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

[1]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[2]  Ernst Rank,et al.  The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics , 2012 .

[3]  M. Rumpf,et al.  3D Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients , 2011, SIAM J. Sci. Comput..

[4]  D. F. Rogers,et al.  An Introduction to NURBS: With Historical Perspective , 2011 .

[5]  Giancarlo Sangalli,et al.  Some estimates for h–p–k-refinement in Isogeometric Analysis , 2011, Numerische Mathematik.

[6]  Fehmi Cirak,et al.  Immersed b-spline (i-spline) finite element method for geometrically complex domains , 2011 .

[7]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

[8]  J. Dolbow,et al.  Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements , 2010 .

[9]  Ralf-Peter Mundani,et al.  The finite cell method for geometrically nonlinear problems of solid mechanics , 2010 .

[10]  E. Rank,et al.  Numerical investigations of foam-like materials by nested high-order finite element methods , 2009 .

[11]  C. Engwer,et al.  An unfitted finite element method using discontinuous Galerkin , 2009 .

[12]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[13]  V. Coffman,et al.  Modelling Microstructures with OOF2 , 2009 .

[14]  S. Esmaeili,et al.  Compressive properties of a new metal–polymer hybrid material , 2009 .

[15]  Isaac Harari,et al.  An efficient finite element method for embedded interface problems , 2009 .

[16]  A. Öchsner,et al.  Computed tomography based finite element analysis of the thermal properties of cellular aluminium , 2009 .

[17]  H. Tippur,et al.  Processing, compression response and finite element modeling of syntactic foam based interpenetrating phase composite (IPC) , 2009 .

[18]  P. Geubelle,et al.  Generalized finite element method for modeling nearly incompressible bimaterial hyperelastic solids , 2008 .

[19]  P. Wriggers.  Nonlinear Finite Element Methods , 2008 .

[20]  Alessandro Reali,et al.  Duality and unified analysis of discrete approximations in structural dynamics and wave propagation : Comparison of p-method finite elements with k-method NURBS , 2008 .

[21]  Ernst Rank,et al.  The finite cell method for three-dimensional problems of solid mechanics , 2008 .

[22]  Maciej Paszyński,et al.  Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications , 2007 .

[23]  Ernst Rank,et al.  Applying the hp–d version of the FEM to locally enhance dimensionally reduced models , 2007 .

[24]  L. Joskowicz,et al.  A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. , 2007, Journal of biomechanical engineering.

[25]  Ernst Rank,et al.  Finite cell method , 2007 .

[26]  Alessandro Reali,et al.  Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint) , 2007 .

[27]  R. Glowinski,et al.  Distributed Lagrange multipliers based on fictitious domain method for second order elliptic problems , 2007 .

[28]  Barbara Wohlmuth,et al.  Stable Lagrange multipliers for quadrilateral meshes of curved interfaces in 3D , 2007 .

[29]  E. Rank,et al.  Axisymmetric pressure boundary loading for finite deformation analysis using p-FEM , 2007 .

[30]  L. Demkowicz.  One and two dimensional elliptic and Maxwell problems , 2006 .

[31]  P. Steinmann,et al.  A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities , 2006 .

[32]  E. Ramm,et al.  Interface material failure modeled by the extended finite-element method and level sets , 2006 .

[33]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[34]  Peter Wriggers,et al.  An Introduction to Computational Micromechanics , 2004 .

[35]  P. Hansbo,et al.  A finite element method for the simulation of strong and weak discontinuities in solid mechanics , 2004 .

[36]  Tom Lyche,et al.  T-spline simplification and local refinement , 2004, ACM Trans. Graph..

[37]  Lucy T. Zhang,et al.  Immersed finite element method , 2004 .

[38]  Barbara I. Wohlmuth,et al.  Mortar Finite Elements for Interface Problems , 2004, Computing.

[39]  F. Han,et al.  Compressive behavior and energy absorbing characteristic of open cell aluminum foam filled with silicate rubber , 2003 .

[40]  I. Doležel,et al.  Higher-Order Finite Element Methods , 2003 .

[41]  Jean-François Remacle,et al.  A computational approach to handle complex microstructure geometries , 2003 .

[42]  Eitan Grinspun,et al.  Natural hierarchical refinement for finite element methods , 2003 .

[43]  Josef Hoschek,et al.  Handbook of Computer Aided Geometric Design , 2002 .

[44]  Ulrich Reif,et al.  Multigrid methods with web-splines , 2002, Numerische Mathematik.

[45]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[46]  I. Babuska,et al.  The generalized finite element method , 2001 .

[47]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[48]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[49]  D. P. Mok,et al.  Algorithmic aspects of deformation dependent loads in non‐linear static finite element analysis , 1999 .

[50]  O. C. Zienkiewicz,et al.  A new cloud-based hp finite element method , 1998 .

[51]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[52]  L. Schumaker,et al.  Surface Fitting and Multiresolution Methods , 1997 .

[53]  E. Rank,et al.  hp‐Version finite elements for geometrically non‐linear problems , 1995 .

[54]  E. Rank.  Adaptive remeshing and h-p domain decomposition , 1992 .

[55]  Peter Wriggers,et al.  A note on finite‐element implementation of pressure boundary loading , 1991 .

[56]  David R. Forsey,et al.  Hierarchical B-spline refinement , 1988, SIGGRAPH.

[57]  Long Chen.  FINITE ELEMENT METHOD , 2013 .

[58]  John A. Evans,et al.  Isogeometric analysis using T-splines , 2010 .

[59]  B. Simeon,et al.  Adaptive isogeometric analysis by local h-refinement with T-splines , 2010 .

[60]  T. Hughes,et al.  Efficient quadrature for NURBS-based isogeometric analysis , 2010 .

[61]  Ulrich Heisserer,et al.  High-order finite elements for material and geometric nonlinear finite strain problems , 2008 .

[62]  D. Owen,et al.  Computational methods for plasticity : theory and applications , 2008 .

[63]  P. Angot,et al.  A Fictitious domain approach with spread interface for elliptic problems with general boundary conditions , 2007 .

[64]  J. Tinsley Oden,et al.  An hp Adaptive Method Using Clouds C , 2006 .

[65]  Lars Ole Schwen,et al.  Composite Finite Elements for Complicated Microstructures , 2006 .

[66]  Peter Hansbo,et al.  AN UNFITTED FINITE ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS , 2001 .

[67]  A. Derose,et al.  Subdivision for modeling and animation , 2000 .

[68]  Gerald Farin,et al.  Curves and surfaces for cagd , 1992 .

[69]  K. Höllig.  Finite element methods with B-splines , 1987 .

[70]  Michael J. Miller,et al.  Introduction to Computer Graphics , 1984, Developing Graphics Frameworks with Python and OpenGL.

[71]  Ekkehard Ramm,et al.  Displacement dependent pressure loads in nonlinear finite element analyses , 1984 .