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Singular boundary method for diffuse type dynamic data reconstruction

A dynamic data, diffusion-type technology, applied in complex mathematical operations and other directions, can solve the problems of complex, time-consuming and labor-intensive process of diffusion data reconstruction technology, saving computing time and memory requirements, and the method is simple, fast, and easy to implement. Effect

Inactive Publication Date: 2016-07-13
HOHAI UNIV
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  • Application Information

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Problems solved by technology

[0006] Purpose of the invention: Aiming at the defects of complicated and time-consuming and labor-intensive reconstruction process of existing diffuse data, the present invention aims to provide a simple and efficient gridless method to reconstruct diffuse dynamic data, so as to save reconstruction time , to improve refactoring efficiency

Method used

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  • Singular boundary method for diffuse type dynamic data reconstruction
  • Singular boundary method for diffuse type dynamic data reconstruction
  • Singular boundary method for diffuse type dynamic data reconstruction

Examples

Experimental program
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Effect test

Embodiment 1

[0082] Consider the following two-dimensional diffusion equation initial boundary value problem on [0,1]×[0,1]:

[0083] The initial and boundary conditions are as follows

[0084]

[0085]

[0086] The analytical solution to this problem is

[0087]

[0088] Wherein the diffusion coefficient k=0.5.

[0089] In order to verify the effectiveness of the method, we choose the time step and space step to be Δt=0.005 and Δl=0.1 respectively, and the parameters in the empirical formula are: a=-16.73, b=-0.7618, c=-23.69, d = -0.7018, e = 1.099. according to figure 2 Arrange the source points in the manner shown, image 3 A comparison is given between the exact solution of the function value at the point (0.5,0.5) and the numerical result obtained by using the empirical formula singular boundary method proposed by the present invention. It can be seen from the figure that the reconstructed value is quite consistent with the exact value, and its maximum absolute error i...

Embodiment 2

[0091] In order to investigate the calculation efficiency and accuracy of the present invention to the three-dimensional diffusion problem, consider the following diffusion problem on [0,1]×[0,1]×[0,1]:

[0092] The initial and boundary conditions are

[0093] u(x,y,z,t=0)=sin(πx)+sin(πy)+sin(πz)

[0094]

[0095] The analytical solution to this problem is

[0096]

[0097] Wherein the diffusion coefficient k=0.1.

[0098] 216 source points are arranged inside the area at the initial moment, and 127 source points are arranged on the boundary, the time step and space step are respectively Δt=0.05 and Δl=1 / 6, and the parameters in the empirical formula are: a=- 160.9, b=9.392, c=-15.35, d=-0.3473, e=1.503. We reconstructed the function value of the point (0.5, 0.5, 0.5) at different moments by using the singular boundary method of the reverse interpolation technique and the singular boundary method of the empirical formula respectively. The comparison of the results ob...

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Abstract

The invention discloses a singular boundary method for diffuse type dynamic data reconstruction. The singular boundary method is applicable to the reconstruction problem of fluid flow, heat and mass transfer, image processing and other relevant diffuse type data. A time dependent elementary solution is adopted as a base function of interpolation, and no laplace transformation or finite difference method is needed to discrete time items; an empirical formula is adopted for calculating source point intensity factors. According to the method, existing standard mesh generation difficulty is effectively avoided, and numerical integration processing is also avoided; in addition, a special structure of an interpolation matrix is utilized, an equation does not need to be solved in the whole calculation process, calculation time and memory requirements are greatly reduced, calculation errors are reduced, and calculation efficiency is improved. A new, simple and efficient tool is provided for diffuse type dynamic data reconstruction.

Description

technical field [0001] The invention belongs to the field of diffuse dynamic data reconstruction, and in particular relates to a diffuse dynamic data reconstruction method based on a gridless singular boundary method. Background technique [0002] Diffusion issues, in oil extraction, environmental pollution, disease epidemics, chemical reactions, news transmission, coal mine gas explosions, farmland moisture, water conservancy projects, ecological issues, housing infrastructure, nerve conduction, drug distribution in the human body, and superconductivity, liquid crystals, combustion and many other fields of natural science and engineering technology. Therefore, it is of great practical engineering and application value to develop numerical methods with high precision, less time consumption, and simple calculation to deal with diffusion dynamic data. [0003] Looking at domestic and foreign methods for reconstructing diffuse dynamic data, there are finite element method, bou...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/10
CPCG06F17/10
Inventor 陈文王发杰
Owner HOHAI UNIV
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