Solution of the inhomogeneous Maxwell's equations using a Born series

Area of Science:

• Computational electromagnetics
• Numerical analysis
• Physics

Background:

• Solving inhomogeneous Maxwell's equations is crucial for various electromagnetic simulations.
• Existing methods like finite difference time domain (FDTD) can be computationally intensive.
• Accurate and efficient numerical solutions are needed for complex electromagnetic problems.

Purpose of the Study:

• To present a novel algorithm for the numerical solution of inhomogeneous Maxwell's equations.
• To improve the computational efficiency of solving the vector wave equation for the electric field.
• To provide a faster alternative to existing numerical techniques while maintaining accuracy.

Main Methods:

• The algorithm solves the inhomogeneous vector wave equation by expressing the electric field solution as a convergent Born series.
• This method leverages series expansion to approximate the solution iteratively.
• The computational approach avoids the extensive grid discretizations typical of FDTD.

Main Results:

• The proposed algorithm achieves solutions with accuracy comparable to 2D FDTD calculations.
• The numerical solutions are computed over three orders of magnitude faster than 2D FDTD.
• Demonstrates significant computational speedup for electromagnetic wave simulations.

Conclusions:

• The Born series approach provides a highly efficient method for solving inhomogeneous Maxwell's equations.
• This algorithm represents a substantial advancement in computational electromagnetics, enabling faster simulations.
• The findings suggest potential for broader application in electromagnetic design and analysis.