ABSTRACT

A solution method for an inverse problem of determining the time-dependent lowest order coefficient of the 2D bioheat Pennes equation with nonlocal boundary conditions and total energy integral overdetermination condition recently appeared in literature is analysed and improved. Improvements include convective boundary condition into the model, the development of an accurate forward solver, accurate determination of total energy, and the proposal of a method for the numerical treatment of the inverse problem from noisy data. In the method, the 2D bioheat Pennes equation is solved by the method of lines based on a highly accurate pseudospectral approach, and sought coefficient values are estimated by the Levenberg–Marquardt method with the discrepancy principle as stopping rule. Numerical experiments are reported to illustrate effectiveness of the proposed method.

摘要

分析并改进了近期文献中出现的具有非局部边界条件和总能量积分超定条件的二维生物热Pennes方程的瞬态最低阶系数求反问题的求解方法。改进包括模型中的对流边界条件、精确正向求解器的开发、总能量的精确确定以及从噪声数据中数值处理逆问题的方法的建议。该方法采用基于高精度伪谱方法的直线法求解二维生物热Pennes方程，并以差异原理为停止准则，采用Levenberg-Marquardt方法估计求得系数值。