IETI – Isogeometric Tearing and Interconnecting

Highlights ► A new IsogEometric Tearing and Interconnecting (IETI) method is proposed. ► Exact geometry representation of IGA and solver design of FETI methods are combined. ► Coupling conditions for interfaces, including hanging knots, are discussed. ► Efficient preconditioning techniques for the interface problem are presented. ► Some local refinement options for IGA are discussed.

[1]  Liping Liu THEORY OF ELASTICITY , 2012 .

[2]  C. Farhat,et al.  Optimal convergence properties of the FETI domain decomposition method , 1994 .

[3]  T. Hughes,et al.  B¯ and F¯ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements , 2008 .

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

[5]  Tom Lyche,et al.  Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis , 2010 .

[6]  G. Sangalli,et al.  IsoGeometric Analysis using T-splines , 2012 .

[7]  Olof B. Widlund,et al.  Dual‐primal FETI methods for linear elasticity , 2006 .

[8]  Thomas J. R. Hughes,et al.  On linear independence of T-spline blending functions , 2012, Comput. Aided Geom. Des..

[9]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[10]  Hendrik Speleers,et al.  THB-splines: The truncated basis for hierarchical splines , 2012, Comput. Aided Geom. Des..

[11]  T. Hughes,et al.  Isogeometric fluid-structure interaction: theory, algorithms, and computations , 2008 .

[12]  Olaf Steinbach,et al.  Boundary Element Tearing and Interconnecting Methods , 2003, Computing.

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

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

[15]  Bert Jüttler,et al.  Enhancing isogeometric analysis by a finite element-based local refinement strategy , 2012 .

[16]  Régis Duvigneau,et al.  Parameterization of computational domain in isogeometric analysis: Methods and comparison , 2011 .

[17]  Niels Leergaard Pedersen,et al.  Discretizations in isogeometric analysis of Navier-Stokes flow , 2011 .

[18]  O. Widlund,et al.  FETI and Neumann--Neumann Iterative Substructuring Methods: Connections and New Results , 1999 .

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

[20]  G. Sangalli,et al.  Isogeometric analysis in electromagnetics: B-splines approximation , 2010 .

[21]  J. Mandel,et al.  Convergence of a substructuring method with Lagrange multipliers , 1994 .

[22]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[23]  B. Simeon,et al.  A hierarchical approach to adaptive local refinement in isogeometric analysis , 2011 .

[24]  Jiansong Deng,et al.  Polynomial splines over hierarchical T-meshes , 2008, Graph. Model..

[25]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[26]  Bert Jüttler,et al.  Existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis , 2011 .

[27]  Elaine Cohen,et al.  Volumetric parameterization and trivariate b-spline fitting using harmonic functions , 2008, SPM '08.

[28]  D. Rixen,et al.  FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method , 2001 .

[29]  Timothy A. Davis,et al.  Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

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

[31]  Luca F. Pavarino,et al.  Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains , 2008 .

[32]  Chang-Ock Lee,et al.  A Preconditioner for the FETI-DP Formulation with Mortar Methods in Two Dimensions , 2004, SIAM J. Numer. Anal..

[33]  Olaf Steinbach,et al.  The all-floating boundary element tearing and interconnecting method , 2009, J. Num. Math..

[34]  T. Hughes,et al.  Local refinement of analysis-suitable T-splines , 2012 .

[35]  H. Nguyen-Xuan,et al.  Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids , 2011 .

[36]  Jan Mandel,et al.  On the convergence of a dual-primal substructuring method , 2000, Numerische Mathematik.

[37]  U. Langer,et al.  Coupled Finite and Boundary Element Tearing and Interconnecting solvers for nonlinear potential problems , 2006 .

[38]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[39]  Jiansong Deng,et al.  Polynomial splines over general T-meshes , 2010, The Visual Computer.

[40]  Olof B. Widlund,et al.  DUAL-PRIMAL FETI METHODS FOR THREE-DIMENSIONAL ELLIPTIC PROBLEMS WITH HETEROGENEOUS COEFFICIENTS , 2022 .

[41]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[42]  John Hart,et al.  ACM Transactions on Graphics , 2004, SIGGRAPH 2004.

[43]  Martin Aigner,et al.  Swept Volume Parameterization for Isogeometric Analysis , 2009, IMA Conference on the Mathematics of Surfaces.

[44]  Daniel Rixen,et al.  Preconditioning the FETI Method for Problems with Intra- and Inter-Subdomain Coefficient Jumps , 1997 .

[45]  Z. Dostál,et al.  Total FETI—an easier implementable variant of the FETI method for numerical solution of elliptic PDE , 2006 .

[46]  T. Hughes,et al.  ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES , 2006 .

[47]  S. Timoshenko,et al.  Theory of Elasticity (3rd ed.) , 1970 .

[48]  Bert Jüttler,et al.  Volumetric Geometry Reconstruction of Turbine Blades for Aircraft Engines , 2010, Curves and Surfaces.

[49]  Elaine Cohen,et al.  Volumetric parameterization of complex objects by respecting multiple materials , 2010, Comput. Graph..

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

[51]  Olof B. Widlund,et al.  A Domain Decomposition Method with Lagrange Multipliers and Inexact Solvers for Linear Elasticity , 2000, SIAM J. Sci. Comput..

[52]  John A. Evans,et al.  Isogeometric finite element data structures based on Bézier extraction of NURBS , 2011 .

[53]  M. Scott,et al.  On the Nesting Behavior of T-splines , 2011 .

[54]  G. Sangalli,et al.  IsoGeometric analysis using T-splines on two-patch geometries , 2011 .

[55]  Ahmad H. Nasri,et al.  T-splines and T-NURCCs , 2003, ACM Trans. Graph..

[56]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

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