Conjugate gradient finite element model solving method and system based on sparse convolution preprocessing

By employing the conjugate gradient finite element model method with sparse convolution preprocessing and training a preprocessing sub-generator using a sparse convolution U-net network, the problem of low efficiency in solving large-scale sparse linear equation systems is solved, achieving efficient and stable solutions in various structural systems.

CN122333882APending Publication Date: 2026-07-03BEIJING UNIV OF TECH
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Patent Information

Authority / Receiving Office
CN Β· China
Patent Type
Applications(China)
Current Assignee / Owner
BEIJING UNIV OF TECH
Filing Date
2026-04-09
Publication Date
2026-07-03

AI Technical Summary

Technical Problem

When solving large-scale sparse linear equation systems in structural engineering, the applicability of traditional preprocessing methods is limited. Deep learning preprocessing research lacks adaptability and generalization ability in engineering scenarios, making it difficult to construct stable and efficient preprocessors, resulting in low computational efficiency.

Method used

A conjugate gradient finite element model method with sparse convolution preprocessing is adopted. The preprocessor generator is trained by sparse convolution U-net network to reduce the condition number of stiffness matrix and construct high-quality preprocessors. Combined with sparse convolutional neural network, the convergence speed is significantly improved and the solution time is reduced.

Benefits of technology

Achieving stable acceleration of 150%-420% in various structural systems improves solution efficiency and forms a unified and scalable preprocessing framework for structural engineering, applicable to beam element, solid element and hybrid element structures, and reduces computational costs.

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Abstract

This application relates to a method and system for solving conjugate gradient finite element models based on sparse convolution preprocessing. The method includes establishing a structural finite element model, generating a structural stiffness matrix A and a load vector b, and constructing a linear equation system Ax=b, where A is a sparse symmetric positive definite matrix. A preprocessing sub-generator is constructed by training different structures using a sparse convolutional neural network. The stiffness matrix A is input into the preprocessing sub-generator to obtain a preprocessing factor. A symmetric positive definite preprocessor is constructed based on the preprocessing factor. The linear equation system Ax=b is solved using the preprocessed conjugate gradient method to obtain the displacement response vector x. This application optimizes the condition number of the preprocessed matrix to improve convergence speed and reduce solution time. It adapts the sparse convolutional U-net structure to large-scale sparse matrices, improving training efficiency and forming a unified and scalable preprocessing framework for structural engineering, providing a general and efficient preprocessing strategy for large-scale finite element model analysis.
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