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首页> 外文期刊>Engineering analysis with boundary elements >Reconstruction of inaccessible boundary value in a sideways parabolic problem with variable coefficients-Forward collocation with finite integration method
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Reconstruction of inaccessible boundary value in a sideways parabolic problem with variable coefficients-Forward collocation with finite integration method

机译：变系数侧身抛物线问题中不可访问的边值的重构-有限积分的正向搭配

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摘要

We investigate a sideways problem of reconstructing an inaccessible boundary value for parabolic equation with variable coefficients. Formulating the sideways problem into a sequence of well-posed direct problems (DP) and a system of Ordinary Differential Equations (ODE), we combine the recently developed finite integration method (FIM) with radial basis functions (RBF) to iteratively obtain the solution of each DP by solving an ill-posed linear system. The use of numerical integration instead of finite quotient formula in FIM completely avoids the well known roundoff-discretization errors problem in finite difference method and the use of RBF as forward collocation method (FCM) gives a truly meshless computational scheme. For tackling the ill-posedness of the sideways problem, we adapt the traditional Tikhonov regularization technique to obtain stable solution to the system of ODEs. Convergence analysis is then derived and error estimate shows that the error tends to zero when perturbation δ→0. We can then obtain highly accurate and stable solution under some assumptions. Numerical results validate the feasibility and effectiveness of the proposed numerical algorithms.
机译：我们研究了一个侧向问题，该问题为可变系数的抛物线方程重建了一个不可访问的边界值。将侧向问题表达为一系列正定直接问题（DP）和一个常微分方程组（ODE），我们将最近开发的有限积分方法（FIM）与径向基函数（RBF）结合起来以迭代方式获得解通过解一个不适定的线性系统来求解每个DP。在FIM中使用数值积分代替有限商公式完全避免了有限差分法中众所周知的舍入离散误差问题，而RBF作为正向搭配方法（FCM）的使用提供了真正的无网格计算方案。为了解决横向问题的不适定性，我们采用了传统的Tikhonov正则化技术来获得ODE系统的稳定解。然后进行收敛分析，误差估计表明，当扰动δ→0时，误差趋于零。然后我们可以在某些假设下获得高度准确和稳定的解决方案。数值结果验证了所提出数值算法的可行性和有效性。

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