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Fast isogeometric analysis numerical simulation method based on multiple grids

A technology of isogeometric analysis and numerical simulation, applied in electrical digital data processing, special data processing applications, instruments, etc., can solve problems such as time-consuming and low efficiency in solving linear equations, so as to accelerate convergence speed, reduce time-consuming, The effect of improving efficiency

Inactive Publication Date: 2013-07-24
UNIV OF SCI & TECH OF CHINA
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Problems solved by technology

[0003] The purpose of the present invention is to propose a fast isogeometric analysis numerical simulation method based on multi-grid, to solve the problem of low efficiency and time-consuming in solving linear equations in high-precision numerical simulation, and to realize fast numerical simulation

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  • Fast isogeometric analysis numerical simulation method based on multiple grids

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Embodiment 1

[0020] This embodiment is a specific illustration of the operation process of the fast numerical simulation method proposed by the present invention. figure 1 A schematic flowchart of the fast isogeometric analysis numerical simulation method of this embodiment is given. Below in conjunction with accompanying drawing, the detailed analysis of the operation process of the fast isogeometric analysis numerical simulation method proposed by the present invention is as follows:

[0021] In this embodiment, the two-dimensional Poisson equation is specifically used as the simulation object. The two-dimensional Poisson equation is defined as -ΔU=f, where the domain of definition is , f is a function defined above Ω. In order to solve the partial differential equation, boundary conditions need to be given. Here, the homology boundary condition is used, that is, U is at the boundary The upper value is 0, and the NURBS parameters of the domain Ω need to be given. The NURBS parameter...

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Abstract

The invention provides a fast isogeometric analysis numerical simulation method based on multiple grids. The fast isogeometric analysis numerical simulation method based on the multiple grids is characterized in that an expanded control vertex is used for transforming an exact solution corresponding to a current geometric representation into a space formed by a primary function of the next geometric representation in an expansion mode; the exact solution is used as an initial solution of a system of linear equations, wherein the system of linear equations corresponds to the next geometric representation; an iterative algorithm is used for carrying out iteration on the basis of the initial solution, so that the convergence rate of the iterative algorithm is greatly increased, time consumed for solving the system of linear equations is shortened, and efficiency of numerical simulation of isogeometric analysis is improved. Through the fast isogeometric analysis numerical simulation method based on the multiple grids, the result of the solution at each time is fully utilized, and under the situation that the figure of degree of freedom is very large (more than 60,000), the solution of a linear system can be carried out quickly; and experimental results show that in the face of a large-scale linear system, time which is consumed for solving the large-scale linear system when the fast isogeometric analysis numerical simulation method based on the multiple grids is used can be reduced by more than 90% compared with time which is consumed for solving the large-scale linear system when an existing basic numerical simulation method is used.

Description

technical field [0001] The invention belongs to the technical field of electrical digital data processing, and in particular relates to a fast isogeometric analysis numerical simulation method based on multiple grids. Background technique [0002] Numerical simulation, also known as computer simulation, is a method that uses numerical calculation and image display to study engineering and physical problems (http: / / baike.baidu.com / view / 1196149.htm). An important application of numerical simulation is to use numerical methods to perform various analyzes on models that use computer-aided design, including force analysis, deformation analysis, and heat conduction analysis. Currently, finite element analysis is mainly used to solve the corresponding partial differential equations. The process of numerical simulation is generally a cycle, solving partial differential equations on a grid, analyzing the solution results, and stopping the solution if the accuracy is sufficient, othe...

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Application Information

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IPC IPC(8): G06F17/50
Inventor 顾乃杰郭利财任开新黄章进
Owner UNIV OF SCI & TECH OF CHINA
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