Reconstructing a space-dependent source term via the quasi-reversibility method
Reconstructing a space-dependent source term via the quasi-reversibility method
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DOI：
10.48550/arxiv.2210.09112
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
L. Nguyen;Huong T. Vu
中科院分区：
文献类型：
--
作者：
L. Nguyen;Huong T. Vu
本文的目的是解决一个重要的反源问题，它来自著名的逆散射问题。我们建议截断的控制方程的解决方案的一个特殊的基础L2的傅立叶级数。由此得到一个线性椭圆型方程组。该系统的解是控制方程解的傅里叶系数。在计算这些傅里叶系数之后，我们可以直接找到所需的源函数。数值例子。
The aim of this paper is to solve an important inverse source problem which arises from the well-known inverse scattering problem. We propose to truncate the Fourier series of the solution to the governing equation with respect to a special basis of L2. By this, we obtain a system of linear elliptic equations. Solutions to this system are the Fourier coefficients of the solution to the governing equation. After computing these Fourier coefficients, we can directly find the desired source function. Numerical examples are presented.