Weighted graph based ordering techniques for preconditioned conjugate gradient methods
This work is a report about the results of seven new ordering techniques for improving the incomplete LU-factorization based preconditioned conjugate gradient solution of the Neumann problem of anisotropic partial differential equations of the form \[ \sum^n_{i= 1} {\partial\over \partial x_i} \Biggl(K_i {\partial u\over \partial x_i}\Biggr)= q,\quad x_i\in (0, 1),\quad i= 1,\dots, n, \] where \(K_i\), \(i= 1,\dots, n\) are different in magnitude. The ordering techniques suggested and analyzed are some modifications of the reverse Cuthill-McKee ordering algorithm; they are in some sense matrix coefficient sensitive algorithms. Numerical tests are given in tables showing that the idea of the construction works in the practice. The time required to perform ordering and the time required to perform PCG solver iteration vary significantly (factors are 1-4 and 0.5-- 3.4, respectively) depending on the ordering technique choosen.
reverse Cuthill-McKee ordering algorithm
scientific article; zbMATH DE number 773822
scientific article