. Int. J. Numer. Meth. Engng, 2005, 62: 1341-1359
155. C. Daux, N. Moes, J. Dolbow, N. Sukumar, T. Belytschko. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering, 2000, 48: 1741-1760
156. J. Dolbow. An extended finite element method with discontinuous enrichment for applied mechanics. Ph. D. Thesis, Northwestern University, 1999
157. T. Belytschko, N. Moes, C. Parimi. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering, 2001, 50: 993-1013
158. J. Dolbow, N. Moes, T. Belytschko. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 2000, 36: 235-260
159. N. Sukumar, N. Moes, B. Moran, T. Belytschko. Extended finite element method for three-dimensional crack modeling. International Journal for Numerical Methods in Engineering, 2000, 48(11): 1549-1570
160. N. Sukumar, D. Chopp, N. Moes, T. Belytschko. Modeling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190: 6183-6200
161. M. Stolarska, D. Chopp, N. Moes, T. Belytschko. Modeling crack growth by level sets and the extended finite element method. International Journal for Numerical Methods in Engineering, 2001, 51: 943-960
162. N. Sukumar, D. Chopp, B. Moran. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics, 2003, 70(1): 29-48
163. H. Ji, D. Chopp and J. E. Dolbow. A hybrid extended finite element/level set method for modeling phase transformations. Int. J. Numer. Meth. Engng, 2002, 54: 1209-1233
164. T. Belytschko, C. Parimi, N. Moes, N. Sukumar and S. Usui, Structured Extended Finite Element Methods for Solids Defined by Implicit Surfaces, International Journal for Numerical Methods in Engineering, 2003, 56: 609-635
165.N. Sukumar, Z. Y. Huang, J.-H. Prevost and Z. Suo, Partition of Unity Enrichment for Bimaterial Interface Cracks. International Journal for Numerical Methods in Engineering, 2004, 59: 1075-1102
166.G. Ventura, B. Moran and T. Belytschko, Dislocations by partition of unity. Int. J. Numer. Meth. Engng, 2005, 62: 1463-1487
167.P. Ortiz, E. Sanchez. An improved partition of unity finite element model for diffraction problems. Int. J. Numerical Methods Eng.2001, 50: 2727-2740
168.O. Laghrouche, P. Bettess. Short wave modelling using special finite elements. Journal of Computational Acoustics. 2000, 8:189-210
169.O. Laghrouche, P. Bettess, R.J. Astley. Modelling of short wave diffraction problems using approximating system of plane waves. Int. J. Numerical Methods Eng. 2002, 54: 1501-1533
170.O. Laghrouche, P. Bettess, E. Perrey-Debain and J. Trevelyan. Plane wave basis for wave scattering in three dimension. Communication in Numerical Methods in Engineering, 2003, 19: 715-723
171.E. Perrey-Debain, O. Laghrouche, P. Bettess and J. Trevelyan. Plane wave basis finite elements and boundary elements for three dimensional wave scattering. Phil. Trans. R. Soc. Lond. A, 2004, 362: 561-577
172.R.J. Astley and P. Gamallo, Special short wave elements for flow acoustics, Comput. Methods Appl. Mech. Engrg., 2005, 194: 341-353
173.P. Ortiz. Finite elements using plane wave basis for scattering of surface water waves, Philos. Trans. R.Soc. Lond. A, 2004,362: 525-540
174.P. Bettess. Special wave basis finite elements for very short wave refraction and scattering problems. Commun. Numer. Methods Engrg. 2004, 20: 291-298
175.O. Laghrouche, P. Bettess, E. Perrey-Debain and J. Trevelyan. Wave interpolation finite elements for Helmholtz problems with jumps in the wave speed. Computer Methods in Applied Mechanics and Engineering, 2005, 194: 367-381
176.C. Farhat, 1. Harari, L. Franca. The discontinuous enrichment method. Comput. Meth. Appl. Mech. Engng., 2001, 190:6455-6479
177.C. Farhat, I. Harari, U. Hetmanuk, A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, Comput. Methods Appl. Mech. Engrg. 2003, 192: 1389-1419
178.P. Bettess, J. Shirron, O. Laghrouche, B. Peseux, R. Sugimoto and J. Trevelyan. A numerical integration scheme for special finite elements for the Helmholtz equation. Int. J. Numerical Methods Eng. 2003,56:531-552.
179.R. Sugimoto, P. Bettess and J. Trevelyan. A numerical integration scheme for special quadrilateral finite elements for Helmholtz equation. Communications in Numerical Methods in Eng. 2003, 19:
233-245.
180. E. Perrey-Debain, J. Trevelyan and P. Bettess. Wave boundary elements: a theoretical overview presenting some applications in scatterings of short waves. Engineering Analysis with Boundary Elements, 2004, 28: 131-141
181. C. A. Duarte, J. T. Oden. Hpclouds: a h-p meshless method. Numerical Methods for Partial Differential Equations, 1996, 12: 673-705
182. M. A. Biot. Theory of propagation of elastic waves in a fluid-saturated porous solid Ⅰ: Low frequency range. Journal of the acoustical society of America, 1956, 28(2): 168-178
183. M. A. Biot. Theory of propagation of elastic waves in a fluid-saturated porous solid Ⅱ: Higher frequency range. Journal of the acoustical society of America, 1956, 28(2): 179-191
184. J. Ghaboussi, E. L. Wilson. Variational formulation of dynamics of fluid-saturated porous elastic solids. J. Eng, Mech. Div, ASCE, 1972, 98: 947-963
185. O. C. Zienkiewicz, T. Shiomi. Dynamic behaviour of saturated porous media: The generalized Biot formulation and its numerical solution. Int. J. for Numer. and Anal. Methods in Geomechanics, 1984, 8: 71-96
186. B. R. Simon, JSS Wu, O. C. Zienkiewicz, etal. Evaluation of u-w and u-π finite element methods for the dynamic response of saturated porous media using one-dimensional models. Int. J. Num. Analyt. Meth. Geom., 1986, 10(5): 461-482
187. B. R. Simon, JSS Wu, O. C. Zienkiewicz. Evaluation of higher order, mixed and hermitean finite element procedures for dynamics analysis of saturated porous media using one-dimensional models. Int. J. Num. Analyt. Meth. Geom., 1986, 10(5): 483-499
188.门福录.波在饱水孔隙弹性介质中的传播问题.地球物理学报,1965,14(2):107-114
189.门福录.波在饱含流体的孔隙水介质中的传播问题.地球物理学报,1981,24(1):64-75
190. C. Truesdell, R. A. Toupin. The classical field theories. SpringerVerlag, 1960, Handbuch derphysic bd3(1)
191.R.M.Bowen.混合物理论。第一版,江苏科技出版社,1983
192. R. M. Bowen, K. M. Reinicke. Plane progressive waves in a binary mixture of linear elastic materials. J. Appl. Mech., 1978, 45: 493-499
193. R. M. Bowen. Compressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci., 1982, 20(6): 697-735
194. R. M. Bowen. Plane progressive waves in a heat conducting fluid saturated porous materiall with relaxing porosity. Acta Mechanica, 1983, 46: 189-206
195. W. Derski. Thermomecanique lineaire des milieux poreux. ENSM Nantes. 1982
196.苗天德,朱久江。对饱和多孔介质波动问题中本构关系的探讨。力学学报,1995,27(5):536-543
197.章根德。固体—流体混合物连续介质理论及其在工程上的应用。力学进展,1993,23(1):58-68
198.刘占芳,严波,唐录成。饱和多孔弹性材料中加速度波的传播。重庆大学学报(自然科学版),1998,21(2):7-15
199.严波,刘占芳,张湘伟。流体饱和多孔介质中波传播问题的有限元分析。应用数学和力学,1999,20(12):1235-1244
200.赵成刚,杜修力,崔杰。固体、流体多相多孔介质中的波动理论及其数值模拟的进展。力学进展,1998,28(1):84-92
201.陈少林,廖振鹏。两相介质动力学问题的研究进展。地震工程与工程振动,2002(2):1-8
202.刘颖。冲击荷载作用下含液饱和多孔介质中应力波传播问题的研究。工学博士论文,大连理工大学,2002
203.刘凯欣,刘颖。液饱和多孔介质中三维应力波的传播。力学学报,2003,35(4):469-473
204.李锡夔,张俊波,张洪武。含液体非弹性多孔介质中波传播过程的失稳与逸散性。应用数学和力学,2002,23(1):31-46
205. Xikui Li, Junbo Zhang, Hongwu Zhang. Instabilily of wave propagation in saturated poroelastoplastic media. Int. J. Numer. Anal. Meth. Geomech., 2002, 26: 563-578
2. Karl F. Graff. Wave motion in elastic solids. First edition, American, Ohio state university press, 1975, 3-8
3.杨桂通,张善元。弹性动力学。第1版,中国铁道出版社,1988,3-5
4. Julius Miklowitz. Elastic waves and waveguides. First edition, Amsterdam, North-holland publishing company, 1978, 2-12
5. Z. Alterman, F. C. Karal. Propagation of elastic waves in layered media by finite difference methods. Bull. Seism. Soc. Am, 1968, 58: 367-398
6. Z. Alterman, D. Loewenthal. Seismic wave in a quarter and three quarter plane. Geophys. J. Roy. Astr. Soc., 1970, 20: 101-126
7. D. M. Boore. Finite-difference methods for seismic wave propagation in heterogeneous materials. in Methods in Computational physics. 1972, 11. B. A. Bolt, ed., Academic Press, Inc.
8. R. M. Alford, K. Kelly, D. Boore. Accuracy of finite difference modeling of the acoustic wave equation. Geophysics, 1974, 39: 834-842
9. J. Virieux. SH-wave propagation in heterogeneous media: Velocity-stress finite difference method. Geophysics, 1984, 49: 1933-1957
10. J. Virieux. P-SV wave propagation in heterogeneous media: Velocity-stress finite difference method. Geophysics, 1986, 51: 889-901
11. A. R. Levander. Fourth-order finite difference P-SV Seismograms. Geophysics, 1988, 53: 1425-1436
12. E. Crase. High-order(space and time) finite-difference modeling of elastic wave equation. Expand Abstract of 60th SEG Mth, 1990, 987-991
13. R. W. Graves. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bull. Seism. Soci. Am., 1996, 86(4): 1091-1106
14. S. A. Magnier, R Mora, Tarantola. Finite difference on minimal grids. Geophysics, 1994, 59: 1435-1443
15.周家纪,贺振华。模拟地震波传播的大网格快速差分算法。地球物理学报,1994,37:450-454
16.周家纪,王铎。用最佳差分方法计算P-SV波。哈尔滨工业大学学报,1994,26(1):85-89
17. Jianfeng Zhang. Quadrangle-grid velocity-stress finite-difference method for elastic-wave-propagation simulation. Geophys. J. Int., 1997, 131: 127-134
18.张剑锋。弹性波数值模拟的非规则网格差分法。地球物理学报,1998,41:357-366
19.孙卫涛,杨慧珠。双相各向异性介质弹性波场有限差分正演模拟。固体力学学报,2004,25(1):21-28
20.孙卫涛,杨慧珠,舒继武。非均匀介质弹性波动方程的不规则网格有限差分方法。计算力学学报,21(2):135-142
21.田小波,吴庆举,曾融生。弹性波场数值模拟的隐式差分多重网格算法。地球物理学报,47(1):81-87
22.王秀明,张海澜。用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法。中国科学,G辑,2004,34(5):481-493
23.裴正林。任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟。石油地球物理勘探,39(6):629-635
24. H. Kreiss, J. Oliger. Comparison of accurate methods for the integration of hyperbolic equations. Tellus, 1972, 24: 199-215
25. S. A. Orszag. Comparison of pseudospectral and spectral approximation. Stud. Appl. Math., 1972, 51: 253-259
26. J. Gazdag. Modeling of the acoustic wave equation with transform method. Geophysics, 1981, 46(6): 854-859
27. D. Kosloff, E. Baysal. Forward modeling by a fourier method. Geophysics, 1982, 47: 1402-1412
28. B. Fornberg. The pseudospectral method: Comparisons with finite differences for the elastic wave equation. Geophysics, 1987, 52: 483-501
29. E. Tessmer, D. Kosloff. A. Behle. Elastic wave propagation simulation in the presence of surface topography. Geophys. J. Int., 1992, 108: 621-632
30. E. Tessmer, D. Kosloff. 3-D elastic modeling with surfacee topography by a Chebychev spectral method. Geophysics, 1994, 59: 464-473
31.侯安宁,何樵登.各向异性介质中弹性波传播特征的伪谱法模拟研究.石油物探,1993,34(2):36-45
32.石玉梅。流体饱和多孔介质中弹性波运动方程的解—伪谱法,西南石油学院学报,1995,17(1):34-37
33.傅旦丹,何樵登。正交各向异性介质地震弹性波场的伪谱法正演模拟。石油物探。2001,40(3):8-14
34.马永旺,詹正彬,顾汉明。伪谱法地震波传播数值模拟。石油物探,2001,40(2):42-48
35.张光莹。含分布裂缝岩石的本构及波传播特性研究。工学博士论文,国防科技大学,2003
36.张光莹,曾新吾。伪谱法模拟各向异性/非均质介质中弹性波的传播。国防科技大学学报,2002,24:18-22
37.马德堂,朱光明。有限元法与伪谱法混合求解弹性波动方程。地球科学与环境学报,2004,26(1):61-64
38.寇哲君,程建钢,黄文彬,姚振汉。结构动力分析显隐式混合积分并行算法及实现。清华大学学报,1999,39(4):21-24
39. T. Belytschko and T. J. R. Hughes. Computational methods in mechanics. First Edition, Elsevier, Amsterdam, 1983
40. Claes Johnson. Discontinuous Galerkin finite element methods for second order hyperbolic problems. Computer Methods in Applied Mechanics and Engineering. 1993, 107: 117-129
41. Torbjorn Ekevid and Nils-Erik Wiberg, Wave propagation-explicit code for parallel computing, European congress on computational methods in applied sciences and engineering, Barcelona, 11-14 September 2000
42. T. J. R. Hughes, G. M. Hulbert. Space-time finite element methods for elastodynamics: Formulations and error estimates. Comput. Methods Appl. Mech. Engrg., 1988, 66: 339-363
43. G. M. Hulbert, T. J. R. Hughes. Space-time finite element methods for second-order hyperbolic equations. Comput. Methods Appl. Mech. Engrg., 1990, 84: 327-348
44. G. M. Hulbert. Time finite element methods for structural dynamics. Int. J. Numer. Methods Eng., 1992, 33: 307-331
45. G. M. Hulbert. Space-time finite element methods for second order hyperbolic equations. Comput. Ph. D. Thesis, Department of Mechanical Engineering, Stanford University, Stanford, 1989
46. Wiberg NE, Li XD. Adaptive finite element procedures for linear and non-linear dynamics. Int. J. Numer. Methods Eng., 1999, 46: 1781-1802
47. Li XD, Wiberg NE. Structural dynamic analysis by a time-discontinuous Galerkin finite element method. Int. J. Numer. Methods Eng., 1996, 39: 2131-2152
48. Li XD, Wiberg NE. Implementation and adaptivity of a space-time finite element method for structural dynamics. Comput. Methods Appl. Mech. Eng., 1998, 156: 211-229
49. Xikui Li, Dongmei Yao, R. W. Lewis. A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media. Int. J. Numer. Methods Eng. 2003, 57: 1775-1800
50.李锡夔,姚冬梅。弹塑性结构动力学和波传播问题的间断Galerkin有限元法。固体力学学报,2003,24(4):399-409
51.廖振鹏,杨光。稳态SH波动的有限元模拟。地震学报,1994,16(1):96-105
52.李小军,廖振鹏,关慧敏。粘弹性场地地形对地震动影响分析的显式有限元—有限差分方法。地震学报,1995,17(3):362-369
53.景立平,廖振鹏。波动方程的应力-速度有限元解耦交叠格式。地震工程与工程振动,2000,20(4):1-7
54.廖振鹏。透射边界与无穷远辐射条件。中国科学E辑,2001,31(3):254-262
55.廖振鹏。工程波动导论。第2版,北京,科学出版社,2002
56.廖振鹏。近场波动的数值模拟。力学进展,1997,27(2):193-212
57.张剑锋。一种高精度有限元弹性波场正演方法。石油地球物理勘探,1994,29(1):29-36
58.杨光,刘增武。地下隧道工程地震动分析的有限元—人工透射边界方法。工程力学,1994,11(4):122-130
59. Lei Jiang, J. B. Haddow. A finite element solution of plane wave propagation in inhomogeneous linear viscoelastic solids. Journal of Sound and Vibration, 1995, 184(3): 429-438
60. G. W. Ma, H. Hao, Y. X. Zhou, Modeling of wave propagation induced by underground explosion. Computers and Geotechnics, 1998, 22(3/4): 283-303
61. J. A. Smirnova, L. V. Zhigilei, B. J. Garrison. A combined molecular dynamics and finite element method technique applied to laser induced pressure wave propagation. Compute Physics Communications, 1999, 118: 11-16
62. J. F. Semblat, J. J. Brioist. Efficiency of higher order finite elements for the analysis of seismic wave propagation. Journal of Sound and Vibration, 2000, 231(2): 460-467
63.刘天云,刘光廷,刘颖黎。无限域波动问题的有限元模型。工程力学,2002,19(2):22-25
64. A. Zerwer, M. A. Polak, J. C. Santamarina. Rayleigh wave propagation for the Detection of Near Surface Discontinuities: finite element Modeling. Journal of Nondestructive Evaluation, 2003, 22(2): 39-52
65. K. Morgan, O. Hassan, J. Peraire. A time domain unstructured grid approach to simulation of electromagnatic scattering in piecewise homogeneous media. Computer Methods in Applied Mechanics and Engineering, 1996, 134: 17-36
66. K. Morgan, P. J. Brookes, O. Hassan and N. P. Weatherill. Parallel processing for the simulation of problems involving scattering of electromagnetic waves, Compt. Meth. Appl. Mech. Eng., 1998, 152: 157-174
67. K. J. Marfurt. Accuracy of finite-difference and finite-element modeling of the scalar wave equations. Geophysics, 1984, 49: 533-549
68. K. J. Marfurt. Analysis of higher order finite-element methods. Numerical Modeling of Seismic Wave Propagation, Society of Exploration Geophysicists, K. R. Kelly, K. J. Marfurt (Eds.), 1990, 516-520.
69. W. A. Mulder. Spurious modes in finite-element discretizations of the wave equation may not be all that bad. Appl. Numer. Math., 1999, 30: 425-445
70. M. N. Guddati and B. Yue. Modified integration rules for reducing dispersion error in finite element methods. Comp. Methods Appl. Mech. Eng., 2004, 193: 275-287
71. A. Deraemaeker, I. Babuska, P. Bouillard. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimension. Int. J. Numerical Methods Eng. 1999, 46(4): 471-499
72. F. Ihlenburg, I. Babuska. Finite element solution to the Helmholtz equation with high wavenumber part Ⅰ: the h-version of the FEM. Computers Math. Applic. 1995, 30: 9-37
73. F. Ihlenburg, I. Babuska. Finite element solution of the Helmholtz equation with high wave number part Ⅱ: the h-p version of the FEM. SIAM J. Numer. Anal. 1997, 34: 315-358
74. O. C. Zienkiewicz. Achievements and some unsolved problems of the finite element method. Int. J. Numerical Methods Eng. 2000, 47: 9-28
75.应隆安。无限元方法。第1版,北京,北京大学出版社,1992
76. P. Bettess, O. C. Zienkiewicz. Diffraction and refraction of surface waves using finite and infinite elements. International Journal for Numerical Methods in Engineering. 1977, 11: 1271-1290
77. P. Bettess. Infinite Elements. First edition, Penshaw Press, Sunderland, U. K., 1992.
78. R. J. Astley, W. Eversman. Finite element formulations for acoustical radiation. Journal of Sound and Vibration, 1983, 88: 47-64
79. R. J. Astley. Wave envelope and infinite elements for acoustical radiation. International Journal for Numerical Methods in Fluids, 1983, 3: 507-526
80. R. J. Astley. Finite element, wave envelope formulation for acoustical radiation in moving flows. Journal of Sound and Vibration, 1985, 13: 471-485
81. A. V. Parrett, W. Eversman. Wave envelope and finite element approximations for turbofan noise radiation in flight. AIAA Journal, 1986, 24: 753-760
82. O. C. Zienkiewicz, K. Bando, P. Bettess, C. Emson, T. C. Chiam. Mapped infinite elements for exterior wave problems. International Journal for Numerical Methods in Engineering, 1985, 21: 1229-1252
83. J. Gorranson, C. Davidsson. Three dimensional infinite elements for wave propagation. Journal of Sound and Vibration, 1987, 115: 556-559.
84. E. T. Moyer. Performance of mapped infinite elements for exterior wave scattering applications. Communications in Applied Numerical Methods, 1992, 8: 27-39
85. D. S. Burnett. Three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. Journal of The Acoustical Society of America, 1994, 96: 2798-2816
86. R. J. Astley. Mapped spheroidal elements for unbounded wave problems. International Journal for Numerical Methods in Engineering, 1998, 41: 1235-1254
87. L. G. Olson, K-J Bathe. Infinite element for transient fluid-structure interactions. Engineering Computation 1985, 2: 319-329
88. T. L. Geers. Doubly asymptotic approximations for transient motions of submerged structures. Journal of The Acoustical Society of America, 1978, 64: 1500-1508
89. R. J. Astley. A transient infinite element for Multi-dimensional acoustic radiation. DE Vol. 84-2, Design Engineering Technical Conference, Vol. 3 Part B, ASME, 1995; 97-111
90. R. J. Astley. Transient wave envelope elements for wave problems. Journal of Sound and Vibration, 1996, 192: 245-261
91. R. J. Astley, J-P. Coyette, L. Cremers. Three dimensional wave-envelope elements of variable order for acoustic radiation and scattering. Part 2. Formulation in the time domain. Journal of The Acoustical Society of America, 1998, 103: 64-72
92. R. J. Astley. Transient spheroidal elements for unbounded wave problems. Computer Methods in Applied Mechanics and Engineering, 1998; 164(1-2): 3-15
93. R. J. Astley. Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. Int. J. Numer. Meth. Engng, 2000, 49: 951-976
94. C. A. Brebbia. Recent advances in boundary elements. First edition, London, Pentech Press, 1978
95.杜庆华等。我国工程中边界元方法研究的十年。力学与实践,1989,11(1):3-6
96.C.A.Brabbia,王嘉新译。对边界元若干基本概念和重要文献的综述。力学进展,1993,23(1):121-134
97. N. Atalla, R. J. Bernhard. Review of numerical solutions for low-frequency structural-acoustic problems. Applied Acoustics, 1994, 43: 271-294
98. D. E. Bescos. Boundary element methods in dynamic analysis. Applied Mechanics Reviews, 1987, 40: 1-23
99. D. E. Bescos. Boundary element methods in dynamic analysis part Ⅱ(1986-1996). Applied Mechanics Reviews, 1997, 50: 149-197
100.刘恩儒,J.H.Queen,张中杰,陈东。裂缝诱导的多次散射波边界元法模拟。中国科学(E辑),2000,30(5):395-402
101. M. Schanz. Application of 3D time domain boundary element formulation to wave propagation in poroelastic solids. Engineering analysis with boundary elements, 2001, 25: 363-376
102.张楚汉,刘海笑。层状与各向异性介质波动问题的时域边界元法及工程应用。重庆建筑大学学报,2000,22(6):100-104
103.刘海笑,张楚汉。层状介质波动问题的时域边界元模型及实验。清华大学学报(自然科学版),2002,42(2):34-37
104.冯仰德,汪越胜,章梓茂。单侧摩擦约束夹杂物的瞬态弹性波散射的时域边界元分析-反平面情况。固体力学学报,2002,23(3):301-305
105. Y. D. Feng, Y. S. Wang, Z. M. Zhang. Transient scattering of SH waves from an inclusion with a unilateral frictional contact interface-a 2D time domain boundary element analysis. Communications in Numerical Methods in Engineering, 2003, 19(1): 25-36
106.曹志远,曾三平。爆炸波作用下地下防护结构与围岩的非线性动力相互作用分析。爆炸与冲击,2003,23(5):385-390
107.曹志远,曾三平。含地下孔洞层状半空间中瞬态波的传播。同济大学学报,2004,32(2):202-207
108. J. A. M. Carrer, W. J. Mansur. Time-dependent fundamental solution generated by a not impulsive source in the boundary element method analysis of the 2D scalar wave equation. Commun. Numer. Meth. Engng., 2002, 18: 277-285
109. C. D. Wang, M. H. Meylan. A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate. Journal of Fluids and Structures, 2004, 19: 557-572
110. A. T. Patera. A spectral element method for fluid dynamics: laminar flow in a channel expansion. Journal of Computational Physics, 1984, 54: 468-488
111. Y. Maday, A. T. Patera. Spectral element methods for the incompressible Naview-Stokes equations. In State of the Art Survey in Computational Mechanics. Noor AK, Oden JT(eds), 1989: 71-143
112. Geza Seriani. 3-D large-scale wave propagation modeling by spectral element method on Cray T3E multiprocessor. Comput. Methods. Appl. Mech. Engrg., 1998, 164: 235-247
113. R. Al-Khoury, A. Scarpas, C. Kasbergen, J. Blaauwendraad. Spectral element technique for efficient parameter identification of layered media. Part Ⅰ. Forward calculation. International Journal of Solids and Structures, 2001, 38: 1605-1623.
114. R. Al-Khoury, C. Kasbergen, A. Scarpas, J. Blaauwendraad. Spectral element technique for efficient parameter identification of layered media. Part Ⅱ. Inverse calculation. International Journal of Solids and Structures, 2001, 38: 8753-8772.
115. R. Al-Khoury, C. Kasbergen, A. Scarpas, J. Blaauwendraad. Poroelastic spectral element for wave propagation and parameter identification in multi-layer systems. International Journal of Solids and Structures, 2002, 39: 4073-4091
116. A. Chakraborty, S. Gopalakrishnan. A spectrally formulated finite element for wave propagation analysis in layered composite media. International Journal of Solids and Structures, 2004, 41: 5155-5183
117. D. Komatitsch, J. P. Vilotte, R. Vai, J. Castillo-Covarrubias, F. Sanchez-Sesma. The spectral element method for elastic wave equations-Application to 2-D and 3-D seismic problems. Int. J. Numer. Meth. Engng., 1999, 45: 1139-1164
118. Dimitri Komatitsch and Jeroen Tromp. Spectral-element simulations of global seismic wave propagation, Part Ⅰ: Validation. Geophysical Journal International, 2002, 149: 390-412
119. Dimitri Komatitsch and Jeroen Tromp. Spectral-element simulations of global seismic wave propagation, Part Ⅱ: 3-D models, oceans, rotation, and gravity. Geophysical Journal International, 2002, 150: 303-318
120. J. Zhang, T. Liu. P-SV wave propagation in heterogeneous media: grid method. Geophys. J. Int., 1999, 136: 431-438.
121.张剑锋,刘铁林。三维非均匀介质中弹性波传播的数值模拟。固体力学学报,2001,22(4):356-360
122. T. Liu, K. Liu and J. Zhang, Unstructured grid method for stress wave propagation in elastic media. Comp. Methods Appl. Mech. Eng., 2004, 193: 2427-2452
123. J. H. Lin, W. S. Zhang and F. W. Williams, Pseudo-excitation algorithm for non-stationary random seismic responses, Engineering Structures, 1994, 16(4): 270-276
124. J. H. Lin, Y. Zhao and Y. H. Zhang. Accurate and highly efficient algorithms for structural stationary/ non-stationary Random responses. Computer Method in Applied Mechanics and Engineering, 2001, 191(1-2): 103～111
125.林家浩,张亚辉。随机振动的虚拟激励法。第一版,北京,科学出版社,2004
126. W. X. Zhong, J. H. Lin, Q. Gao. The Precise Computation for Random Wave Propagation in Stratified Materials. World Conference of Computational Mechanics-5(WCCM-V), Vienna 2002
127.钟万勰,纪峥。理性有限元。计算结构力学及其应用,1996,13(1):1-8
128.钟万勰,纪峥。平面理性元的收敛性证明。计算力学学报,1997,29(6):676-685
129. J. M. Melenk. On generalized finite element methods. Ph. D dissertation, University of Maryland, College Park, MD, 1995
130. J. M. Melenk and I. Babuska. The partition of unity finite element method: Basic theory and applications. Comp. Methods Appl. Mech. Eng. 1996, 139: 289-314
131. J. M. Melenk and I. Babuska. The partition of unity finite element method. Int. J. Numerical Methods Eng. 1997, 40: 727-758
132. C. A. M. Duarte. The hp cloud method. Ph. D. dissertation, University of Texas at Austin, TX, 1996
133. C. A. M. Duarte and J. T. Oden. An hp adaptive method using clouds. Comp. Methods Appl. Mech. Eng. 1996, 139: 237-262
134. J. T. Oden, C. A. M. Duarte and O. C. Zienkiewicz. A new cloud-based hp finite element method. Comp. Methods Appl. Mech. Eng. 1998, 153: 117-126
135.梁国平,何江衡。广义有限元法——类新的逼近空间。力学进展,1995,25(4):562-565
136. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45: 601-620
137. Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46: 131-150
138.栾茂田,田荣,杨庆。广义节点有限元法。计算力学学报。2000,17(2):192-200
139.栾茂田.田荣,杨庆。平面广义四节点等参单元GQ4及其性能探讨。力学学报,2002,34(4):578-585
140. T. strouboulis, K. Copps and I. Babuska. The generalized finite element method: an example of its implementation and illustration of its performance. Int. J. numer. Methods engrg., 2000, 47: 1401-1417.
141. C. A. Duarte, I. Babuska, J. T. Oden. Generalized finite element methods for three-dimensional structural mechanics problems. Computers and Structures, 2000, 77(2): 215-232.
142. T. Strouboulis, I. Babuska and K. Copps. The design and analysis of the Generalized Finite Element Method, Comput. Methods Appl. Mech. Engrg., 2000, 181: 43-69
143.刘欣,朱德懋。基于单位分解的新型有限元方法研究。计算力学学报,2000,17(4):422-427
144.彭自强,王水林,葛修润。单位分解法、无网格法、数值流形方法之形函数的内在联系。岩石力学与工程学报,2002,21(增2):2429-2431
145.彭自强,李小凯,葛修润。广义有限元法对动态裂纹扩展的数值模拟。岩石力学与工程学报,2004,23(18):3132-3137
146. C. A. Duarte, O. N. Hamzeh, T. J. Liszka, W. W. Tworzydlo. A Generalized Finite Element Method for the Simulation of Three-Dimensional Crack Propagation. Comput. Methods Appl. Mech. Engrg., 2001, 190: 2227-2262
147. T. Strouboulis, K. Copps, I. Babuska. The generalized finite element method. Comput. Methods Appl. Mech. Engrg., 2001, 190: 4081-4193
148. T. Strouboulis, L. Zhang, I. Babuska. Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids. Comput. Methods Appl. Mech. Engrg., 2003, 192: 3109-3161
149. I. Babuska, U. Banerjee, J. E. Osborn. On principles for the selection of shape functions for the Generalized Finite Element Method. Comput. Methods Appl. Mech. Engrg., 2002, 191: 5595-5629
150. C. A. Duarte, I. Babuska. Mesh-independent p-orthotropic enrichment using the generalized finite element method. Int. J. Numer. Meth. Engng., 2002, 55: 1477-1492
151. F. B. Barros, S. P. B. Proen, C. S. de Barcellos. On error estimator and p-adaptivity in the generalized finite element method. Int. J. Numer. Meth. Engng., 2004, 60: 2373-2398
152.邵国建,王卫国,苏静波。地下工程开挖计算的广义有限元法。岩石力学与工程学报,2004,23(10):1694-1699
153. T. Strouboulis, L. Zhang and I. Babuska. p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems. Int. J. Numer. Meth. Engng, 2004, 60: 1639-1672
154. J. Fish and Z. Yuan. Multiscale enrichment based on partition of unity. Int. J. Numer. Meth. Engng, 2005, 62: 1341-1359
155. C. Daux, N. Moes, J. Dolbow, N. Sukumar, T. Belytschko. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering, 2000, 48: 1741-1760
156. J. Dolbow. An extended finite element method with discontinuous enrichment for applied mechanics. Ph. D. Thesis, Northwestern University, 1999
157. T. Belytschko, N. Moes, C. Parimi. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering, 2001, 50: 993-1013
158. J. Dolbow, N. Moes, T. Belytschko. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 2000, 36: 235-260
159. N. Sukumar, N. Moes, B. Moran, T. Belytschko. Extended finite element method for three-dimensional crack modeling. International Journal for Numerical Methods in Engineering, 2000, 48(11): 1549-1570
160. N. Sukumar, D. Chopp, N. Moes, T. Belytschko. Modeling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190: 6183-6200
161. M. Stolarska, D. Chopp, N. Moes, T. Belytschko. Modeling crack growth by level sets and the extended finite element method. International Journal for Numerical Methods in Engineering, 2001, 51: 943-960
162. N. Sukumar, D. Chopp, B. Moran. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics, 2003, 70(1): 29-48
163. H. Ji, D. Chopp and J. E. Dolbow. A hybrid extended finite element/level set method for modeling phase transformations. Int. J. Numer. Meth. Engng, 2002, 54: 1209-1233
164. T. Belytschko, C. Parimi, N. Moes, N. Sukumar and S. Usui, Structured Extended Finite Element Methods for Solids Defined by Implicit Surfaces, International Journal for Numerical Methods in Engineering, 2003, 56: 609-635
165.N. Sukumar, Z. Y. Huang, J.-H. Prevost and Z. Suo, Partition of Unity Enrichment for Bimaterial Interface Cracks. International Journal for Numerical Methods in Engineering, 2004, 59: 1075-1102
166.G. Ventura, B. Moran and T. Belytschko, Dislocations by partition of unity. Int. J. Numer. Meth. Engng, 2005, 62: 1463-1487
167.P. Ortiz, E. Sanchez. An improved partition of unity finite element model for diffraction problems. Int. J. Numerical Methods Eng.2001, 50: 2727-2740
168.O. Laghrouche, P. Bettess. Short wave modelling using special finite elements. Journal of Computational Acoustics. 2000, 8:189-210
169.O. Laghrouche, P. Bettess, R.J. Astley. Modelling of short wave diffraction problems using approximating system of plane waves. Int. J. Numerical Methods Eng. 2002, 54: 1501-1533
170.O. Laghrouche, P. Bettess, E. Perrey-Debain and J. Trevelyan. Plane wave basis for wave scattering in three dimension. Communication in Numerical Methods in Engineering, 2003, 19: 715-723
171.E. Perrey-Debain, O. Laghrouche, P. Bettess and J. Trevelyan. Plane wave basis finite elements and boundary elements for three dimensional wave scattering. Phil. Trans. R. Soc. Lond. A, 2004, 362: 561-577
172.R.J. Astley and P. Gamallo, Special short wave elements for flow acoustics, Comput. Methods Appl. Mech. Engrg., 2005, 194: 341-353
173.P. Ortiz. Finite elements using plane wave basis for scattering of surface water waves, Philos. Trans. R.Soc. Lond. A, 2004,362: 525-540
174.P. Bettess. Special wave basis finite elements for very short wave refraction and scattering problems. Commun. Numer. Methods Engrg. 2004, 20: 291-298
175.O. Laghrouche, P. Bettess, E. Perrey-Debain and J. Trevelyan. Wave interpolation finite elements for Helmholtz problems with jumps in the wave speed. Computer Methods in Applied Mechanics and Engineering, 2005, 194: 367-381
176.C. Farhat, 1. Harari, L. Franca. The discontinuous enrichment method. Comput. Meth. Appl. Mech. Engng., 2001, 190:6455-6479
177.C. Farhat, I. Harari, U. Hetmanuk, A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, Comput. Methods Appl. Mech. Engrg. 2003, 192: 1389-1419
178.P. Bettess, J. Shirron, O. Laghrouche, B. Peseux, R. Sugimoto and J. Trevelyan. A numerical integration scheme for special finite elements for the Helmholtz equation. Int. J. Numerical Methods Eng. 2003,56:531-552.
179.R. Sugimoto, P. Bettess and J. Trevelyan. A numerical integration scheme for special quadrilateral finite elements for Helmholtz equation. Communications in Numerical Methods in Eng. 2003, 19:
233-245.
180. E. Perrey-Debain, J. Trevelyan and P. Bettess. Wave boundary elements: a theoretical overview presenting some applications in scatterings of short waves. Engineering Analysis with Boundary Elements, 2004, 28: 131-141
181. C. A. Duarte, J. T. Oden. Hpclouds: a h-p meshless method. Numerical Methods for Partial Differential Equations, 1996, 12: 673-705
182. M. A. Biot. Theory of propagation of elastic waves in a fluid-saturated porous solid Ⅰ: Low frequency range. Journal of the acoustical society of America, 1956, 28(2): 168-178
183. M. A. Biot. Theory of propagation of elastic waves in a fluid-saturated porous solid Ⅱ: Higher frequency range. Journal of the acoustical society of America, 1956, 28(2): 179-191
184. J. Ghaboussi, E. L. Wilson. Variational formulation of dynamics of fluid-saturated porous elastic solids. J. Eng, Mech. Div, ASCE, 1972, 98: 947-963
185. O. C. Zienkiewicz, T. Shiomi. Dynamic behaviour of saturated porous media: The generalized Biot formulation and its numerical solution. Int. J. for Numer. and Anal. Methods in Geomechanics, 1984, 8: 71-96
186. B. R. Simon, JSS Wu, O. C. Zienkiewicz, etal. Evaluation of u-w and u-π finite element methods for the dynamic response of saturated porous media using one-dimensional models. Int. J. Num. Analyt. Meth. Geom., 1986, 10(5): 461-482
187. B. R. Simon, JSS Wu, O. C. Zienkiewicz. Evaluation of higher order, mixed and hermitean finite element procedures for dynamics analysis of saturated porous media using one-dimensional models. Int. J. Num. Analyt. Meth. Geom., 1986, 10(5): 483-499
188.门福录.波在饱水孔隙弹性介质中的传播问题.地球物理学报,1965,14(2):107-114
189.门福录.波在饱含流体的孔隙水介质中的传播问题.地球物理学报,1981,24(1):64-75
190. C. Truesdell, R. A. Toupin. The classical field theories. SpringerVerlag, 1960, Handbuch derphysic bd3(1)
191.R.M.Bowen.混合物理论。第一版,江苏科技出版社,1983
192. R. M. Bowen, K. M. Reinicke. Plane progressive waves in a binary mixture of linear elastic materials. J. Appl. Mech., 1978, 45: 493-499
193. R. M. Bowen. Compressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci., 1982, 20(6): 697-735
194. R. M. Bowen. Plane progressive waves in a heat conducting fluid saturated porous materiall with relaxing porosity. Acta Mechanica, 1983, 46: 189-206
195. W. Derski. Thermomecanique lineaire des milieux poreux. ENSM Nantes. 1982
196.苗天德,朱久江。对饱和多孔介质波动问题中本构关系的探讨。力学学报,1995,27(5):536-543
197.章根德。固体—流体混合物连续介质理论及其在工程上的应用。力学进展,1993,23(1):58-68
198.刘占芳,严波,唐录成。饱和多孔弹性材料中加速度波的传播。重庆大学学报(自然科学版),1998,21(2):7-15
199.严波,刘占芳,张湘伟。流体饱和多孔介质中波传播问题的有限元分析。应用数学和力学,1999,20(12):1235-1244
200.赵成刚,杜修力,崔杰。固体、流体多相多孔介质中的波动理论及其数值模拟的进展。力学进展,1998,28(1):84-92
201.陈少林,廖振鹏。两相介质动力学问题的研究进展。地震工程与工程振动,2002(2):1-8
202.刘颖。冲击荷载作用下含液饱和多孔介质中应力波传播问题的研究。工学博士论文,大连理工大学,2002
203.刘凯欣,刘颖。液饱和多孔介质中三维应力波的传播。力学学报,2003,35(4):469-473
204.李锡夔,张俊波,张洪武。含液体非弹性多孔介质中波传播过程的失稳与逸散性。应用数学和力学,2002,23(1):31-46
205. Xikui Li, Junbo Zhang, Hongwu Zhang. Instabilily of wave propagation in saturated poroelastoplastic media. Int. J. Numer. Anal. Meth. Geomech., 2002, 26: 563-578