Finite-difference frequency domain electromagnetics with the void space domain decomposition method.

Area of Science:

• Computational electromagnetics
• Numerical methods for wave propagation

Background:

• The finite-difference frequency domain (FDFD) method is valuable for inverse design problems.
• Existing FDFD methods can be computationally intensive and limited by domain size.
• Network bandwidth is a critical bottleneck for the finite-difference time domain (FDTD) method.

Purpose of the Study:

• Introduce a novel algorithm, the void space domain decomposition (VSDD) method, for FDFD solutions.
• Enhance the scalability and efficiency of FDFD simulations.
• Address the network bandwidth limitations inherent in FDTD methods.

Main Methods:

• Developed the void space domain decomposition (VSDD) algorithm.
• Implemented VSDD for solving electromagnetic problems using FDFD.
• Compared VSDD performance against traditional FDTD methods in terms of speed, domain size, and network bandwidth.

Main Results:

• VSDD achieves solve speeds comparable to FDTD.
• VSDD enables simulation domains 10 times larger or more with standard compute resources.
• Network bandwidth requirements for VSDD are reduced by approximately 35 times compared to FDTD.
• VSDD avoids solving a matrix equation spanning the entire problem domain.
• Voxel operation counts are similar between VSDD and FDTD.

Conclusions:

• The VSDD method presents a significant advancement for FDFD simulations.
• VSDD overcomes key limitations of FDTD, offering enhanced scalability and efficiency.
• This new algorithm facilitates larger and more complex inverse design problems in electromagnetics.