In this paper,we propose an accelerated search-extension method (ASEM) based on the interpolated coeffcient finite element method,the search-extension method (SEM) and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems,but also reduces the expensive computation greatly. The numerical results in 1-D and 2-D cases will show the effciency of our approach.
