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Volumn 10, Issue 7, 2005, Pages 725-735

Some notes on the general boundary element method for highly nonlinear problems

Author keywords

General boundary element method; Homotopy analysis method; Nonlinear partial differential equations

Indexed keywords

NONLINEAR EQUATIONS; NUMERICAL METHODS; VISCOUS FLOW;

EID: 12344288379     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2004.04.003     Document Type: Article
Times cited : (13)

References (56)
  • 1
    • 0003424393 scopus 로고
    • The boundary element method for engineers
    • Plymouth: Pentech Press
    • Brebbia C.A. The boundary element method for engineers 1978 Pentech Press Plymouth
    • (1978)
    • Brebbia, C.A.1
  • 4
    • 0041332794 scopus 로고
    • The generalized BEM for non-linear problems
    • C. A. Brebbia (Ed.), Southampton: Computational Mechanics Publications
    • Tosaka N. Kakuda K. The generalized BEM for non-linear problems. In: Brebbia C.A. (Ed.). Boundary elements X: (1) Mathematical and computational aspects 1988 1-17 Computational Mechanics Publications Southampton
    • (1988) Boundary Elements X: (1) Mathematical and Computational Aspects , pp. 1-17
    • Tosaka, N.1    Kakuda, K.2
  • 5
    • 0000344777 scopus 로고
    • A boundary element approach for non-linear boundary-value problems
    • Zheng R. Phan-Thien N. Coleman C.J. A boundary element approach for non-linear boundary-value problems Comput. Mech. 8 1991 71-86
    • (1991) Comput. Mech. , vol.8 , pp. 71-86
    • Zheng, R.1    Phan-Thien, N.2    Coleman, C.J.3
  • 6
    • 0001143872 scopus 로고
    • Transforming the domain integrals to the boundary using approximate particular solutions: A boundary element approach for nonlinear problems
    • Zheng R. Phan-Thien N. Transforming the domain integrals to the boundary using approximate particular solutions: A boundary element approach for nonlinear problems Appl. Numer. Math. 10 5 1992 435
    • (1992) Appl. Numer. Math. , vol.10 , Issue.5 , pp. 435
    • Zheng, R.1    Phan-Thien, N.2
  • 7
    • 0017723511 scopus 로고
    • An advanced boundary integral equation method for three-dimensional thermoelasticity
    • Rizzo F.J. Shippy D.J. An advanced boundary integral equation method for three-dimensional thermoelasticity Int. J. Numer. Meth. Eng. 11 1977 1753-1768
    • (1977) Int. J. Numer. Meth. Eng. , vol.11 , pp. 1753-1768
    • Rizzo, F.J.1    Shippy, D.J.2
  • 8
    • 85196191040 scopus 로고
    • A boundary element approach to some nonlinear equations from fluid mechanics
    • C.A. Brebbia (Ed.), Berlin: Springer
    • Danson D.J. A boundary element approach to some nonlinear equations from fluid mechanics. In: Brebbia C.A. (Ed.). Boundary element methods 1981 Springer Berlin
    • (1981) Boundary Element Methods
    • Danson, D.J.1
  • 10
    • 0042188651 scopus 로고
    • New development in the dual reciprocity method
    • C. A. Brebbia, S. Kim, T. A. Osswald, H. Power (Eds.), Southampton: Computational Mechanics Publications
    • Partridge P.W. New development in the dual reciprocity method. In: Brebbia C.A. Kim S. Osswald T.A. Power H. (Eds.). Boundary elements VXII 1995 11-18 Computational Mechanics Publications Southampton
    • (1995) Boundary Elements VXII , pp. 11-18
    • Partridge, P.W.1
  • 12
    • 0003254102 scopus 로고
    • Dual reciprocity boundary element method based on complete set global shape functions
    • Southampton
    • Cheng AH, Grille S, Lafe O. Dual reciprocity boundary element method based on complete set global shape functions. In: BEM XV, Southampton, 1993
    • (1993) BEM XV
    • Cheng, A.H.1    Grille, S.2    Lafe, O.3
  • 13
    • 0031076671 scopus 로고    scopus 로고
    • Hybrid approximation functions in the dual reciprocity boundary element method
    • Partridge P.W. Sensale B. Hybrid approximation functions in the dual reciprocity boundary element method Commun. Numer. Meth. Eng. 13 1997 83-94
    • (1997) Commun. Numer. Meth. Eng. , vol.13 , pp. 83-94
    • Partridge, P.W.1    Sensale, B.2
  • 14
    • 0032072738 scopus 로고    scopus 로고
    • 3D structural vibration by the dual reciprocity BEM
    • Agnantiaris J.P. Polyzos D. Beskos D.E. 3D structural vibration by the dual reciprocity BEM Comput. Mech. 21 1998 372-381
    • (1998) Comput. Mech. , vol.21 , pp. 372-381
    • Agnantiaris, J.P.1    Polyzos, D.2    Beskos, D.E.3
  • 15
    • 0032733502 scopus 로고    scopus 로고
    • The DRM-MD integral equation method: An efficient approach for the numerical solution of domain dominant problems
    • Popov V. Power H. The DRM-MD integral equation method: An efficient approach for the numerical solution of domain dominant problems Int. J. Numer. Meth. Eng. 44 1999 327-353
    • (1999) Int. J. Numer. Meth. Eng. , vol.44 , pp. 327-353
    • Popov, V.1    Power, H.2
  • 16
    • 0345148900 scopus 로고    scopus 로고
    • A poly-region boundary element method for incompressible viscous fluid flows
    • Grigoriev M.M. Dargush G.F. A poly-region boundary element method for incompressible viscous fluid flows Int. J. Numer. Meth. Eng. 46 1999 1127-1158
    • (1999) Int. J. Numer. Meth. Eng. , vol.46 , pp. 1127-1158
    • Grigoriev, M.M.1    Dargush, G.F.2
  • 17
    • 0033880191 scopus 로고    scopus 로고
    • The DRM sub-domain decomposition approach to solve the two-dimensional Navier-Stokes systems of equations
    • Power H. Mingo R. The DRM sub-domain decomposition approach to solve the two-dimensional Navier-Stokes systems of equations Eng. Anal. Boundary Elements 24 2000 107-119
    • (2000) Eng. Anal. Boundary Elements , vol.24 , pp. 107-119
    • Power, H.1    Mingo, R.2
  • 18
    • 0035095836 scopus 로고    scopus 로고
    • Comparison between continuous and discontinuous boundary elements in the multi-domain dual reciprocity method for the solution of the two-dimensional Navier-Stokes equations
    • Florez W.F. Power H. Comparison between continuous and discontinuous boundary elements in the multi-domain dual reciprocity method for the solution of the two-dimensional Navier-Stokes equations Eng. Anal. Boundary Elements 25 2001 57-69
    • (2001) Eng. Anal. Boundary Elements , vol.25 , pp. 57-69
    • Florez, W.F.1    Power, H.2
  • 19
    • 0036467597 scopus 로고    scopus 로고
    • DRM multidomain mass conservative interpolation approach for the BEM solution of the two-dimensional Navier-Stokes equations
    • Florez W.F. Power H. DRM multidomain mass conservative interpolation approach for the BEM solution of the two-dimensional Navier-Stokes equations Comp. Math. Appl. 43 2002 457-472
    • (2002) Comp. Math. Appl. , vol.43 , pp. 457-472
    • Florez, W.F.1    Power, H.2
  • 20
    • 0036502632 scopus 로고    scopus 로고
    • Multi-domain mass conservative dual reciprocity method for the solution of the non-Newtonian Stokes equations
    • Florez W.F. Power H. Multi-domain mass conservative dual reciprocity method for the solution of the non-Newtonian Stokes equations Appl. Math. Model. 26 2002 397-419
    • (2002) Appl. Math. Model. , vol.26 , pp. 397-419
    • Florez, W.F.1    Power, H.2
  • 21
    • 0036671041 scopus 로고    scopus 로고
    • Modeling of 3D transversely piezoelectric and elastic bimaterials using the boundary element method
    • Liew K.M. Liang J. Modeling of 3D transversely piezoelectric and elastic bimaterials using the boundary element method Computational Mechanics 29 2002 151-162
    • (2002) Computational Mechanics , vol.29 , pp. 151-162
    • Liew, K.M.1    Liang, J.2
  • 23
    • 0025197594 scopus 로고
    • Fundamental solutions of the streamfunction-vorticity formulation of the Navier-Stokes equation
    • Rodriguez-Prada H.A. Pironti F. Saez A.E. Fundamental solutions of the streamfunction-vorticity formulation of the Navier-Stokes equation Int. J. Numer. Meth. Fluids 10 1990 1-12
    • (1990) Int. J. Numer. Meth. Fluids , vol.10 , pp. 1-12
    • Rodriguez-Prada, H.A.1    Pironti, F.2    Saez, A.E.3
  • 24
    • 0027579840 scopus 로고
    • A boundary element formulation using the SIMPLE method
    • Grigoiev M.M. A boundary element formulation using the SIMPLE method Int. J. Numer. Meth. Fluids 16 1993 549-579
    • (1993) Int. J. Numer. Meth. Fluids , vol.16 , pp. 549-579
    • Grigoiev, M.M.1
  • 25
    • 0030361909 scopus 로고    scopus 로고
    • Pressure correction DRBEM solution for heat transfer and fluid flow in incompressible viscous fluids
    • Rahaim C.P. Kassab A.J. Pressure correction DRBEM solution for heat transfer and fluid flow in incompressible viscous fluids Eng. Anal. Boundary Elements 18 1996 65-272
    • (1996) Eng. Anal. Boundary Elements , vol.18 , pp. 65-272
    • Rahaim, C.P.1    Kassab, A.J.2
  • 26
    • 0032681632 scopus 로고    scopus 로고
    • Primitive variable dual reciprocity boundary element method solution of incompressible Navier-Stokes equations
    • Sarler B. Kuhn G. Primitive variable dual reciprocity boundary element method solution of incompressible Navier-Stokes equations Eng. Anal. Boundary Elements 23 1998 443-455
    • (1998) Eng. Anal. Boundary Elements , vol.23 , pp. 443-455
    • Sarler, B.1    Kuhn, G.2
  • 27
    • 5544240744 scopus 로고    scopus 로고
    • Computational fluid dynamics by boundary-domain integral method
    • Škerget L. Hriberšek M. Kuhn G. Computational fluid dynamics by boundary-domain integral method Int. J. Numer. Mech. Eng. 46 1999 1291-1311
    • (1999) Int. J. Numer. Mech. Eng. , vol.46 , pp. 1291-1311
    • Škerget, L.1    Hriberšek, M.2    Kuhn, G.3
  • 28
    • 0035885080 scopus 로고    scopus 로고
    • Boundary element analysis of driven cavity flow for low and moderate Reynolds number
    • Aydin M. Fenner R.T. Boundary element analysis of driven cavity flow for low and moderate Reynolds number Int. J. Numer. Meth. Fluids 37 2001 45-64
    • (2001) Int. J. Numer. Meth. Fluids , vol.37 , pp. 45-64
    • Aydin, M.1    Fenner, R.T.2
  • 29
    • 49049143188 scopus 로고
    • High-Re solutions for imcompressible Navier-Stokes equations and a multi-grid method
    • Ghia U. Ghia K.N. Shin C.T. High-Re solutions for imcompressible Navier-Stokes equations and a multi-grid method J. Comput. Phys. 48 1982 387-411
    • (1982) J. Comput. Phys. , vol.48 , pp. 387-411
    • Ghia, U.1    Ghia, K.N.2    Shin, C.T.3
  • 30
    • 0043208674 scopus 로고
    • The quite general boundary element method for strongly nonlinear problems
    • C.A. Brebbia, S. Kim, T.A. Osswald, H. Power (Eds.), Southampton and Boston: Computational Mechanics Publications
    • Liao S.J. The quite general boundary element method for strongly nonlinear problems. In: Brebbia C.A. Kim S. Osswald T.A. Power H. (Ed.). Boundary elements XVII 1995 67-74 Computational Mechanics Publications Southampton and Boston
    • (1995) Boundary Elements XVII , pp. 67-74
    • Liao, S.J.1
  • 31
    • 0030246235 scopus 로고    scopus 로고
    • General boundary element method for nonlinear problems
    • Liao S.J. Chwang A.T. General boundary element method for nonlinear problems Int. J. Numer. Meth. Fluids 23 1996 467-483
    • (1996) Int. J. Numer. Meth. Fluids , vol.23 , pp. 467-483
    • Liao, S.J.1    Chwang, A.T.2
  • 32
    • 0030258876 scopus 로고    scopus 로고
    • High-order boundary element method formulations for strongly nonlinear problems governed by quite general nonlinear differential operators
    • Liao S.J. High-order boundary element method formulations for strongly nonlinear problems governed by quite general nonlinear differential operators Int. J. Numer. Meth. Fluids 23 1996 739-751
    • (1996) Int. J. Numer. Meth. Fluids , vol.23 , pp. 739-751
    • Liao, S.J.1
  • 33
    • 0031141048 scopus 로고    scopus 로고
    • High-order boundary element method formulations for strongly nonlinear problems governed by quite general nonlinear differential operators (Part 2)
    • Liao S.J. High-order boundary element method formulations for strongly nonlinear problems governed by quite general nonlinear differential operators (Part 2) Int. J. Numer. Meth. Fluids 24 1997 863-873
    • (1997) Int. J. Numer. Meth. Fluids , vol.24 , pp. 863-873
    • Liao, S.J.1
  • 34
    • 0031223353 scopus 로고    scopus 로고
    • Boundary element method for general nonlinear differential operators
    • Liao S.J. Boundary element method for general nonlinear differential operators Eng. Anal. Boundary Element 20 2 1997 91-99
    • (1997) Eng. Anal. Boundary Element , vol.20 , Issue.2 , pp. 91-99
    • Liao, S.J.1
  • 35
    • 0031675017 scopus 로고    scopus 로고
    • On the general boundary element method
    • Liao S.J. On the general boundary element method Eng. Anal. Boundary Elements 21 1998 39-51
    • (1998) Eng. Anal. Boundary Elements , vol.21 , pp. 39-51
    • Liao, S.J.1
  • 36
    • 0033212739 scopus 로고    scopus 로고
    • On the general boundary element method and its further generalization
    • Liao S.J. On the general boundary element method and its further generalization Int. J. Numer. Meth. Fluids 31 1999 627-655
    • (1999) Int. J. Numer. Meth. Fluids , vol.31 , pp. 627-655
    • Liao, S.J.1
  • 37
    • 0031249470 scopus 로고    scopus 로고
    • General boundary element method for nonlinear heat transfer problems governed by hyperbolic heat conduction equation
    • Liao S.J. General boundary element method for nonlinear heat transfer problems governed by hyperbolic heat conduction equation Comput. Mech. 20 5 1997 397-406
    • (1997) Comput. Mech. , vol.20 , Issue.5 , pp. 397-406
    • Liao, S.J.1
  • 38
    • 0033098677 scopus 로고    scopus 로고
    • General boundary element method for unsteady nonlinear heat transfer problems
    • Liao S.J. Chwang A.T. General boundary element method for unsteady nonlinear heat transfer problems Int. J. Numer. Heat Transfer (part B) 35 2 1999 225-242
    • (1999) Int. J. Numer. Heat Transfer , vol.35 , Issue.2 PART B , pp. 225-242
    • Liao, S.J.1    Chwang, A.T.2
  • 39
    • 0036027456 scopus 로고    scopus 로고
    • A direct boundary element approach for unsteady non-linear heat transfer problems
    • Liao S.J. A direct boundary element approach for unsteady non-linear heat transfer problems Eng. Anal. Boundary Elements 26 2002 55-59
    • (2002) Eng. Anal. Boundary Elements , vol.26 , pp. 55-59
    • Liao, S.J.1
  • 41
    • 0012835662 scopus 로고
    • The proposed homotopy analysis technique for the solution of nonlinear problems
    • Ph.D. thesis, Shanghai Jiao Tong University
    • Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D. thesis, Shanghai Jiao Tong University, 1992
    • (1992)
    • Liao, S.J.1
  • 43
    • 0000494305 scopus 로고    scopus 로고
    • An explicit, totally analytic approximation of Blasius viscous flow problems
    • Liao S.J. An explicit, totally analytic approximation of Blasius viscous flow problems Int. J. Non-Linear Mech. 34 4 1999 759-778
    • (1999) Int. J. Non-Linear Mech. , vol.34 , Issue.4 , pp. 759-778
    • Liao, S.J.1
  • 44
    • 0032640240 scopus 로고    scopus 로고
    • A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate
    • Liao S.J. A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate J. Fluid Mech. 385 1999 101-128
    • (1999) J. Fluid Mech. , vol.385 , pp. 101-128
    • Liao, S.J.1
  • 45
    • 0037170485 scopus 로고    scopus 로고
    • Analytic solutions of the temperature distribution in Blasius viscous flow problems
    • Liao S.J. Campo A. Analytic solutions of the temperature distribution in Blasius viscous flow problems J. Fluid Mech. 453 2002 411-425
    • (2002) J. Fluid Mech. , vol.453 , pp. 411-425
    • Liao, S.J.1    Campo, A.2
  • 46
    • 0042354097 scopus 로고    scopus 로고
    • On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet
    • Liao S.J. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet J. Fluid Mech. 488 2003 189-212
    • (2003) J. Fluid Mech. , vol.488 , pp. 189-212
    • Liao, S.J.1
  • 47
    • 0037300634 scopus 로고    scopus 로고
    • Homotopy analysis of nonlinear progressive waves in deep water
    • Liao S.J. Cheung K.F. Homotopy analysis of nonlinear progressive waves in deep water J. Eng. Math. 45 2 2003 105-116
    • (2003) J. Eng. Math. , vol.45 , Issue.2 , pp. 105-116
    • Liao, S.J.1    Cheung, K.F.2
  • 48
    • 0141961626 scopus 로고    scopus 로고
    • On the homotopy analysis method for nonlinear problems
    • Liao S.J. On the homotopy analysis method for nonlinear problems Appl. Math. Comput. 147 2004 499-513
    • (2004) Appl. Math. Comput. , vol.147 , pp. 499-513
    • Liao, S.J.1
  • 49
    • 0041764457 scopus 로고    scopus 로고
    • Exact flow of a third grade fluid past a porous plate using homotopy analysis method
    • Ayub M. Rasheed A. Hayat T. Exact flow of a third grade fluid past a porous plate using homotopy analysis method Int. J. Eng. Sci. 41 2003 2091-2103
    • (2003) Int. J. Eng. Sci. , vol.41 , pp. 2091-2103
    • Ayub, M.1    Rasheed, A.2    Hayat, T.3
  • 50
    • 0141927321 scopus 로고    scopus 로고
    • On the explicit analytic solutions of an Oldroyd 6-constant fluid
    • Hayat T. Khan M. Ayub M. On the explicit analytic solutions of an Oldroyd 6-constant fluid Int. J. Eng. Sci. 42 2004 123-135
    • (2004) Int. J. Eng. Sci. , vol.42 , pp. 123-135
    • Hayat, T.1    Khan, M.2    Ayub, M.3
  • 54
    • 0012885756 scopus 로고
    • Methods of dynamics calculation and testing for thin-walled structures
    • Moscow: Mashinostroyenie in Russian
    • Karmishin A.V. Zhukov A.I. Kolosov V.G. Methods of dynamics calculation and testing for thin-walled structures 1990 Mashinostroyenie Moscow in Russian
    • (1990)
    • Karmishin, A.V.1    Zhukov, A.I.2    Kolosov, V.G.3
  • 56
    • 0036028178 scopus 로고    scopus 로고
    • An analytic approximation of the drag coefficient for the viscous flow past a sphere
    • Liao S.J. An analytic approximation of the drag coefficient for the viscous flow past a sphere Int. J. Non-Linear Mech. 37 2002 1-18
    • (2002) Int. J. Non-Linear Mech. , vol.37 , pp. 1-18
    • Liao, S.J.1


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