SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2489-A2513, January 2020.
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the scalar auxiliary variable (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 preserves 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.

中文翻译：

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保留梯度流的标量辅助变量方案的全局约束

SIAM科学计算杂志，第42卷，第4期，第A2489-A2513页，2020年1月。
我们开发了几种有效的数值方案，它们精确地保留了约束梯度流的全局约束。我们的方案基于标量辅助变量（SAV）方法和拉格朗日乘数方法。它们与无约束梯度流的SAV方案一样有效，即仅需要在每个时间步求解具有恒定系数的线性方程式，再加上可以以可忽略的成本求解的附加非线性代数系统，可以无条件地保持能量稳定并精确地保留约束梯度流的全局约束。充分的数值结果为相场囊泡膜和最佳分配模型被提出来验证所提出的数值方案的有效性和准确性。