A Numerical Method for Filtering the Noise in the Heat Conduction Problem

Yao Sun, Xiaoliang Wei, Zibo Zhuang and Tian Luan
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Yao Sun: College of Science, Civil Aviation University of China, Tianjin 300300, China
Xiaoliang Wei: College of Science, Civil Aviation University of China, Tianjin 300300, China
Zibo Zhuang: Flight Technology College, Civil Aviation University of China, Tianjin 300300, China
Tian Luan: School of Mathematics and Statics, Beihua University, Jilin 132013, China

Mathematics, 2019, vol. 7, issue 6, 1-13

Abstract: In this paper, we give an effective numerical method for the heat conduction problem connected with the Laplace equation. Through the use of a single-layer potential approach to the solution, we get the boundary integral equation about the density function. In order to deal with the weakly singular kernel of the integral equation, we give the projection method to deal with this part, i.e., using the Lagrange trigonometric polynomials basis to give an approximation of the density function. Although the problems under investigation are well-posed, herein the Tikhonov regularization method is not used to regularize the aforementioned direct problem with noisy data, but to filter out the noise in the corresponding perturbed data. Finally, the effectiveness of the proposed method is demonstrated using a few examples, including a boundary condition with a jump discontinuity and a boundary condition with a corner. Whilst a comparative study with the method of fundamental solutions (MFS) is also given.

Keywords: laplace equation; jump discontinuity; boundary element method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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