Fast isogeometric boundary element method based on independent field approximation

• We present an alternative isogeometric BEM for elasticity on NURBS patches.
• Boundary data and geometry are approximated independently which avoids redundancies.
• Hierarchical matrices provide almost linear computational complexity.
• Comparison of different Ansatz functions on NURBS patches.
• The results show optimal convergence for all tested orders.

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology are demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.