摘要
为了更好地求解氧扩散问题,给出了一种半光滑牛顿算法。首先在离散格式上采用Crank-Nicolson方法,其次在迭代算法上使用非线性互补函数,将求解非线性互补问题转化为求解基于非线性互补函数的半光滑方程组,进而用广义牛顿法求解,避免约束条件带来的计算困难。最后给出该算法在满足超线性收敛条件下的数值实验结果,验证该算法对解决氧扩散问题的可行性。
This paper gave a semismooth Newton algorithm for solving the oxygen diffusion.The Crank-Nicolson method was used in the discrete format,and then the nonlinear complementary function was used in the iterative algorithm.The solution of the nonlinear complementarity problem is transformed into solving the semismooth system of equations based on the nonlinear complementary function,and then the generalized Newton method was used to solve the problem to avoid calculation difficulties caused by constraints.The numerical experimental results of the algorithm under the condition of super-linear convergence were given to verify the feasibility of the algorithm to solve the oxygen diffusion problem.
作者
曹梦霖
宇振盛
CAO Meng-lin;YU Zhen-sheng(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)
出处
《广西大学学报（自然科学版）》
CAS
北大核心
2022年第3期797-803,共7页
Journal of Guangxi University（Natural Science Edition）
基金
全国行业职业教育教学指导委员会教育改革创新项目(HBKC213014)。
关键词
半光滑牛顿算法
移动边界问题
非线性互补算法
有限差分法
偏微分方程
最优化
semismooth Newton algorithm
moving boundary problem
nonlinear complementarity algorithm
finite difference scheme
partial differential equation
optimization
