Numerical Simulation of Heat Conduction Problems by a New Fast Multipole Hybrid Boundary-Node Method

Abstract

The fast multipole method (FMM) is an effective technique to reduce the computational cost in solving large-scale problems. In this article, a new fast multipole hybrid boundary-node method (FM-HBNM) is presented to solve three-dimensional heat conduction problems. In the new FM-HBNM, a diagonal form for translation operators is used and the computational cost of the multipole to local (M2L) translation is further reduced. Formulations for the new FM-HBNM are derived. The computational costs for the original and new FM-HBNM are estimated. The numerical results show that a speed-up about 2–3 times can be achieved by the new FM-HBNM.

Acknowledgments

Financial support for the project from the National Natural Science Foundation of China (No. 51378234) and the National Basic Research Program of China (973 Program: 2011CB013800) is gratefully acknowledged.