Method for processing special saddle point problem

A processing method and saddle point technology, which is applied in the field of processing special saddle point problems, can solve problems such as large storage space, long computing time, and affecting data results

Inactive Publication Date: 2019-08-09
ZHENGZHOU UNIVERSITY OF AERONAUTICS
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Problems solved by technology

[0004] However, with the rapid development of science and technology, the order of linear equations generated in practical problems is getting higher and higher. Using iterative methods to solve them will require a large amount of storage space, long computing time or super high-performance computers. There are many limitations in the application
At the same time, in the process of data processing, due to the influence of external interference, it will lead to output errors, which will affect the data results.

Method used

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  • Method for processing special saddle point problem
  • Method for processing special saddle point problem
  • Method for processing special saddle point problem

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Embodiment 2

[0128] The present invention also discloses another processing method for the saddle point problem:

[0129] For the saddle point problem resulting from the discretization of the discretized hybrid time-harmonic Maxwell equations:

[0130]

[0131] According to the structural characteristics of this saddle point problem, two structured augmentation-free and Schur-free block triangulation preprocessors (11), (12) are designed:

[0132]

[0133]

[0134] For the designed preconditioner, it is analyzed that its construction and application cost are equivalent to the existing augmentation-free and Schur-free block-diagonal preconditioners, and the clustering of eigenvalues ​​when the parameters are optimally selected is analyzed. At the same time, to make up for the original block diagonal preconditioner can only solve the deficiency of k2<1, and to expand its scope of application.

[0135] For asymmetric saddle point problems with singular (1,1) blocks:

[0136]

[...

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Abstract

The invention discloses a method for processing a special saddle point problem, which converts an original linear system into an equivalent linear system easy to solve and enables a preprocessing matrix P-1A to be provided with better spectral properties than an original matrix, so that the convergence speed of the algorithm is increased, and the calculation efficiency of the algorithm is improved; and the shielding effect is improved, the external interference is reduced, and data errors are prevented.

Description

technical field [0001] The invention belongs to the technical field of saddle point problem processing, and more specifically relates to a processing method for a special saddle point problem. Background technique [0002] The saddle point problem is widely used in many scientific and engineering problems, such as fluid mechanics, optimization, hybrid finite element approximation of elliptic partial differential equations, etc. For the study of numerical solution methods for various types of saddle point problems, many scholars at home and abroad have given many effective numerical solution methods. When the scale of the problem is small, many classic methods can be effectively solved, such as LU decomposition method, Gauss-Seidel method, SOR method, conjugate gradient method, etc. [0003] However, when the order of the matrix is ​​large, many classical methods often cannot give satisfactory calculation results due to the influence of computer CPU calculation time, memory ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/12G06F17/16
CPCG06F17/12G06F17/16
Inventor 张理涛吴世良李建磊刘敬怀左宪禹赵建峰李奕赵莹超闫芳宋佳丽
Owner ZHENGZHOU UNIVERSITY OF AERONAUTICS
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