二维三温能量方程组离散求解的两个新预处理技术

二维三温能量方程离散后得到的稀疏线性代数方程组中,系数矩阵各行的对角占优性相差十分悬殊,矩阵元素相差也十分大.针对前一问题,提出了改善对角占优性的一个新比例化方法.针对后一问题,利用每次舍弃前计算多个行的技术提出了多行ILUT预条件方法.最后,将对角占优性改善技术、多行ILUT与对角元比例化技术、RCM排序联合使用于实际的能量方程离散求解中,取得了较好的加速效果.

Two Preconditioning Techniques for Two-dimensional Three-temperature Energy Equations

In a sparse linear system derived from two-dimensional three-temperature energy equations, the diagonal dominan varies greatly from row to row and so is the magnitude of the elements. We provide a new scaling method to improve the diagonal dominance. As ILUT is used to the derived linear system, it reserves the number of elements in each row and several relatively large elements related to the photon are dropped due to the large difference among elements. To improve the equality of the ILUT, we provide a new method named multiple row ILUT(MRILUT), in which multiple rows are computed before dropping. The provided methods are embedded into a preconditioned Krylov subspace method to solve the actual two-dimensional energy equations with three temperatures. The number of iteration at each time step and the total computation time are both greatly reduced.