Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates

Abstract

Efficient and accurate numerical schemes, based on the scalar auxiliary variable (SAV) approach, are proposed to find the ground state solutions of one- and multi-component Bose-Einstein Condensates (BECs). Two types of SAV schemes are proposed: the first is based on the original SAV scheme for the imaginary time gradient flow of BECs which is accurate for the dynamic evolution; the second is a modified SAV scheme based on the normalized imaginary time gradient flow and leads to fast convergence towards the steady state solutions. Detailed numerical comparison with existing methods based on projection to the constrained space indicates that the modified SAV schemes are more efficient, particularly for the multi-component BECs.