论文标题
一种新型的Lagrange乘数方法，放松梯度流
A novel Lagrange Multiplier approach with relaxation for gradient flows
论文作者
论文摘要
在本文中，我们提出了一种新型的Lagrange乘数方法，称为零因素（ZF）方法来解决一系列梯度流问题。基于新算法的数值方案是无条件的能量稳定的，并且不需要任何额外的假设条件。我们还证明，具有特定零因子的ZF方案导致流行的SAV型方法。为了降低计算成本并提高准确性和一致性，我们提出了一种零因素方法，并将其命名为“放松的零因子（RZF）方法”，以设计用于梯度流的无条件能量稳定方案。相对于更接近原始能量的改良能量，RZF方案可以被证明是无条件的能量稳定的，并提供了非常简单的计算过程。引入的零因子的变化与非线性自由能高度一致，这意味着引入的ZF方法是捕获非线性自由能的急剧耗散的一种非常有效的方法。提供了几个数值示例，以证明该方法的提高效率和准确性。
In this paper, we propose a novel Lagrange Multiplier approach, named zero-factor (ZF) approach to solve a series of gradient flow problems. The numerical schemes based on the new algorithm are unconditionally energy stable with the original energy and do not require any extra assumption conditions. We also prove that the ZF schemes with specific zero factors lead to the popular SAV-type method. To reduce the computation cost and improve the accuracy and consistency, we propose a zero-factor approach with relaxation, which we named the relaxed zero-factor (RZF) method, to design unconditional energy stable schemes for gradient flows. The RZF schemes can be proved to be unconditionally energy stable with respect to a modified energy that is closer to the original energy, and provide a very simple calculation process. The variation of the introduced zero factor is highly consistent with the nonlinear free energy which implies that the introduced ZF method is a very efficient way to capture the sharp dissipation of nonlinear free energy. Several numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.
