瞬态热传导方程精细积分方法中对称性的利用

摘要

采用精细积分法求解瞬态热传导方程时, 对指数矩阵进行变换后使其具有对称性,利用这一特性可使存贮量和计算量降低一半. 变换后指数矩阵的带宽特性不变, 采用子域精细积分可进一步提高算法的计算与存储效率.%The precise time integration (PTI) proposed fortransient linear system can give almost accurate numerical results atthe integration point. But when the dimensions of the system is verylarge, the computational efficiency is a big problem. In this paper, thesymmetry of the exponential matrix in the precise time integration for transientheat conduction is obtained by employing some transformation. Usingthis symmetry, the computational amount and the storage of PTI can bereduced nearly 50%. Moreover, the matrix is banded when the time steplength is small. The computational efficiency of the precise timeintegration can also be greatly improved. Numerical examplesvalidate the algorithm both in efficiency and precision.