二维Helmholtz方程不适定问题的一种算子软化正则法
An Operator Mollification Method to Ill-posed Problem for Two-dimensional Helmholtz Equation
本文研究带有混合边界的二维Helmholtz方程不适定问题.为了获得稳定的数值解,利用基于de la ValléePoussin算子的软化正则方法,得到了正则近似解,给出正则近似解与精确解之间在先验参数选取规则之下的误差估计,并通过数值实验检验了数据有噪声扰动时方法的有效性和稳定性.
In this paper, the ill-posed Cauchy problem for two-dimensional Helmholtz equation with mixed boundary is investigated. To obtain stable numerical solution, a mollification regularization method with the de la Vallée Poussin operator is proposed. Error estimate between the exact solution and its approximation is given under the proper choice of a priori parameter. A numerical experiment shows that our procedure is effective and stable with respect to perturbations of noise in the data.
Helmholtz方程 / 不适定问题 / de la Vallé / e Poussin算子 / 软化法 / 误差估计 {{custom_keyword}} /
Helmholtz equation / ill-posed / de la vallée Poussin operator / mollification method / error estimate {{custom_keyword}} /
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国家自然科学基金资助项目(11961054)
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