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首页> 外文期刊>Journal of Computational Physics >Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements
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Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

机译：辐射输运方程的有限阶球面谐波扩展格式。

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摘要

We propose the P_N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the PN approximation is compared against Monte Carlo simulations and other state-of-the-art methods.
机译：我们提出了一个基于有限元框架的P_N近似值，用于解决以光学层析成像为主要应用领域的辐射传输方程。关键思想是根据与源的接近度和局部散射系数，采用可变阶球谐展开进行角离散化。与在域中各处各处均等地采用高阶扩展相比，该方案显示出了较高的计算效率。此外，数值方法还可以准确描述在真实样本（如婴儿大脑）的正向建模中遇到的空隙区域。在三个模型问题上证明了该方法的准确性，其中将PN近似值与Monte Carlo仿真和其他最新方法进行了比较。

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