论文标题
抛物线PDE问题的隐式runge-kutta方法的新块预处理
A New Block Preconditioner for Implicit Runge-Kutta Methods for Parabolic PDE Problems
论文作者
论文摘要
针对寄生抛物线部分微分方程的隐式runge-kutta时间集成，引入了基于块$ ldu $分解基于块$ ldu $分解的新的$ ldu $分解。比较该预处理的条件数和特征值分布，以及与文献中其他的数值实验：Block Jacobi，Block Gauss-Seidel，以及优化的块盖块高斯 - seidel方法，Mardal和Nilssen [{\ em Modeling and Sidefification and Sidefietification and Sidefietification and Contifification and Contraction and Contififice and Conteral}，27（27（27），27（2006），ppppppppppppppppppp pp p pp pp pp pp。实验是在两个测试问题上进行的，一个$ 2D $热方程和模型对流扩散问题，使用隐式runge-kutta方法具有两个到七个阶段。我们发现，新的预定器优于其他预言，随着空间离散化的完善，随着时间顺序的增加，改进变得越来越明显。
A new preconditioner based on a block $LDU$ factorization with algebraic multigrid subsolves for scalability is introduced for the large, structured systems appearing in implicit Runge-Kutta time integration of parabolic partial differential equations. This preconditioner is compared in condition number and eigenvalue distribution, and in numerical experiments with others in the literature: block Jacobi, block Gauss-Seidel, and the optimized block Gauss-Seidel method of Staff, Mardal, and Nilssen [{\em Modeling, Identification and Control}, 27 (2006), pp. 109-123]. Experiments are run on two test problems, a $2D$ heat equation and a model advection-diffusion problem, using implicit Runge-Kutta methods with two to seven stages. We find that the new preconditioner outperforms the others, with the improvement becoming more pronounced as spatial discretization is refined and as temporal order is increased.
