Geometry independent field approximations in finite and boundary element methods

In collaboration with Prof. Gang Xu, Hangzhou Dianzi University, Hangzhou, P.R.China

Legato team members:  S. Tomar, E. Atroshchenko

In isogeometric analysis the same basis functions are used for the exact representation of the CAD-geometry and approximation of the solution fields. However, in some cases, such representations may not be efficient, since the properties of the geometry may be different from the properties of the solution fields. To overcome this deficiency, the Legato team has been working on developing the geometry independent field approximations in both, finite and boundary element methods.

The main idea of the geometry independent field approximations:

gifa1

Example: The error maps for Laplace’s equation with the homogeneous Dirichlet BCs: NURBS geometry + PHT-splines solution field:

error_map

 

Future work:

The directions of the future research include:

  • Mathematical foundations of the method
  • Construction of the solution spaces, best suitable for analysis, from the geometry parameterization
  • Adaptive solution refinement and error estimates

     

For the technical details see:

Gang Xu, Elena Atroshchenko, Weiyin Ma, Stephane P.A. Bordas, Geometry-Independent Field approximaTion (GIFT) for Adaptive Spline-Based Finite Element Analysis, http://hdl.handle.net/10993/14029

 

Conference presentations:

E. Atroshchenko, X. Peng, J. Hale, S. Tomar, S.P.A. Bordas, Boundary Element Method with NURBS-geometry and independent field approximations in plane elasticity, 1st Pan-American Congress on Computational Mechanics (PANACM), Buenos Aires, Argentina, 2014, http://hdl.handle.net/10993/18627

E. Atroshchenko, X. Peng, S.P.A. Bordas, Isogeometric boundary element method in plane micropolar elasticity, 11th World Congress on Computational Mechanics (WCCM), Barcelona, Spain, 2014

G. Xu, E. Atroshchenko, S.P.A. Bordas, Geometry-independent field approximation for spline-based Finite Element Methods, 11th World Congress on Computational Mechanics (WCCM), Barcelona, Spain, 2014, http://hdl.handle.net/10993/14029