AN ISOGEOMETRIC BOUNDARY ELEMENT METHOD WITH FAST MULTIPOLE EXPANSION APPLIED TO PROBLEMS OF HEAT CONDUCTION

Resumo

This work presents an isogeometric formulation of the fast multipole boundary element
method and its application in heat conduction problems. The formulation is developed using complex
variables, expansion of fundamental solutions in Taylor series and using NURBS as shape functions. To
reduce the computational cost and facilitate implementation, NURBS are decomposed into Bezier curves, ́
making the isogeometric formulation more similar to the traditional boundary element method. Since
influence matrices are not explicitly assembled, it is necessary to use an iterative method for solving
the linear system. The generalized minimum residue method (GMRES) was chosen, based on previous
work. A description of the hierarchical data structure and of the implemented algorithm is presented.
Validation is performed by comparing results of the proposed formulation with those of the conventional
boundary element formulation. The computational cost of both formulations are analyzed showing the
advantages of the proposed formulation for large scale problems (problems with more than 100 thousand
degrees for freedom).