Efficient Continuation Methods for Computing Ground States of Quasi-2D Rotating Dipolar Bose-Einstein Condensates
Algorithm 2
A two-parameter continuation algorithm for computing the ground state of a quasi-2D rotating dipolar BEC.
Input:
the initial value of the parameter .
the final value of the parameter .
accuracy tolerance for .
Step 1. Use Algorithm 1 to compute the ground state solution of (18)–(20) with . Set this solution as .
Step 2. Add as the second continuation parameter and trace the ground state solution curve of (18)–(20) until :
Use as the starting point and set .
whiledo
(i) .
(ii) Compute and .
(iii) Treat and as the continuation parameters simultaneously, and perform the predictor-corrector process once to obtain a solution of (18) with under the normalization condition (20). Set this solution as .
(iv) Set and compute ,.
(v) .
(vi) Use as the initial guess and perform Newton’s method to solve (18) with and (20) simultaneously. Set this solution as .
(vii) Compute and .
(viii) Repeat the procedure (v)–(vii) until , then set which is the ground state solution of (18)–(20) with .
