Preconditioning techniques for nonsymmetric and indefinite linear systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
A parallel genetic algorithm for the set partitioning problem
A parallel genetic algorithm for the set partitioning problem
On the Incomplete Cholesky Decomposition of a Class of Perturbed Matrices
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Tetrahedral Mesh Generation for Environmental Problems over Complex Terrains
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Parameter Estimation in a Three-Dimensional Wind Field Model Using Genetic Algorithms
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Advances in Engineering Software - Special issue on evolutionary optimization of engineering problems
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The efficiency of a finite element mass consistent model for wind field adjustment depends on the stability parameter @a which allows adjustment from a strictly horizontal wind to a pure vertical one. Each simulation with the wind model leads to the resolution of a linear system of equations, the matrix of which depends on a function @e(@a), i.e., (M+@eN)x"@e=b"@e, where M and N are constant, symmetric and positive definite matrices with the same sparsity pattern for a given level of discretization. The estimation of this parameter may be carried out by using genetic algorithms. This procedure requires the evaluation of a fitness function for each individual of the population defined in the searching space of @a, that is, the resolution of one linear system of equations for each value of @a. Preconditioned Conjugate Gradient algorithm (PCG) is usually applied for the resolution of these types of linear systems due to its good convergence results. In order to solve this set of linear systems, we could either construct a different preconditioner for each of them or use a single preconditioner constructed from the first value of @e to solve all the systems. In this paper, an intermediate approach is proposed. An incomplete Cholesky factorization of matrix A"@e is constructed for the first linear system and it is updated for each @e at a low computational cost. Numerical experiments related to realistic wind field are presented in order to show the performance of the proposed preconditioning strategy.