Efficient Continuation Methods for Computing Ground States of Quasi-2D Rotating Dipolar Bose-Einstein Condensates
Algorithm 1
A single-parameter continuation algorithm for computing the ground state of a quasi-2D rotating dipolar BEC.
Input:
the -th iterate of the iterative continuation scheme.
accuracy tolerance for two consecutive bifurcation points.
accuracy tolerance for .
,.
Step 1. Compute the first bifurcation point of (18) with .
while ( or )do
(i) .
(ii) Treat as the continuation parameter and use the classical continuation algorithm to trace the ground state solution curve of (18) with until the constraint (20) is satisfied. Set this solution as .
(iii) Compute and .
(iv) Compute the first bifurcation point of (18) with .
end
Step 2. Set and ,.
while ( or )do
(i) .
(ii) Use the approximate solution as the initial guess, and perform the Newton method to solve (18) with and (20) simultaneously.
(iii) Set the approximate solution obtained in (ii) by .
