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

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.