Eddy Current Analysis Using Volume Integral Equations
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Solution Overview
Problem
Existing methods for analyzing eddy currents in electronic devices, such as finite elements methods and partial element equivalent circuit (PEEC) methods, face challenges including heavy calculations, singular integrals, and high computational complexity, which limit their ability to handle large problems and complex geometries, particularly when dealing with curved shapes or non-aligned objects.
Innovation Solution
A computer-implemented method using volume-uniform basis functions for numerical simulations, allowing for efficient computation of eddy currents in conductive objects, including those with complex geometries, by employing a Galerkin method and singularity extraction techniques to reduce memory footprint and increase computational speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing methods (FEM, PEEC, VI) are used to analyze eddy currents, then the analysis can be performed on conductive elements, but the computational complexity and memory consumption grow with the square of the number of elements
Solution Approach 1:
The patent segments the conductive body into a mesh of finite elements, allowing the complex eddy current problem to be divided into smaller, manageable parts. Each element can be processed independently, reducing the overall computational burden while maintaining analysis accuracy across the entire structure.
Solution Approach 2:
The patent changes the mathematical formulation by using volume integral equations with edge elements, transforming the problem from traditional FEM to a different mathematical framework. This parameter change in the underlying equations enables reduced computational complexity while preserving solution accuracy.
2Manufacturing precision
If the number of mesh elements is increased to model complex geometries, then the analysis accuracy improves, but the memory consumption and computation time increase significantly
Solution Approach 1:
The patent applies segmentation by creating a mesh of finite elements that can be dynamically adjusted in number and complexity. This allows high-accuracy modeling of complex geometries using a manageable number of elements, avoiding the need for excessive memory consumption while maintaining manufacturing precision.
Solution Approach 2:
The patent uses partial element equivalent circuit methods that selectively model only the necessary conductive elements and their interactions. This partial action approach provides sufficient accuracy for complex geometries without requiring excessive computational resources, balancing precision with resource consumption.
3Productivity
If traditional integration methods (Gaussian rules) are used to compute integrals, then the calculations can be performed, but errors and approximations are introduced leading to inaccuracy
Solution Approach 1:
The patent substitutes traditional numerical integration methods (Gaussian rules) with an alternative mathematical formulation using volume integral equations and edge elements. This replacement eliminates the need for approximate numerical integration, providing exact analytical results while maintaining computational efficiency and avoiding integration errors.
4Reliability
If full 3D modeling is performed to capture all electromagnetic interactions, then the analysis completeness improves, but the processing time and hardware requirements increase
Solution Approach 1:
The patent segments the 3D electromagnetic problem into a mesh of finite elements, allowing complete 3D analysis to be performed through systematic processing of individual elements. This segmentation enables comprehensive electromagnetic interaction capture while reducing processing time through parallelizable element-wise computations and efficient algorithms.
Solution Approach 2:
The patent performs preliminary actions by pre-computing and storing electromagnetic interaction matrices and other computational resources before the main analysis. This preliminary processing reduces the time required during actual eddy current calculation, enabling complete 3D modeling without excessive processing time penalties.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables accurate and efficient analysis of eddy currents in complex electronic devices, reducing memory consumption and computational time, allowing for larger and more complex problems to be analyzed on relatively simple processing systems without sacrificing accuracy.
Implementation Method 1
A method of analysis of a conductive body (e.g., printed-circuit-board, PCB) immersed in an electromagnetic field produced by at least one source of electromagnetic energy
Implementation Method 2
computation of a double volume integral involves strongly singular multiple integrals
Data Source
AI summary
Techniques of computing values of physical parameters of a conductive body immersed in an electromagnetic field produced by at least one source of electromagnetic energy are provided.