论文标题
关于第四阶梯度流的SAV-DG方法
On the SAV-DG method for a class of fourth order gradient flows
论文作者
论文摘要
对于一类第四阶梯度流问题，标量辅助变量（SAV）时间离散化与无惩罚的不连续的Galerkin（DG）空间离散化会导致SAV-DG方案。这些方案是线性的，并且无条件的能量稳定。但是，由于密度系数矩阵，降低的线性系统求解相当昂贵。在本文中，我们提供了一个程序，以预先评估分段多项式空间中的辅助变量。结果，当利用共轭梯度（CG）求解器时，$ o（\ Mathcal {n}^2）$的计算复杂性降低至$ O（\ Mathcal {n}）$。这种混合SAV-DG方法更有效，能够提供高精度的令人满意的结果。这也与解决SAV-DG方案的完整增强系统进行了比较。
For a class of fourth order gradient flow problems, integration of the scalar auxiliary variable (SAV) time discretization with the penalty-free discontinuous Galerkin (DG) spatial discretization leads to SAV-DG schemes. These schemes are linear and shown unconditionally energy stable. But the reduced linear systems are rather expensive to solve due to the dense coefficient matrices. In this paper, we provide a procedure to pre-evaluate the auxiliary variable in the piecewise polynomial space. As a result, the computational complexity of $O(\mathcal{N}^2)$ reduces to $O(\mathcal{N})$ when exploiting the conjugate gradient (CG) solver. This hybrid SAV-DG method is more efficient and able to deliver satisfactory results of high accuracy. This was also compared with solving the full augmented system of the SAV-DG schemes.
