Hierarchical Reduced-Order Matrix Generation for Numerical Analysis
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Solution Overview
Problem
Current model-based development techniques require excessive calculation time and computer resources when dealing with large-scale degree of freedom in numerical analysis, particularly due to the need for inverse matrix calculations for entire structures.
Innovation Solution
A hierarchical reduced-order matrix generation device that divides the entire structure into partial structures, calculating reduced-order matrices using eigenmodes and static modes in each partial structure, thereby reducing the computational burden and resource requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If the entire structure is decomposed into partial structures for degeneration, then the calculation time and computer resources are reduced, but the complexity of the decomposition process and matrix generation increases
Solution Approach 1:
The patent applies segmentation by dividing the entire structure into multiple partial structures (first partial structure, second partial structure, etc.) along with their corresponding boundary regions and internal regions. This allows the numerical analysis to be performed on smaller sub-problems rather than the entire large-scale model, significantly reducing calculation time and computer resource requirements while maintaining the overall structural integrity through hierarchical assembly.
Solution Approach 2:
The patent implements a hierarchical nested structure where partial structures are assembled within boundary regions, which are in turn assembled to form the complete structure. The matrix generation process follows this nesting by first generating reduced-order matrices for internal regions, then assembling them with boundary region matrices to create the complete system matrix, allowing complex problems to be solved through systematic combination of simpler components.
2Measurement precision
If inverse matrix calculation is performed on the internal region, then the reduced-order matrix is generated accurately, but the computer memory requirements and calculation time increase significantly
Solution Approach 1:
The patent extracts and eliminates the internal region degrees of freedom by forming the reduced-order matrix through the relationship between boundary region matrices and internal region matrices. Instead of performing inverse matrix calculation on the entire large internal region, the method extracts only the necessary relationships at the boundary regions, significantly reducing memory requirements while maintaining accuracy through the preserved boundary interface characteristics.
Solution Approach 2:
The patent applies partial action by performing inverse matrix calculation only on the reduced-order matrices of partial structures rather than on the complete large-scale model. This partial approach calculates only the necessary inverse matrices for the boundary regions and internal regions separately, reducing the total computational burden and memory usage while achieving the same accuracy for the overall system response.
3Manufacturing precision
If large-scale degree of freedom is applied to the model, then the analysis can capture more detailed characteristics, but the calculation time and computer resources become excessive
Solution Approach 1:
The patent introduces dynamic adaptability by allowing the degree of freedom to be dynamically adjusted at different hierarchical levels. The boundary region can retain appropriate degrees of freedom for capturing detailed characteristics, while internal regions can be reduced to minimal degrees of freedom or eliminated entirely. This dynamic approach maintains analysis precision for critical areas while significantly improving calculation efficiency by reducing the overall model size.
Solution Approach 2:
The patent applies local quality by differentiating the treatment of different regions: boundary regions retain higher degrees of freedom to capture detailed characteristics and maintain precision, while internal regions are reduced or eliminated to improve calculation efficiency. This localized differentiation allows the model to achieve high precision where needed without the computational burden of high precision throughout the entire model.
Data Source
AI summary
During model-based development, a processing target is sometimes broken down into partial structures. At such time, a long calculation time and a large quantity of computer resources are required if each partial structure has a large number of degrees of freedom. The present invention is a hierarchical reduced-order matrix generation device 600 that generates a hierarchical reduced-order matrix for performing numerical analysis of a physical object, and has: a storage unit 62 that stores physical object data indicating properties of the physical object; and a computation unit 61 that generates a hierarchical reduced-order matrix for a model of the physical object data. The computation unit 61 divides the overall structure into a plurality of partial structures, and calculates the reduced-order matrix using a unique mode and a static mode of each of the divided plurality of partial structures.