Conductor Mesh Initialization Using Straight Skeleton Width Mapping
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Solution Overview
Problem
Conventional 3D electro-magnetic solvers face challenges in generating an initial mesh for electrical circuit designs, as they often rely on wavelength-based meshing techniques that fail to accurately capture the complex geometry of conductors, leading to inaccurate simulations and excessive processing time.
Innovation Solution
A method that estimates the width of a conductor along its entire structure without a physical starting point, using a straight skeleton representation to determine mesh cells based on varying widths, allowing for a more efficient initial mesh generation that adapts to the conductor's geometry.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional wavelength-based meshing techniques are used, then the mesh generation process is simple and fast, but the mesh accuracy fails to capture complex conductor geometry
Solution Approach 1:
The conductor is segmented into multiple sections along its backbone, with each section having its own local width measurement and corresponding mesh density. This allows the mesh to adapt to geometric variations while maintaining a systematic generation process.
Solution Approach 2:
The mesh density is made local rather than uniform, with each mesh element's size determined by the local conductor width at that position. This captures complex geometry accurately while keeping the overall process manageable through automated width-based calculations.
2Measurement precision
If randomized ray-shooting is used to estimate local width, then the process is computationally simple, but the width estimation accuracy is poor
Solution Approach 1:
The randomized ray-shooting method is replaced with a deterministic geometric approach using straight skeletons. This substitution provides accurate width estimation through mathematical computation rather than statistical sampling, improving precision without sacrificing efficiency.
Solution Approach 2:
The approach changes from estimating width through randomized sampling to calculating it directly from the straight skeleton geometry. This parameter transformation from statistical estimation to deterministic calculation achieves both accuracy and efficiency.
3Measurement precision
If constant width assumption is made throughout the conductor structure, then the mesh generation is straightforward, but the mesh accuracy deteriorates for conductors with varying widths
Solution Approach 1:
The mesh generation process becomes dynamic rather than static, with mesh density automatically adjusting along the conductor backbone based on local width variations. This allows accurate representation of varying geometries while maintaining systematic generation through automated width-based calculations.
Solution Approach 2:
The conductor width is pre-calculated at multiple points along the backbone before mesh generation, using the straight skeleton approach. This preliminary width determination enables subsequent mesh elements to be sized appropriately for each location, achieving accuracy without complex iterative processes.
4Reliability
If initial mesh is generated far from final mesh, then fewer iterations are needed, but simulation accuracy suffers and processing time increases
Solution Approach 1:
The initial mesh is prepared in advance with accurate width information from straight skeleton analysis, positioning it much closer to the final converged mesh. This preliminary action with accurate geometric data reduces the number of refinement iterations needed, improving both accuracy and convergence speed.
Solution Approach 2:
The initial mesh uses width parameters derived from straight skeleton geometry rather than uniform or estimated values. This parameter change brings the initial mesh closer to the final solution, reducing iterative refinement needs and improving computational efficiency.
Data Source
AI summary
A method determines an initial mesh for a conductor in an electronic circuit design to enable more efficient simulation of electro-magnetic properties of the conductor. The method includes parsing a three-dimensional representation of a conductor as multiple vertices of a closed polygon, each vertex joining corresponding edges of the polygon; obtaining a straight skeleton of the conductor by moving the edges inwardly toward a center of the polygon at a constant speed in a self-parallel manner; determining widths of the conductor at multiple points along the straight skeleton as a function of the edges moving inwardly at the constant speed; constructing a backbone of the conductor, including registering the widths of the conductor along the conductor backbone; providing mesh cells on the conductor backbone using predetermined scaling factors of the registered widths of the conductor backbone; and generating the initial mesh for the conductor based on the mesh cells.