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Volumn 200, Issue 47-48, 2011, Pages 3358-3380

An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry

Author keywords

Complex geometries; Finite Cell Method; Hierarchical refinement; High order B spline finite elements; Interface problems; Regular grid

Indexed keywords

COMPLEX GEOMETRIES; FINITE CELL METHOD; HIERARCHICAL REFINEMENT; HIGH-ORDER; INTERFACE PROBLEMS; REGULAR GRIDS;

EID: 80052656654     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2011.08.002     Document Type: Article
Times cited : (128)

References (81)
  • 1
    • 69249211118 scopus 로고    scopus 로고
    • An unfitted finite element method using discontinuous Galerkin
    • Bastian P., Engwer C. An unfitted finite element method using discontinuous Galerkin. Int. J. Numer. Methods Engrg. 2009, 79:1557-1576.
    • (2009) Int. J. Numer. Methods Engrg. , vol.79 , pp. 1557-1576
    • Bastian, P.1    Engwer, C.2
  • 3
    • 79955936082 scopus 로고    scopus 로고
    • Some estimates for h-p-k-refinement in isogeometric analysis
    • Beirão da Veiga L., Buffa A., Rivas J., Sangalli G. Some estimates for h-p-k-refinement in isogeometric analysis. Numer. Math. 2011, 118(2):271-305.
    • (2011) Numer. Math. , vol.118 , Issue.2 , pp. 271-305
    • Beirão da Veiga, L.1    Buffa, A.2    Rivas, J.3    Sangalli, G.4
  • 8
    • 0038451461 scopus 로고    scopus 로고
    • Compressive behavior and energy absorbing characteristic of open cell aluminum foam filled with silicate rubber
    • Chen H.F., Han F.S. Compressive behavior and energy absorbing characteristic of open cell aluminum foam filled with silicate rubber. Scr. Mater. 2003, 49:583-586.
    • (2003) Scr. Mater. , vol.49 , pp. 583-586
    • Chen, H.F.1    Han, F.S.2
  • 9
    • 67649400371 scopus 로고    scopus 로고
    • Compressive properties of a new metal-polymer hybrid material
    • Cluff D.R.A., Esmaeili S. Compressive properties of a new metal-polymer hybrid material. J. Mater. Sci. 2009, 44:3867-3876.
    • (2009) J. Mater. Sci. , vol.44 , pp. 3867-3876
    • Cluff, D.R.A.1    Esmaeili, S.2
  • 10
    • 34547629767 scopus 로고    scopus 로고
    • Studies of refinement and continuity in isogeometric structural analysis
    • Cottrell J.A., Hughes T.J.R., Reali A. Studies of refinement and continuity in isogeometric structural analysis. Comput. Methods Appl. Mech. Engrg. 2007, 196:4160-4183.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 4160-4183
    • Cottrell, J.A.1    Hughes, T.J.R.2    Reali, A.3
  • 15
    • 64049100257 scopus 로고    scopus 로고
    • An efficient finite element method for embedded interface problems
    • Dolbow J., Harari I. An efficient finite element method for embedded interface problems. Int. J. Numer. Methods Engrg. 2009, 78:229-252.
    • (2009) Int. J. Numer. Methods Engrg. , vol.78 , pp. 229-252
    • Dolbow, J.1    Harari, I.2
  • 18
    • 34447103175 scopus 로고    scopus 로고
    • Applying the hp-d version of the FEM to locally enhance dimensionally reduced models
    • Düster A., Niggl A., Rank E. Applying the hp-d version of the FEM to locally enhance dimensionally reduced models. Comput. Methods Appl. Mech. Engrg. 2007, 196:3524-3533.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 3524-3533
    • Düster, A.1    Niggl, A.2    Rank, E.3
  • 20
    • 77955107950 scopus 로고    scopus 로고
    • Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements
    • Embar A., Dolbow J., Harari I. Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements. Int. J. Numer. Methods Engrg. 2010, 83:877-898.
    • (2010) Int. J. Numer. Methods Engrg. , vol.83 , pp. 877-898
    • Embar, A.1    Dolbow, J.2    Harari, I.3
  • 23
    • 80053460338 scopus 로고    scopus 로고
    • FlagShyp 08 Version 2.30, Nonlinear FE solver developed by J. Bonet and R. Wood, 2008. Available from: .
    • FlagShyp 08 Version 2.30, Nonlinear FE solver developed by J. Bonet and R. Wood, 2008. Available from: http://www.flagshyp.com.
  • 24
    • 33751084043 scopus 로고    scopus 로고
    • Stable Lagrange multipliers for quadrilateral meshes of curved interfaces in 3D
    • Flemisch B., Wohlmuth B. Stable Lagrange multipliers for quadrilateral meshes of curved interfaces in 3D. Comput. Methods Appl. Mech. Engrg. 2007, 196:1589-1602.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 1589-1602
    • Flemisch, B.1    Wohlmuth, B.2
  • 25
    • 0024062018 scopus 로고
    • Hierarchical B-spline refinement
    • Forsey D., Bartels R. Hierarchical B-spline refinement. Comput. Graph. 1988, 4:205-212.
    • (1988) Comput. Graph. , vol.4 , pp. 205-212
    • Forsey, D.1    Bartels, R.2
  • 26
    • 78650831150 scopus 로고    scopus 로고
    • The extended/generalized finite element method: an overview of the method and its applications
    • Fries T.P., Belytschko T. The extended/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Methods Engrg. 2010, 84:253-304.
    • (2010) Int. J. Numer. Methods Engrg. , vol.84 , pp. 253-304
    • Fries, T.P.1    Belytschko, T.2
  • 27
    • 33751084830 scopus 로고    scopus 로고
    • Distributed lagrange multipliers based on fictitious domain method for second order elliptic problems
    • Glowinski R., Kuznetsov Y. Distributed lagrange multipliers based on fictitious domain method for second order elliptic problems. Comput. Methods Appl. Mech. Engrg. 2007, 196:1498-1506.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 1498-1506
    • Glowinski, R.1    Kuznetsov, Y.2
  • 28
    • 0031538248 scopus 로고    scopus 로고
    • Composite finite elements for the approximation of PDEs on domains with complicated micro-structures
    • Hackbusch W., Sauter S.A. Composite finite elements for the approximation of PDEs on domains with complicated micro-structures. Numer. Math. 1997, 75:447-472.
    • (1997) Numer. Math. , vol.75 , pp. 447-472
    • Hackbusch, W.1    Sauter, S.A.2
  • 29
    • 0037159814 scopus 로고    scopus 로고
    • An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
    • Hansbo A., Hansbo P. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg. 2002, 191:537-552.
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 537-552
    • Hansbo, A.1    Hansbo, P.2
  • 30
    • 3142681642 scopus 로고    scopus 로고
    • A finite element method for the simulation of strong and weak discontinuities in solid mechanics
    • Hansbo A., Hansbo P. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Methods Appl. Mech. Engrg. 2004, 193:3523-3540.
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 3523-3540
    • Hansbo, A.1    Hansbo, P.2
  • 31
    • 33744941609 scopus 로고    scopus 로고
    • Interface material failure modeled by the extended finite-element method and level sets
    • Hettich T., Ramm E. Interface material failure modeled by the extended finite-element method and level sets. Comput. Methods Appl. Mech. Engrg. 2008, 195:4753-4767.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 4753-4767
    • Hettich, T.1    Ramm, E.2
  • 32
    • 80053442588 scopus 로고    scopus 로고
    • High-order finite elements for material and geometric nonlinear finite strain problems, PhD thesis, Chair for Computation in Engineering, Technische Universität München, Shaker, Aachen, 2008.
    • U. Heisserer, High-order finite elements for material and geometric nonlinear finite strain problems, PhD thesis, Chair for Computation in Engineering, Technische Universität München, Shaker, Aachen, 2008.
    • Heisserer, U.1
  • 33
    • 0036556979 scopus 로고    scopus 로고
    • Multigrid methods with web-splines
    • Höllig K., Reif U., Wipper J. Multigrid methods with web-splines. Numer. Math. 2002, 91:237-256.
    • (2002) Numer. Math. , vol.91 , pp. 237-256
    • Höllig, K.1    Reif, U.2    Wipper, J.3
  • 34
  • 36
    • 21044443461 scopus 로고    scopus 로고
    • Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
    • Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Engrg. 2005, 194:4135-4195.
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , pp. 4135-4195
    • Hughes, T.J.R.1    Cottrell, J.A.2    Bazilevs, Y.3
  • 37
    • 52749086594 scopus 로고    scopus 로고
    • Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS
    • Hughes T.J.R., Reali A., Sangalli G. Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS. Comput. Methods Appl. Mech. Engrg. 2008, 197:4104-4124.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.197 , pp. 4104-4124
    • Hughes, T.J.R.1    Reali, A.2    Sangalli, G.3
  • 39
    • 55949105200 scopus 로고    scopus 로고
    • Processing, compression response and finite element modeling of syntactic foam based interpenetrating phase composite (IPC)
    • Jhaver R., Tippur H. Processing, compression response and finite element modeling of syntactic foam based interpenetrating phase composite (IPC). Mater. Sci. Engrg. A 2009, 499:507-517.
    • (2009) Mater. Sci. Engrg. A , vol.499 , pp. 507-517
    • Jhaver, R.1    Tippur, H.2
  • 40
    • 33745790155 scopus 로고    scopus 로고
    • Multiresolution techniques
    • Morgan Kaufman Publishers, San Francisco, G. Farin, J. Hoschek, M.S. Sim (Eds.)
    • Kobbelt L. Multiresolution techniques. Handbook of Computer Aided Geometric Design 2002, 343-361. Morgan Kaufman Publishers, San Francisco. G. Farin, J. Hoschek, M.S. Sim (Eds.).
    • (2002) Handbook of Computer Aided Geometric Design , pp. 343-361
    • Kobbelt, L.1
  • 41
    • 0013235437 scopus 로고    scopus 로고
    • Adaptive and linearly independent multilevel B-splines
    • Vanderbilt University Press, A.L. Méhauté, C. Rabut, L.L. Schumaker (Eds.)
    • Kraft R. Adaptive and linearly independent multilevel B-splines. Surface Fitting and Multiresolution Methods 1997, 209-218. Vanderbilt University Press. A.L. Méhauté, C. Rabut, L.L. Schumaker (Eds.).
    • (1997) Surface Fitting and Multiresolution Methods , pp. 209-218
    • Kraft, R.1
  • 42
    • 84989432290 scopus 로고
    • Hp-version finite elements for geometrically non-linear problems
    • Krause R., Mücke R., Rank E. hp-version finite elements for geometrically non-linear problems. Commun. Numer. Methods Engrg. 1995, 11:887-897.
    • (1995) Commun. Numer. Methods Engrg. , vol.11 , pp. 887-897
    • Krause, R.1    Mücke, R.2    Rank, E.3
  • 44
    • 3042749452 scopus 로고    scopus 로고
    • Mortar finite elements for interface problems
    • Lamichhane B., Wohlmuth B. Mortar finite elements for interface problems. Computing 2004, 72:333-348.
    • (2004) Computing , vol.72 , pp. 333-348
    • Lamichhane, B.1    Wohlmuth, B.2
  • 45
    • 80053437887 scopus 로고    scopus 로고
    • Lapack Version 3.2.2, Linear Algebra Package, 2010. Available from: .
    • Lapack Version 3.2.2, Linear Algebra Package, 2010. Available from: http://www.netlib.org/lapack/.
  • 46
    • 33744937342 scopus 로고    scopus 로고
    • A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities
    • Mergheim J., Steinmann P. A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities. Comput. Methods Appl. Mech. Engrg. 2006, 195:5037-5052.
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 5037-5052
    • Mergheim, J.1    Steinmann, P.2
  • 48
    • 0032642477 scopus 로고    scopus 로고
    • Algorithmic aspects of deformation dependent loads in non-linear static finite element analysis
    • Mok D.P., Wall W.A., Bischoff M., Ramm E. Algorithmic aspects of deformation dependent loads in non-linear static finite element analysis. Engrg. Comput. 1999, 16(5):601-618.
    • (1999) Engrg. Comput. , vol.16 , Issue.5 , pp. 601-618
    • Mok, D.P.1    Wall, W.A.2    Bischoff, M.3    Ramm, E.4
  • 49
    • 80053452299 scopus 로고    scopus 로고
    • Netgen Version 4.9.13, Tetrahdral mesh generator developed by Joachim Schöberl, 2010. Available from.
    • Netgen Version 4.9.13, Tetrahdral mesh generator developed by Joachim Schöberl, 2010. Available from: http://sourceforge.net/projects/netgen-mesher.
  • 51
    • 80053444903 scopus 로고    scopus 로고
    • PARDISO Solver Project, Direct solver developed by O. Schenk, K. Gärtner et al., 2010. Available from.
    • PARDISO Solver Project, Direct solver developed by O. Schenk, K. Gärtner et al., 2010. Available from: http://www.pardiso-project.org.
  • 52
    • 34748910579 scopus 로고    scopus 로고
    • Finite Cell Method: h- and p- extension for embedded domain methods in solid mechanics
    • Parvizian J., Düster A., Rank E. Finite Cell Method: h- and p- extension for embedded domain methods in solid mechanics. Comput. Mech. 2007, 41:122-133.
    • (2007) Comput. Mech. , vol.41 , pp. 122-133
    • Parvizian, J.1    Düster, A.2    Rank, E.3
  • 54
    • 80053451142 scopus 로고    scopus 로고
    • 3D composite finite elements for elliptic boundary value problems with discontinuous coefficients, SIAM Journal on Scientific Computing (submitted for publication).
    • T. Preusser, M. Rumpf, S. Sauter, L.O. Schwen, 3D composite finite elements for elliptic boundary value problems with discontinuous coefficients, SIAM Journal on Scientific Computing (submitted for publication).
    • Preusser, T.1    Rumpf, M.2    Sauter, S.3    Schwen, L.O.4
  • 55
    • 33751037366 scopus 로고    scopus 로고
    • A fictitious domain approach with spread interface for elliptic problems with general boundary conditions
    • Ramière I., Angot P., Belliard M. A fictitious domain approach with spread interface for elliptic problems with general boundary conditions. Comput. Methods Appl. Mech. Engrg. 2007, 196:766-781.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 766-781
    • Ramière, I.1    Angot, P.2    Belliard, M.3
  • 56
    • 0026989498 scopus 로고
    • Adaptive remeshing and h-p domain decomposition
    • Rank E. Adaptive remeshing and h-p domain decomposition. Comput. Methods Appl. Mech. Engrg. 1992, 101:299-313.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.101 , pp. 299-313
    • Rank, E.1
  • 59
    • 78751645365 scopus 로고    scopus 로고
    • Immersed b-spline (i-spline) finite element method for geometrically complex domains
    • Sanches R.A.K., Bornemann P.B., Cirak F. Immersed b-spline (i-spline) finite element method for geometrically complex domains. Comput. Methods Appl. Mech. Engrg. 2011, 200(13-16):1432-1445.
    • (2011) Comput. Methods Appl. Mech. Engrg. , vol.200 , Issue.13-16 , pp. 1432-1445
    • Sanches, R.A.K.1    Bornemann, P.B.2    Cirak, F.3
  • 61
    • 84857137232 scopus 로고    scopus 로고
    • The hp-d adaptive Finite Cell Method for geometrically nonlinear problems of solid mechanics, Int. J. Numer. Methods Engrg. (in press), .
    • D. Schillinger, A. Düster, E. Rank, The hp-d adaptive Finite Cell Method for geometrically nonlinear problems of solid mechanics, Int. J. Numer. Methods Engrg. (in press), doi:10.1002/nme.3289.
    • Schillinger, D.1    Düster, A.2    Rank, E.3
  • 62
    • 0021312293 scopus 로고
    • Displacement dependent pressure loads in nonlinear finite element analyses
    • Schweizerhof K., Ramm E. Displacement dependent pressure loads in nonlinear finite element analyses. Comput. Struct. 1984, 18:1099-1114.
    • (1984) Comput. Struct. , vol.18 , pp. 1099-1114
    • Schweizerhof, K.1    Ramm, E.2
  • 64
    • 70349693647 scopus 로고    scopus 로고
    • Numerical investigations of foam-like materials by nested high-order finite element methods
    • Sehlhorst H.-G., Jänicke R., Düster A., Rank E., Steeb H., Diebels S. Numerical investigations of foam-like materials by nested high-order finite element methods. Comput. Mech. 2009, 45:45-59.
    • (2009) Comput. Mech. , vol.45 , pp. 45-59
    • Sehlhorst, H.-G.1    Jänicke, R.2    Düster, A.3    Rank, E.4    Steeb, H.5    Diebels, S.6
  • 65
    • 0026238022 scopus 로고
    • A note on finite-element implementation of pressure boundary loading
    • Simo J.C., Taylor R.L., Wriggers P. A note on finite-element implementation of pressure boundary loading. Commun. Appl. Numer. Methods 1991, 7:513-525.
    • (1991) Commun. Appl. Numer. Methods , vol.7 , pp. 513-525
    • Simo, J.C.1    Taylor, R.L.2    Wriggers, P.3
  • 67
    • 53549093022 scopus 로고    scopus 로고
    • Generalized finite element method for modeling nearly incompressible bimaterial hyperelastic solids
    • Srinivasan K.R., Matouš K., Geubelle P.H. Generalized finite element method for modeling nearly incompressible bimaterial hyperelastic solids. Comput. Methods Appl. Mech. Engrg. 2008, 197:4882-4893.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.197 , pp. 4882-4893
    • Srinivasan, K.R.1    Matouš, K.2    Geubelle, P.H.3
  • 69
  • 71
    • 80053436642 scopus 로고    scopus 로고
    • Trilinos Version 10.2, Sandia National Laboratories, Los Alamos, NM, 2010. Available from.
    • Trilinos Version 10.2, Sandia National Laboratories, Los Alamos, NM, 2010. Available from: http://trilinos.sandia.gov/.
  • 72
    • 80053447745 scopus 로고    scopus 로고
    • Visual DoMesh 2008 Version 1.1, Mesh generator developed by C. Sorger, Chair for Computation in Engineering, Technische Universität München, 2010.
    • Visual DoMesh 2008 Version 1.1, Mesh generator developed by C. Sorger, Chair for Computation in Engineering, Technische Universität München, 2010.
  • 74
    • 80053460596 scopus 로고    scopus 로고
    • Fast octree-based voxelization of 3D boundary representation objects, Technical report, Lehrstuhl für Bauinformatik, Technische Universität München
    • P. Wenisch, O. Wenisch, Fast octree-based voxelization of 3D boundary representation objects, Technical report, Lehrstuhl für Bauinformatik, Technische Universität München, 2004.
    • (2004)
    • Wenisch, P.1    Wenisch, O.2
  • 77
    • 34447537734 scopus 로고    scopus 로고
    • A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments
    • Yosibash Z., Padan R., Joskowicz L., Milgrom C. A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. J. Biomech. Engrg. 2007, 129:297-309.
    • (2007) J. Biomech. Engrg. , vol.129 , pp. 297-309
    • Yosibash, Z.1    Padan, R.2    Joskowicz, L.3    Milgrom, C.4


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