# Efficient Evaluation of Casimir Force in Arbitrary Three-dimensional Geometries by Integral Equation Methods 

Jie L. Xiong, Mei Song Tong, Phillip Atkins, and Weng Cho Chew ∗ 

Faculty of Engineering, University of Hong Kong, Hong Kong; Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Illinois, USA, 61801 

(Dated: March 22, 2018) 

## Abstract 

In this paper, we generalized the surface integral equation method for the evaluation of Casimir force in arbitrary three-dimensional geometries. Similar to the two-dimensional case, the evalua- tion of the mean Maxwell stress tensor is cast into solving a series of three-dimensional scattering problems. The formulation and solution of the three-dimensional scattering problem is well-studied in classical computational electromagnetics. This paper demonstrates that this quantum electrody- namic phenomena can be studied using the knowledge and techniques of classical electrodynamics. 

