瞬态热传导方程精细积分方法中对称性的利用

THE SYMMETRY OF PRECISE TIME INTEGRATION FOR TRANSIENT HEAT CONDUCTION

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，采用于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 for transient linear system can give almost accurate numerical results at the integration point. But when the dimensions of the system is very large, the computational efficiency is a big problem. In this paper, the symmetry of tile exponential matrix in the precise time integration for transient heat conduction is obtained by employing some transformation. Using this symmetry, the computational amount and the storage of PTI can be reduced nearly 50%. Moreover, the matrix is banded when the time step length is small. The computational efficiency of the precise time integration can also be greatly improved. Numerical examples validate the algorithm both in efficiency and precision.