论文标题
Riemannian辐射转移方程的系数反问题的凸化数值方法
Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation
论文作者
论文摘要
构建了系数逆问题（CIP）的第一种全球收敛数值方法（CIP）用于构建Riemannian辐射转移方程（RRTE）。 This is a version of the so-called \textquotedblleft convexification" method, 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 the RRTE. The presence of the Carleman Weight Function (CWF) in the numerical scheme is the key element which insures the global convergence. Convergence analysis is presented along with the results of numerical experiments, which confirm RRTE的理论控制了散布培养基中的光子在碰撞线之间的地球线路传播时。
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" method, 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 the RRTE. The presence of the Carleman Weight Function (CWF) in the numerical scheme is the key element which insures the global convergence. 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.
