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Concept
Isogeometric analysis
Summary
Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. Currently, it is necessary to convert data between CAD and FEA packages to analyse new designs during development, a difficult task since the two computational geometric approaches are different. Isogeometric analysis employs complex NURBS geometry (the basis of most CAD packages) in the FEA application directly. This allows models to be designed, tested and adjusted in one go, using a common data set.
The pioneers of this technique are Tom Hughes and his group at The University of Texas at Austin. A reference free software implementation of some isogeometric analysis methods is GeoPDEs. Likewise, other implementations can be found online. For instance, PetIGA is an open framework for high performance isogeometric analysis heavily based on PETSc. In addition, MIGFEM is another IGA code which is implemented in Matlab and supports Partition of Unity enrichment IGA for 2D and 3D fracture. Furthermore, G+Smo is an open C++ library for isogeometric analysis. In particular, FEAP is a finite element analysis program which includes an Isogeometric analysis library FEAP IsoGeometric (Version FEAP84 & Version FEAP85). An account of the developments leading up to IGA has been documented in.
Isogeometric analysis presents two main advantages with respect to the finite element method:
There is no geometric approximation error, due to the fact the domain is represented exactly
Wave propagation problems, arising for instance in cardiac electrophysiology, acoustics and elastodynamics, are better described, thanks to the reduction of numerical dispersion and dissipation errors.
In the framework of IGA, the notions of both control mesh and physical mesh are defined.
A control mesh is made by the so called control points and it is obtained by a piecewise linear interpolation of them. Control points play also the role of degrees of freedom (DOFs).
Official source
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