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Fabrication and Operation of a Nano-Optical Conveyor Belt

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A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic

Sadeed B Sayed¹, Yang Liu², Luis J Gomez³

¹School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798.

IEEE Transactions on Antennas and Propagation

|June 20, 2022

Summary

A new butterfly-accelerated volume integral equation (VIE) solver offers faster and more accurate electromagnetic (EM) analysis for complex objects. This method significantly reduces computational costs for high-frequency scattering problems.

Keywords:

Butterfly algorithm direct solver fast solver preconditioners volume integral equation

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Finite Element Modelling of a Cellular Electric Microenvironment

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Published on: May 18, 2021

Area of Science:

Electromagnetics and Computational Physics
Numerical Methods for Engineering

Background:

Electromagnetic (EM) analysis of scattering from heterogeneous objects is computationally intensive.
Existing methods often require substantial memory and processing time, especially for large-scale problems.

Purpose of the Study:

To develop a fast and accurate volume integral equation (VIE) solver for electromagnetic scattering.
To accelerate the analysis of complex, heterogeneous objects using advanced computational techniques.

Main Methods:

Proposed a butterfly-accelerated VIE solver utilizing the hierarchical off-diagonal butterfly (HOD-BF) scheme.
The HOD-BF scheme is employed for system matrix construction and approximate inverse computation (preconditioner).
Analyzed computational complexity and validated through numerical experiments on large-scale structures.

Main Results:

Achieved O(N log N) complexity for system matrix construction and preconditioner inversion, where N is the number of unknowns.
Demonstrated reduced memory and computational time compared to traditional N^2 matrix solvers.
Validated accuracy and efficiency for EM analysis of structures with millions of unknowns and diverse permittivity values.

Conclusions:

The butterfly-accelerated VIE solver provides a significant advancement in computational electromagnetics.
Offers a memory-efficient and time-saving solution for high-frequency EM scattering problems.
Suitable for analyzing large-scale, complex real-world structures.