GeoPDEs: A research tool for Isogeometric Analysis of PDEs

GeoPDEs (http://geopdes.sourceforge.net) is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of the many IGA methods for the discretization of partial differential equations currently studied, mainly based on B-Splines and Non-Uniform Rational B-Splines (NURBS), while being flexible enough to allow users to implement new and more general methods with a relatively small effort. This paper presents the philosophy at the basis of the design of GeoPDEs and its relation to a quite comprehensive, abstract definition of IGA.

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

[2]  Thomas J. R. Hughes,et al.  An isogeometric approach to cohesive zone modeling , 2011 .

[3]  L. Schumaker Spline Functions: Basic Theory , 1981 .

[4]  Ronald H. W. Hoppe,et al.  Finite element methods for Maxwell's equations , 2005, Math. Comput..

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

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

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

[8]  Daniele Boffi Approximation of eigenvalues in mixed form, Discrete Compactness Property, and application to hp mixed finite elements , 2007 .

[9]  Giancarlo Sangalli,et al.  Isogeometric Discrete Differential Forms in Three Dimensions , 2011, SIAM J. Numer. Anal..

[10]  T. Belytschko,et al.  A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM , 2010 .

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

[12]  Carla Manni,et al.  Generalized B-splines as a tool in Isogeometric Analysis , 2011 .

[13]  Giancarlo Sangalli,et al.  IsoGeometric Analysis: Stable elements for the 2D Stokes equation , 2011 .

[14]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[15]  G. Sangalli,et al.  A fully ''locking-free'' isogeometric approach for plane linear elasticity problems: A stream function formulation , 2007 .

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

[17]  John W. Eaton,et al.  Gnu Octave Manual , 2002 .

[18]  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 .

[19]  Dongdong Wang,et al.  An improved NURBS-based isogeometric analysis with enhanced treatment of essential boundary conditions , 2010 .

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

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

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

[23]  ScienceDirect,et al.  Advances in engineering software , 2008, Adv. Eng. Softw..

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

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

[26]  J. Craggs Applied Mathematical Sciences , 1973 .

[27]  T. Hughes,et al.  Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations , 2010 .

[28]  Carla Manni,et al.  Quasi-interpolation in isogeometric analysis based on generalized B-splines , 2010, Comput. Aided Geom. Des..