基于测地距离的基本解方法求解非齐次各向异性IHCP问题

Method of fundamental solutions based on geodesic distance for inhomogeneous inverse heat conduction problems in anisotropic medium.

提出了一种求解非齐次各向异性热传导方程一类反问题IHCP(inverse heat conduction problem)的无网格方法,该方法通过借助基于测地距离的Multiquadric(MQ)作为基函数得到整个时间空间区域上的一个近似特解,然后用基于测地距离的基本解方法直接在整个时间空间区域上对相应的齐次问题进行求解.用截断奇异值分解(TSVD)法求解所得病态线性方程组,用L-曲线准则确定正则化参数.用数值例子验证了该方法的有效性,并分析了数值解的精度与参数Tc、的关系.

A mesbless method for the numerical solution of inhomogeneous inverse heat conduction problems in anisotropic medium is proposed. By using geodesic distance based Multiquadric （MQ） as basis functions, the new approach leads to a global approximation to a particular solution in both the spacial and time domains. Then the geodesic distance based method of fundamental solutions is used to solve the corresponding homogeneous problem. To tackle the ill-conditioning problem of the resultant linear system of equations, the trucated regular value decomposition（TSVD） based on the L-curve criterion is used to choose the regularization parameter. The effectiveness of the algorithm is demonstrated by several numerical examples. The relationships between the accuracy of the numerical solutions and the value of parameters T and c are also investigated.