firb

Isogeometric Discretizations in Continuum Mechanics

a FIRB "Futuro in ricerca" project


Project information

  • Project duration: Apr. 2010 - Nov. 2014

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Project summary

Isogeometric Analysis (IGA in short), based on Non-Uniform Rational B-Splines (NURBS), is a generalization of the classical finite element analysis. It has recently been introduced by Hughes and coworkers in the ICES Report 04-51. The idea is to use NURBS functions instead of piecewise polinomial functions, in the isoparametric way. Therefore, NURBS both span the discrete approximation space and are used for the geometry description. This is consistent with CAD systems, that also use NURBS to represent the geometrical objects. As a result, the isogeometric approach possesses two important features: it makes possible the exact geometric representation of CAD objects and simplifies and generalizes mesh refinement.

The first numerical testing shows that IGA holds great promises, with a substantial increase in the accuracy-to-computational-effort ratio with respect to FEMs. The goal of this project is to develop IGA for continuum mechanics problems, in particular large-deformation incompressible elasticity.


The C++ isogeometric project "igatools"

Within this FIRB research project, Massimiliano Martinelli started coding a C++ isogeometric code for specific application to solid mechanics. In 2012 MAssimiliano Martinelli and Sebastian Pauletti evolved it to a general purpose, modernly designed isogemetric library to numerically solve partial differential equations using isogeometric spaces, with full redesign of the library. This project, denoted igatools is growing thanks to the work of other collaborators and users, and support of co-operating research projects (see igatools web-page for details).

Some of the features are:

  • Object oriented design
  • Dimension independent code through templates
  • Support for parallel processing (MPI/Multithreding)
  • Computational efficiency
  • Extensive and automatic test suite (CDash)
  • Modern bug tracking system (TRAC)
  • Defensing programming
  • Extensive documentation
  • Community support through user group and wiki pages
  • Integration with computer-graphics libraries

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