Parallel versions of some methods with factorized preconditioning matrices for solving elliptic equations on unstructed triangular grids

Parallel versions of the conjugate gradient methods with incomplete factorization type preconditioning and modified incomplete factorization type preconditioning are proposed for solving elliptic equations on unstructed triangular grid on distributed-memory parallel computers. The construction of the parallel versions of the methods is based on the special orderings of nodes of a grid. The main attention devote to the methods of computational domain decomposition, the hierarchical algorithm for partitioning graphs is used. The calculations of model problems demonstrate the admited increase of iteration number with the number of processors for moderate number of processors.