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Method for condensing FETI engineering numerical values based on regional decomposition

A numerical method and area decomposition technology, applied in the direction of CAD numerical modeling, complex mathematical operations, special data processing applications, etc., can solve the problems of "hat" matrix with large storage capacity, difficult calculation, reduction of calculation and storage capacity, etc. Achieve optimal convergence characteristics, reduce storage space, and improve solution efficiency

Active Publication Date: 2021-12-10
NORTHWESTERN POLYTECHNICAL UNIV
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Problems solved by technology

[0004] In order to overcome the problem in the FETI algorithm that when the scale of the floating structure is large, the "hat" matrix has a large storage capacity and is difficult to calculate, the present invention proposes a polycondensation FETI engineering numerical method based on domain decomposition, which reduces the amount of calculation and storage From the point of view, to meet the purpose of modern high-performance computers for engineering designers

Method used

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  • Method for condensing FETI engineering numerical values based on regional decomposition
  • Method for condensing FETI engineering numerical values based on regional decomposition
  • Method for condensing FETI engineering numerical values based on regional decomposition

Examples

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Embodiment 1

[0137] In this example, the two sub-domain plate bending model, the flat plate model geometry L = 100 mm, high H = 10 mm, thick t = 1 mm, material elastic modulus E = 70 GPa, Poisson ratio μ = 0.33, its finite element mesh The quadrilateral shell unit, one end of the tablet adopts fixed constraints (nodes 1 and 6). In order to observe the significant changes in flat-plate migration, the other end of the tablet applies 1000N load (node ​​5), such as figure 2 Indicated.

[0138] Step 1: Simply divide the plate bend finite element model into 2 subdomains, such as image 3 The FETI algorithm and the polycondensation FETI algorithm are respectively employed and solved.

[0139] Step 2: In order to avoid the Iterative Law, the approximation error of the measurement of the convergence threshold is to be solved due to the control convergence threshold, and the low-order frame equation group formed by the simple model can be solved by the direct method.

[0140] Step 3: Different sub-domain...

Embodiment 2

[0154] The present embodiment is a wing model of a typical wing box structure, forming a large-scale structure finite element to be solved by mesh refinement, and a 4-node cluster platform is used to solve the parallel value. The distribution of the inner beam of the wing model, the distribution of ribs and the main geometry of the wing plane shape are respectively Image 6 and Figure 7 Indicated.

[0155] Step 1: First divide the wing geometric model into 4 smaller domains, and then use the software Hypermesh to make a grid score for the area-decomposed model. The entire wing finite element model contains 52593 quadrangular shell units and 3277. Two-node BEAM unit, where the upper and lower skin material constants are set to the Young's modulus E = 70GPa, Poisson ratio μ = 0.33, thickness T = 2mm, the material constant of the spar and the ribs is simple to set up the Young's modulus E = 210GPa , Poisson ratio μ = 0.33, and the thickness of the girder T = 8mm, the cross-sectional a...

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Abstract

The invention discloses a method for condensing FETI engineering numerical values based on regional decomposition. The method comprises the steps of solving a generalized flexibility matrix and a boundary flexibility matrix through constructing a rigid matrix only related to the boundary freedom degree of a floating sub-domain and a rigid body modal matrix of the rigid matrix. The formed new 'hat' matrix can fully utilize and maintain the sparsity of the floating sub-domain rigid matrix, and the order of the new 'hat' matrix is equal to the number of floating sub-domain boundary degrees of freedom and is far smaller than the scale of the original 'hat' matrix, so that the storage space is greatly reduced, and the triangular decomposition solving efficiency of the generalized stiffness matrix is improved; and the calculation of the local flexibility matrix becomes economical and feasible. Meanwhile, an intermediate result of the new 'hat' matrix calculation just provides a Dirichlet preprocessor with a better convergence characteristic for PCPG iterative solution of a frame equation set.

Description

Technical field [0001] The present invention is applicable to the field of aircraft structure numerical simulation, and more particularly to a numerical method of polycondensation Feti engineering based on regional decomposition. Background technique [0002] Solution of the linear equation is one of the key technologies of numerical simulation in science and engineering calculations. In recent years, the state has developed rapidly in the aerospace sector, and the development of these high-precision weapons and equipment has proposed high technical requirements such as refined, lightweight, reliability, and reliability. In the structural finite element analysis, the grid quality and model accuracy should be further improved, so that the size of the linear equation group has risen sharply, which makes a greater challenge for the accuracy and real-timeness of solving. With the development of computer technology and the development of computer cluster systems, high-performance calc...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/23G06F17/12G06F17/16G06F111/10
CPCG06F30/23G06F17/12G06F17/16G06F2111/10Y02T90/00
Inventor 戎宇飞齐雪超袁伟张晓虎孙秦
Owner NORTHWESTERN POLYTECHNICAL UNIV
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