论文标题
反馈控制时间步长适应性的非本地Cahn-Hilliard方程的有限元元素解决方案
Finite element solution of nonlocal Cahn-Hilliard equations with feedback control time step size adaptivity
论文作者
论文摘要
在这项研究中，我们评估了基于反馈控制的时间步骤适应性方案的性能，用于从Ohta-Kawasaki自由能函数中得出的非本地Cahn-Hilliard方程。在配备有误差估计的线性反馈控制理论下，时间适应性方案是重铸造的，该理论可推断从能量稳定的，完全隐含的时间行进方案中获得的解决方案。我们测试具有不同属性的三个时间步长控制器：简单的积分控制器，一个完整的比例综合衍生控制器和PC11预测控制器。我们根据完整的模拟所需的时间步数以及由所需数量的非线性和线性求解器迭代衡量的计算工作的时间步长评估非本地Cahn-Hilliard方程的自适应方案的性能。我们还提供了与三个不同时间步长控制器模拟的质量保护和自由能衰减的数值证据。 PC11预测控制器在所有三维测试用例中都是最好的。
In this study, we evaluate the performance of feedback control-based time step adaptivity schemes for the nonlocal Cahn-Hilliard equation derived from the Ohta-Kawasaki free energy functional. The temporal adaptivity scheme is recast under the linear feedback control theory equipped with an error estimation that extrapolates the solution obtained from an energy-stable, fully implicit time marching scheme. We test three time step controllers with different properties: a simple Integral controller, a complete Proportional-Integral-Derivative controller, and the PC11 predictive controller. We assess the performance of the adaptive schemes for the nonlocal Cahn-Hilliard equation in terms of the number of time steps required for the complete simulation and the computational effort measured by the required number of nonlinear and linear solver iterations. We also present numerical evidence of mass conservation and free energy decay for simulations with the three different time step controllers. The PC11 predictive controller is the best in all three-dimensional test cases.
