The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" principle, which has been pursued by this research group for a number of years for some other CIPs for PDEs. Those PDEs are significantly different from RRTE. The presence of the Carleman Weight Function (CWF) in the numerical scheme is the key element of the convexification. CWF is the function, which is involved as the weight function in the Carleman estimate for the corresponding PDE operator. Convergence analysis is presented along with the results of numerical experiments, which confirm the theory. RRTE governs the propagation of photons in the diffuse medium in the case when they propagate along geodesic lines between their collisions. Geodesic lines are generated by the spatially variable dielectric constant of the medium.
翻译:构建了Riemannian 半径传输方程式( RRTE) 的首个全局一致数字法( CIP ) 。 这是所谓的“ 文字引言分流共化” 原则的版本, 该研究组对其他一些PDE 的 CIP 进行了若干年的研究。 这些PDE 与 RRETE 有很大不同。 数字公式中存在 Carleman Weight 函数( CWF) 是调和的关键元素 。 CWF 是函数, 作为相应的 PDE 操作员 Carleman 估算的权重函数 。 聚合分析与数字实验结果一起提出, 证实了理论。 RUTE 管理在相撞时沿着地德线传播的分散介质中光子的传播。 大地测量线是由介质的空间变异电常生成的。