摘要
提出了一种求解非线性偏微分方程形状优化问题的径向基函数方法.灵敏度分析结果采用的共轭方法;形状的演化通过最优性准则方法得到;控制方程和共轭方程的求解用的是径向基函数方法.由于径向基函数方法是真正的无网格方法,比网格依赖方法有更好的适应性.提供的数值算例说明了所提算法的稳定性和有效性.此外,所得方法可以灵活地与其他优化算法相结合,从而可以解决更复杂的非线性偏微分方程中的最优形状设计问题.
A radial basis function method for solving the shape optimization problem of nonlinear partial differential equation(PDE)is presented.The sensitivity analysis result of the optimal control problem was achieved by the adjoint method,and the shape is updated by the optimality criteria(OC)method.The control equations and the adjoint equations are solved by the radial basis function method.Since the radial basis function method is a true mesh-free method,it has better adaptability than the mesh-dependent method.The numerical example was provided to illustrate the stability and effectiveness of the proposed algorithm.Furthermore,the proposed method is flexible to be coupled with other optimization algorithm,and is intended to solve more complex optimal shape design problems of nonlinear partial differential equations.
作者
段献葆
党妍
秦玲
DUAN Xianbao;DANG Yan;QIN Ling(School of Sciences,Xi'an University of Technology,Xi'an 710048,China)
出处
《应用泛函分析学报》
2020年第1期24-32,共9页
Acta Analysis Functionalis Applicata
基金
国家自然科学基金(11601410,11971377)
陕西省自然科学基金(2019JM-284)。
