Neighborhood Determination in CAE Grid Models
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Solution Overview
Problem
Conventional methods for determining neighbors in a grid model for computer-aided engineering analysis are computationally expensive and time-consuming, especially when dealing with large complex structures, leading to numerical instability in topology optimization.
Innovation Solution
A method that calculates a characteristic length for each element, defining a region of potential neighbors, and uses ordered lists to efficiently separate potential neighbors from non-neighbors by comparing centroid coordinates with established bounds, reducing the need for costly distance calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods (node comparison or distance computation) are used to determine neighbors, then neighbor identification accuracy is improved, but computational time and cost increase significantly
Solution Approach 1:
The patent segments the neighbor determination process into two distinct stages: (1) spatial filtering using bounding boxes to identify potential neighbors, and (2) precise neighbor identification using node sharing detection. This segmentation allows the computationally intensive node comparison to be performed only on a reduced set of candidate elements, significantly reducing overall computational time while maintaining accuracy.
Solution Approach 2:
The patent applies preliminary spatial filtering using bounding boxes before performing the costly node comparison operation. By pre-screening elements based on their spatial proximity to the query element's bounding box, the system eliminates obviously non-neighboring elements before they undergo expensive node-by-node comparison, thus reducing total computational cost.
2Measurement precision
If every node of one element is compared against every node of another element, then neighbor determination accuracy is improved, but computational complexity increases to O(number of nodes squared)
Solution Approach 1:
The patent segments the neighbor determination process into two distinct stages: (1) spatial filtering using bounding boxes to identify potential neighbors, and (2) precise neighbor identification using node sharing detection. This segmentation allows the computationally intensive node comparison to be performed only on a reduced set of candidate elements, significantly reducing overall computational time while maintaining accuracy.
Solution Approach 2:
The patent introduces bounding boxes as an intermediary structure that mediates between the query element and candidate elements. Instead of directly comparing nodes of all elements, the system first compares bounding boxes to filter candidates, then performs node comparison only on the reduced set, thus reducing computational complexity.
3Measurement precision
If distance computation is performed for each element pair, then spatial relationship accuracy is improved, but computational cost increases due to square root calculations
Solution Approach 1:
The patent uses bounding boxes as a cheap, lightweight structure for initial spatial filtering. These bounding boxes are computationally inexpensive to create and compare, serving as a disposable filtering mechanism that eliminates obviously non-neighboring elements before more expensive distance calculations or node comparisons are performed.
Solution Approach 2:
The patent applies preliminary spatial filtering using bounding boxes before performing the costly node comparison operation. By pre-screening elements based on their spatial proximity to the query element's bounding box, the system eliminates obviously non-neighboring elements before they undergo expensive node-by-node comparison, thus reducing total computational cost.
Data Source
AI summary
Improved methods and systems for a neighborhood determination in computer aided engineering analysis are disclosed. According to one aspect, a list of neighbor elements is created for a base element of a grid model representing a structure or an engineering product. The representative node's coordinates of the base element are calculated using corner nodes of the base element. A characteristic length is assigned to the base element. The characteristic length can be determined by users of the computer aided analysis, or be calculated using geometry of the base element. The characteristic length and the representative node collectively define a surface boundary that divides elements in the grid model into two groups. The first group contains potential neighbors, while the second group contains non-neighbors. Only elements in the first group are further processed using traditional procedures to determine whether each of them is indeed a neighbor element according to one of the neighborhood determination criteria.