Extreme-Scale and Multi-Scale Electromagnetic Algorithms

Extreme-Scale and Multi-Scale EM Algorithms

Research Synopsis

As contemporary electronic devices continue to decrease in size and novel meta-materials and meta-surfaces find more applications, the demand for a method capable of addressing multi-scale and extreme-scale modeling and simulation becomes urgent. Unfortunately, the widely used vector wave equations encounter a significant challenge known as the "low-frequency breakdown" catastrophe in the numerical simulation of EM problems. At low frequencies, corresponding to quasi-static and static scenarios, the decoupling of electric and magnetic fields, along with the separation of currents and charges, renders the vector wave equations unable to account for the Gauss’s law. This incomplete representation of physics in electro-(quasi)-static and magneto-(quasi)-static cases leads to the well-known low-frequency breakdown problem. Utilizing quasi-static and static formulations as remedies neglect the inclusion of slowly varying terms in Maxwell’s equations, leading to the omission of crucial physics at low frequencies. Additionally, alternative solutions employing an incomplete Helmholtz decomposition prove challenging for application in large-scale problems.

In this effort, our focus revolves around the development, implementation, validation, and application of a new formulation free of low-frequency breakdown. This innovative approach transcends the limitations of existing formulations, offering a versatile solution applicable across all frequencies — from static (dc) to microwave frequencies and beyond. This novel approach is employed in applications including the modeling of microwave integrated circuits, electrical machine and nonlinear magnetism, and wireless communication using intelligent reflecting surface (IRS) devices.