Adaptive grid-free Galerkin method

A Galerkin method and gridless technology, which is applied in the field of computer-aided engineering analysis, can solve the problems of impossible calculation, increased calculation amount, and large amount of calculation, so as to reduce estimation error, reduce calculation time, and reduce memory Effect

Pending Publication Date: 2018-09-11
HARBIN INST OF TECH SHENZHEN GRADUATE SCHOOL
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  • Abstract
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  • Application Information

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Problems solved by technology

In this case, node encryption is often required to improve the calculation accuracy, but if the problem domain is globally encrypted, it will increase the amount of calculation, especially in the thre

Method used

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  • Adaptive grid-free Galerkin method
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  • Adaptive grid-free Galerkin method

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Experimental program
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Effect test

Embodiment 1

[0051] In order to verify the effect of the program in this paper, the well-known commercial finite element program SEEP / W (Geo-Studio2007) is selected for comparison. The model and calculation parameter settings of the two programs are as follows:

[0052] SEEP / W: 100 vertical grids, grid size 0.01m, linear unit, 2nd order Gaussian integral, time step 468 seconds.

[0053] Meshless method: 101 vertical nodes, node spacing 0.01m, linear basis function, 2nd-order Gaussian integral; the initial time step is 468 seconds.

[0054] Use the above two models to calculate the pressure head at 46 800 seconds. figure 2 The pressure and head distribution curves calculated by gridless and SEEP / W are given. From figure 2 It can be seen that the pressure head calculated by the gridless program proposed by the present invention is closer to the analytical solution than the result of SEEP / W, indicating that the calculation effect of the gridless program proposed by the present invention ...

Embodiment 2

[0056] From figure 2 It can be seen that the uniform node arrangement will make the nodes in some areas too dense, which makes the calculation amount a bit wasteful. In order to ensure the continuity of the calculation results and reduce the amount of calculation, the self-adaptive meshless method program in this paper is used for adaptive analysis. The model and calculation parameters are as follows: the initial model is vertically arranged with 41 nodes; the initial time step is 46800 seconds; the error limit REL takes 10-8; error limit EL takes 0.01.

[0057] image 3 The calculated pressure head distributions before and after adaptive encryption are given. From image 3 It can be seen that there is oscillation in the calculation results before adaptive encryption, but there is no oscillation after adaptive encryption, which shows that adaptive encryption can eliminate oscillation.

[0058] In order to verify the validity of the error estimation method of the present inv...

Embodiment 3

[0060] For the transient problem of unsaturated soil seepage, users often need to obtain the results during the calculation process, so it is necessary to calculate multiple time points in one calculation.

[0061] Figure 5 The pressure and head distribution curves of the adaptive encryption model at 11 700 seconds, 23 400 seconds and 46 800 seconds are given. From Figure 5 It can be seen from the figure that the node densities at these three time points are different, and as time increases, the node density increases, indicating that the adaptive program of the present invention can encrypt the nodes in the problem domain in real time, and the calculation results are close to the analytical solution, indicating that the encryption The calculation results after the node are better.

[0062] In order to save calculation time and amount of calculation, when calculating the next time step, the nodes encrypted in the previous time step are deleted to save running memory. Acco...

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Abstract

The invention discloses an adaptive grid-free Galerkin method. The method mainly comprises the following steps that 1, grid reference points are selected, and an error of reference point field variables serves as an estimation error; 2, vertexes of a background grid serve as nodes, the background grid is encrypted by adopting isoparametric transformation, and meanwhile node encryption is achieved;3, a proper grid segment number is selected, and the background grid is refined multiple times to meet error limitation; 4, after current time step calculation is competed, the nodes encrypted withinthe time step and the refined background grid are deleted, and an initial model serves as a calculation module of the next time step. Accordingly, relative to a non-adaptive grid-free Galerkin method, aiming at high-error region local encryption, after one time step is calculated, an encryption area is coarsened, consumed time and occupied memory can be greatly lowered, after adaptive encryptionis adopted, the estimation error can be lowered, and vibration is eliminated.

Description

technical field [0001] The invention relates to the technical field of computer-aided engineering analysis, in particular to an adaptive gridless Galerkin method. Background technique [0002] When the gridless Galerkin method is used to deal with transient problems, if the nodes are arranged sparsely, the numerical oscillation or even non-convergence of the calculation results will often occur due to the high nonlinearity of the material parameters. In this case, node encryption is often required to improve the calculation accuracy, but if the problem domain is globally encrypted, it will increase the amount of calculation, especially in the three-dimensional problem domain, the global encryption may make the calculation amount very large. It may cause the calculation to be impossible, so only local encryption is performed in the high error area. However, due to the transient characteristics of the problem, the high-error area will change with time, so an accurate error es...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/23
Inventor 陈锐葛云晖刘垒雷李勇勇徐涛赵燕茹
Owner HARBIN INST OF TECH SHENZHEN GRADUATE SCHOOL
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