Preconditioning techniques for non-symmetric matrices with application to temperature calculations of cooled concrete

Preconditioning techniques based on incomplete LU‐decomposition are described for large, sparse, non‐symmetric matrix systems in which the largest part of the coefficient matrix is a symmetric M‐matrix with a very regular sparsity pattern. Some methods are described in which a small part of the matrix with an irregular sparsity pattern is treated very efficiently. The methods are combined with CGSTAB and tested on a non‐stationary diffusion problem in three dimensions. For this type of problems the modified incomplete decomposition as suggested by Gustafsson performs significantly better than the standard incomplete factorization. Also some methods are described to construct preconditioners for large, sparse, non‐symmetric matrices with arbitrary sparsity patterns. Methods in which the sparsity pattern of the preconditioning matrix is based on a drop tolerance are very effective and relatively cheap.