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Two-dimensional finite element mesh generation algorithm for defining boundary based on distance function

A technology of distance function and grid division, applied in computing, image data processing, 3D modeling, etc., can solve problems such as slow speed, difficult interaction, complicated operation, etc., and achieve the effect of reducing complexity

Pending Publication Date: 2021-03-30
CHINA JILIANG UNIV
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Problems solved by technology

These commercial software with the mapping method as the core algorithm are expensive, complicated to operate, and slow in generating large-scale triangular meshes, and the generated complex codes are almost inaccessible. They are usually used as "black boxes" and are rarely Difficult to interact with other code or software, so the user relinquishes control

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  • Two-dimensional finite element mesh generation algorithm for defining boundary based on distance function
  • Two-dimensional finite element mesh generation algorithm for defining boundary based on distance function
  • Two-dimensional finite element mesh generation algorithm for defining boundary based on distance function

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Embodiment Construction

[0035] The present invention uses a symbolic distance function to specify and describe the geometric area to be gridized. Distance Functions D (x, y) specify the shortest distance of any point to the boundary of the domain in the space, where the symbol of the function is positive outside the area, and is negative inside, which is zero on the boundary. This definition is used for the identification point to be located within the geometry or outside. In addition, the gradient of the function points to the direction of the boundary, allowing the external point to be effectively moved back to the domain. Geometric domain ω can implicitly defined as:

[0036] Ω = {x = (x, y) ∈R 2 | d (x) <0} (1)

[0037] With the boundary of the general geometric background, the present invention uses a representation of the distance function, a simple example is a two-dimensional unit circle, which has distance functions d (r) = R-1, where r = sqrt (x ^ 2 + Y ^ 2) is the distance to the origin. For m...

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Abstract

The invention relates to the field of electromagnetic field finite element numerical analysis, in particular to a two-dimensional finite element mesh generation algorithm for defining a boundary basedon a distance function. The method comprises a distance function construction step, a Delaunay triangulation step, and a grid smoothing step; thedistance function construction step is mainly dividedinto two situations, a regular shape is expressed through a geometric function, a boundary contour is abstracted from an irregular shape through an image processing mode, and smoothing processing is carried out on a boundary through a boundary smoothing algorithm based on path optimization; in the Delaunay triangulation step, the topology of a truss is determined through Delaunay triangulation soas to be used in the grid smoothing step, and a quality evaluation function is added, and the number of grid iterations is limited; and in the grid smoothing step, the grid quality and efficiency areimproved through a force-based grid smoothing algorithm. A post-processing module is used for screening different medium boundaries based on a distance function and a second-order Gaussian projectionmethod, giving different boundary excitation conditions according to different application scenes and further conducting solving to obtain a result.

Description

Technical field [0001] The present invention relates to the field of finite element numerical analysis of electromagnetic fields, in particular, to a two-dimensional finite element grid cross-sectional algorithm based on distance function defining boundaries. Background technique [0002] Excellent adaptation field boundary geometry and the ability of the medium physical properties, making the finite element method a dominant analysis and optimization design of various electromagnetic fields, electromagnetic wave engineering issues. In general, finite element analysis is divided into: establishing a model (pre-processing), calculates solving, result processing, and evaluation (post-processing). Among them, the time used in each stage is: 40% -60%, 5% -10%, 30% -50%. Thus, how to discrete the complex field domain in the actual engineering into "limited unit", this sectional problem is extremely critical in the numerical analysis process, directly determines the accuracy and effect...

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Application Information

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IPC IPC(8): G06T17/20
CPCG06T17/20
Inventor 章春锋汪伟安斯光林德辉
Owner CHINA JILIANG UNIV
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