Efficient pretreatment method for special saddle point problems

Abstract

The invention provides an efficient pretreatment method for special saddle point problems. The method includes the steps that according to the structural feature of the saddle point problem (3), structured augmentation-free and Schur complement-free block triangle preconditioners (11) and (12) are designed; spectral analysis is conducted on the designed preconditioners, and it is analyzed that a preconditioning matrix can have better feature value aggregation when appropriate parameters are selected; meanwhile, the defect that an original block opposite angle preconditioner can only solve the problem that k<2> is smaller than 1 is overcome, and the application range is widened; according to the structure feature of the asymmetrical saddle point problem (6) with a singular (1,1) block, a more generalized structured block triangle preconditioner is designed; spectral analysis is conducted on the designed preconditioner (13), the feature value distribution of the designed preconditioning matrix, the corresponding feature vector and the minimal polynomial are studied, and the feature value aggregation when the optimal parameter is selected is analyzed.

Description

technical field [0001] The invention relates to an efficient preprocessing method for special saddle point problems. Background technique [0002] Model problems in most scientific and engineering computing often require the solution of one or a series of large-scale linear systems. The solution of large-scale linear equations often occupies the main part of the entire numerical calculation process, and has become a prominent and important problem in scientific computing, and it also poses challenges to real-time calculation and high-precision analysis. Therefore, how to solve a system of linear equations with a reasonable amount of calculation has become an important subject of numerical calculation methods. One of the most important research topics in computational mathematics today is to efficiently solve the following large sparse linear saddle point systems. [0003] A ‾ x = ...

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Problems solved by technology

[0025] 2) Asymmetric saddle point problem with singular (1,1) block

Finally, it is pointed out that only when k=2, j=-1, the preprocessor There is only one eigenvalue 1, which limits the selection of parameters in order to achieve the optimal effect

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