An application of the integrated penalty method to free boundary problems of laplace equation
An application of the integrated penalty method to free boundary problems of laplace equation
复制标题
积分惩罚法在拉普拉斯方程自由边界问题中的应用
DOI：
10.1080/01630568108816076
复制
发表时间：
1981
影响因子：
1.2
通讯作者：
H. Kawarada
中科院分区：
文献类型：
--
作者：
M. Natori;H. Kawarada
用数值方法求解了在环空中定义的拉普拉斯方程的自由边界问题。将原问题转化为优化问题。状态方程近似为一个带有惩罚项的方程，该方程近似于自由边界上的一个边界条件。通过自由边界的通量由上述罚项的积分计算（积分罚项法）。用有限差分法数值求解了这种惩罚优化问题。采用不完全Cholesky分解结合共轭梯度法求解线性方程组。给出了一些数值算例。
Free boundary problems of Laplace equation defined in the annulus in are numerically solved. The original problem is transformed to an optimization problem. The state equation is approximated by an equation with a penalty term which approximates one of boundary conditions on the free boundary. The flux through the free boundary is calculated by the integration of the penalty term introduced above ( Integrated Penalty Method ). This penalized optimization problem is numerically solved by finite difference method. Incomplete Cholesky decomposition combined with the conjugate gradient method is used to solve systems of linear equations. Some numerical examples are given.