EM Sensitivity Analysis via Fast Frequency Sweep
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Solution Overview
Problem
Current electromagnetic (EM) device design methods, particularly those using the finite-element method (FEM), are inefficient in performing electromagnetic sensitivity analysis due to the time-consuming process of solving large linear systems at multiple frequencies, which hinders design optimization and yield-driven design.
Innovation Solution
The implementation of a fast frequency sweep method based on adjoint/self-adjoint formulas and the single-size matrix Padé via Lanczos (MPVL) method for model order reduction, transforming EM linear systems into single-size matrices to enable direct application of MPVL for EM sensitivity analysis, thereby avoiding repetitive solving processes and reducing computational costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If FEM is used to solve large linear systems at multiple frequencies, then electromagnetic sensitivity analysis can be performed, but the computational time becomes very long
Solution Approach 1:
The patent performs preliminary FEM simulation at a single pre-solution frequency to obtain field solutions and construct the system matrix before the actual sensitivity analysis. This preliminary action allows the subsequent frequency sweep to reuse the constructed matrix and its decomposition, avoiding repetitive solving processes at each frequency point and significantly reducing computational time while maintaining analysis accuracy
Solution Approach 2:
The patent uses the field solutions obtained at the pre-solution frequency as a basis to estimate and compute field solutions at other frequencies through the fast frequency sweep method. By copying and adapting the pre-solution results across the frequency range using the derived adjoint/self-adjoint formulas, the method avoids solving the complete system at each frequency while preserving the necessary electromagnetic sensitivity information
2Measurement precision
If conventional software computes electromagnetic response derivatives at multiple frequencies, then comprehensive sensitivity information is obtained, but computational efficiency decreases
Solution Approach 1:
The patent changes the computational approach by deriving adjoint/self-adjoint formulas that enable efficient computation of electromagnetic response derivatives across the entire frequency range from a single pre-solution. This parameter change in the mathematical formulation allows obtaining comprehensive sensitivity information at multiple frequencies without performing multiple complete FEM solves, thus maintaining derivative accuracy while improving computational efficiency
Solution Approach 2:
The patent creates a universal computational framework where a single pre-solution at one frequency serves multiple purposes: it provides the base field solutions for sensitivity calculation, constructs the system matrix for the fast frequency sweep, and enables derivation of electromagnetic response derivatives across the entire frequency range. This multi-functional use of the pre-solution results eliminates the need for separate computations at each frequency
Data Source
AI summary
The disclosure provides an electromagnetic device design system including: one or more processors of a machine; and computer-storage medium storing instructions, which when executed by the machine, cause the machine to perform operations for EM sensitivity analysis for an electromagnetic (EM) device. The operations include: initiating physical parameters of the EM device, wherein the EM device comprises multiple ports; performing EM simulation for the EM device at a pre-solution frequency using the finite-element method (FEM); applying single-size matrix Padé via Lanczos (MPVL) method in fast frequency sweep and performing EM simulation for the EM device under excitation at each port to obtain field solution of the EM device at frequencies in a frequency range; calculating S-parameters for the multiple ports of the EM device; and calculating derivatives of the S-parameters with respect to one of the physical parameters in the frequency range.