Field Tuning Simulation Using Sensitivity Matrices
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Solution Overview
Problem
Current physical system simulations, particularly for electric and magnetic fields, are computationally expensive and time-consuming due to the need for repeated solving of differential equations during iterative design processes, which hampers productivity in product development.
Innovation Solution
A method that stores baseline electric and magnetic field values and their sensitivities in a computational mesh, allowing for user-adjusted simulations without re-solving the differential equations, using factorized system matrices and linear approximations to quickly update field values based on parameter changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If repeated solving of differential equations is performed during iterative design processes, then accurate simulation results are obtained, but computational time and processing cost increase significantly
Solution Approach 1:
The patent pre-calculates and stores sensitivity information (derivatives of field values with respect to parameters) along with the baseline field values during the initial differential equation solving. This preliminary preparation enables rapid updates during iterative design without requiring repeated full solves, thus resolving the contradiction between accuracy and computational time.
Solution Approach 2:
The patent creates a computational model that copies the essential relationships between parameters and field values through stored sensitivity data. Instead of re-solving the complete differential equations, the system uses the pre-computed sensitivity matrices to generate updated field values, effectively creating a simplified copy of the physical system's response behavior.
2Measurement precision
If full differential equation solving is performed for each parameter adjustment, then accurate updated field values are obtained, but computational resources are excessively consumed
Solution Approach 1:
The system performs preliminary computation of sensitivity matrices during the initial solve, storing these derivatives for later use. This advance preparation reduces the computational energy required during subsequent parameter adjustments, as only simple matrix-vector operations are needed instead of full differential equation solves.
Solution Approach 2:
The patent exploits parameter changes by using the stored sensitivity information to compute updated field values through linear approximation. When parameters change, the system uses the pre-computed derivatives to efficiently calculate new field values without re-solving the differential equations, thereby reducing computational energy consumption while maintaining acceptable accuracy.
3Productivity
If iterative design processes are accelerated, then productivity improves, but simulation accuracy may be compromised
Solution Approach 1:
By pre-computing and storing sensitivity information, the system enables rapid iterative design processes. The stored derivatives allow for quick updates of field values when parameters change, accelerating productivity while maintaining accuracy through the use of mathematically rigorous sensitivity-based updates rather than crude approximations.
Solution Approach 2:
The computational model creates an accurate representation of the physical system's response through stored sensitivity data. This copied behavior allows rapid exploration of design variations with maintained accuracy, as the sensitivity matrices capture the essential physics of how field values respond to parameter changes.
Data Source
AI summary
Systems and methods are described for providing adjustable simulation of electric and magnetic fields of a system. Data is received that is indicative one or more parameters of an object in a three dimensional space. A first system of differential equations is to determine electric and magnetic field values are stored at a plurality of points of the three dimensional space and storing electric and magnetic field values in the computational mesh data structure. A second system of differential equations is solved to determine sensitivities of the determined electric and magnetic fields to changes in a first parameter of the object at points in the three dimensional space. Updated electric and magnetic field values are determined based on a user entered adjustment, the electric and magnetic field values in the computational mesh, and the sensitivities without re-solving the first system of differential equations or the second system of differential equations.