Eigen Augmentation for EM Modeling Speed-Up
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Solution Overview
Problem
Electromagnetic (EM) modeling and simulation of design variants of EM structures are computationally intensive and time-consuming, as conventional methods treat each structure independently, despite similarities with previously modeled structures, leading to significant wastage of resources and time.
Innovation Solution
The method involves augmenting the Krylov subspace of a design variant EM structure with Eigen vectors and Krylov vectors from a previously solved EM structure, using mesh interpolation techniques to accommodate different mesh structures, thereby speeding up the simulation process by reusing computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional EM modeling methods treat each structure independently, then solution accuracy is maintained, but computational time and resources are significantly wasted
Solution Approach 1:
The method performs preliminary EM modeling on a first EM structure to obtain its solution, then reuses this pre-computed solution when modeling a second EM structure that is a design variant of the first structure. This preliminary action avoids redundant computations and significantly reduces modeling time for design variants.
Solution Approach 2:
The method recovers and reuses the solution from the first EM structure when modeling the second EM structure. Instead of discarding the first structure's solution after use, it is retained and applied to accelerate the modeling of design variants, thereby recovering computational value.
2Productivity
If Eigen vectors from a previously solved EM structure are reused for a design variant, then computational efficiency is improved, but additional processing steps are required
Solution Approach 1:
The method uses an intermediary process that determines whether a second EM structure is a design variant of a first EM structure, and if so, retrieves and applies the first structure's solution as an intermediary step. This intermediary mechanism bridges the gap between different structures while maintaining efficiency.
Solution Approach 2:
The method changes the approach from solving each structure independently to reusing solutions based on structural similarity parameters. When design variant parameters are detected, the method switches to a reuse mode that leverages previous computations, thereby improving efficiency despite added complexity.
Data Source
Figure 1(a)~1(b)
Figure 2(a)
Figure 2(b)
AI summary
Techniques for electromagnetic modelling of EM structures are described. Krylov subspace of a second EM structure (104, 504) is augmented with Eigen vectors of a first EM structure (102, 502) to form an augmented space. The second EM structure (104, 504) is a design variant of the first EM structure (102, 502) and the first EM structure (102, 502) is already EM modelled and simulated. Thereafter, Maxwell's equations for the second EM structure (104, 504) are solved using the augmented space.