Efficient Preserving Structure Numerical Methods for Gradient Flows in Eulerian and Lagrangian Coordinates

Speaker:

Qing Cheng, Department of Applied Mathematics, Illinois Institute of Technology

 

Description:

We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient as the SAV schemes for unconstrained gradient flows, i.e., only require solving linear equations with constant coefficients at each time step plus an additional nonlinear algebraic system which can be solved at negligible cost, can be unconditionally energy stable, and preserve exactly the global constraints for constrained gradient flows. Ample numerical results for phase-field vesicle membrane and optimal partition models are presented to validate the effectiveness and accuracy of the proposed numerical schemes.

 

Topic:

Stochastic and Multiscale Modeling and Computation