Variable Mesh Resolution for Finite Element Analysis
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Solution Overview
Problem
Existing mesh generation techniques for physics-based simulations from image data, such as the voxel and VOMAC approaches, suffer from uniform element density, leading to inefficient processing and potential computational intractability due to unnecessary high sampling density requirements, especially in areas of lesser interest.
Innovation Solution
A method that allows for varying mesh resolution within the mesh, enabling smaller elements in regions of interest while maintaining suitable element density in less critical areas, by calculating a distribution of sampling points with localized variations and applying a morphing function to maintain the same topology as a regular structured mesh, thus enabling efficient finite element or finite volume analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If uniform sampling density is used throughout the image data space, then geometric accuracy is maintained across all regions, but computational burden increases unnecessarily in areas of lesser interest
Solution Approach 1:
The patent applies local quality by varying the sampling density according to the local importance of different regions. Critical areas with complex geometry or high curvature receive higher sampling density to maintain geometric accuracy, while less critical regions use lower sampling density to reduce computational burden. This is achieved through an importance metric that evaluates each voxel's significance based on geometric complexity, curvature, and other criteria.
Solution Approach 2:
The patent segments the image data space into multiple regions with different sampling densities based on their geometric characteristics and importance. The segmentation process divides the volume into critical and non-critical regions, allowing independent sampling strategies for each segment. This enables the system to apply high-resolution sampling only where necessary while using coarser sampling elsewhere.
2Manufacturing precision
If higher sampling density is applied to capture complex geometric features, then geometric accuracy improves, but the number of cells increases leading to computational intractability
Solution Approach 1:
The patent implements local quality by assigning different sampling densities to different regions based on their geometric complexity. Regions with high curvature, sharp features, or topological complexity receive higher sampling density to accurately capture geometric details, while simple regions use lower sampling density. This localized approach maintains geometric accuracy where needed while avoiding the proliferation of cells in simpler areas.
Solution Approach 2:
The patent changes the sampling density parameter dynamically based on local geometric characteristics. The sampling density is not fixed but varies as a function of the importance metric, which is computed from geometric features such as curvature, feature size, and topological complexity. This parameter adaptation allows the system to optimize the balance between geometric accuracy and cell count.
3Ease of manufacture
If uniform mesh resolution is used, then implementation is straightforward and robust, but element sizes are constant throughout the volume preventing localized refinement
Solution Approach 1:
The patent introduces dynamics by making the mesh resolution adaptive rather than static. The sampling density and resulting element sizes dynamically adjust according to the local importance metric computed from geometric features. This allows the mesh to automatically refine in critical regions while maintaining coarser resolution elsewhere, providing both localized adaptability and implementation robustness through the systematic importance-based approach.
Data Source
AI summary
A modified VOMAC mesh generation method for image data sampled from an actual object in which mesh resolution can vary locally within the mesh while permitting control of the distortion of cells in the mesh to maintain suitability for performing finite element (or finite volume) analysis on a representation of the object.The method includes computer-implemented instructions that calculate a variable sampling point distribution (SPD) in image data space, the variable SPD having localized variations in SPD within the image data space, and the distribution of sampling points having the same topology as a uniform SPD suitable for obtaining a regular structured is mesh. The method includes generating an indication of the magnitude of cell distortion between the generated mesh and the regular structured meshVarying the mesh resolution may enable smaller elements to be located in regions of particular interest or activity when subsequently performing analysis using the mesh model.