[Legacy Report] Large Scale Computing and Multi-Scale Electromagnetic Modeling from Statics to Nano-Optics

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Computational electromagnetics (CEM) research is important for producing simulation software that have been used for virtual prototyping and the design of major electrical and electronic components. Solving electromagnetics problem is a challenging task, especially when the structure is electrically large and involves multi-scale structures. This kind of structures is often encountered in circuits in electronic packaging, small antenna designs, RFID sensor designs, and antennas on complex platforms. However, more CEM is used in nano-technologies as in nano-electronics, nano-optics, and Casimir force for N/MEMS.

In this presentation, we will give an overview of recent progress in large scale computing in electromagnetics, and discuss various methods to overcome multiscale problems. We will discuss the use of self-box preconditioner, parallel computing, and the equivalence principle algorithm (EPA) to capture the multi-scale physics of complex structures. In this method, complex structures are partitioned into parts by the use of equivalence surfaces. The interaction of electromagnetic field with structures within the equivalence surface is done through scattering operators working via the equivalence currents on the equivalence surfaces. The solution within the equivalence surface can be obtained by various numerical methods. Then the interaction between equivalence surfaces is obtained via the use of translation operators. When accelerated with the mixed-form fast multipole method, large multi-scale problems can be solved in this manner.

We will also discuss the augmented electric field integral equation (A-EFIE) approach in solving the low-frequency breakdown problem as encountered in circuits in electronic packaging. In this method, the EFIE is augmented with an additional charge unknown, and an additional continuity equation relating the charge to the current. The resultant equation, after proper frequency normalization, is frequency stable down to very low frequency. This method does not suffer from the low-frequency breakdown, but it does have the low-frequency inaccuracy problem which can be solved by perturbation method. We will also discuss the augmentation of EPA (A-EPA) to avoid low frequency breakdown, and the hybridization of EPA, A-EPA, and A-EFIE to tackle some multi-scale problems.
Next, we will discuss the use of CEM is used in nano-technologies, as in nano-electronics, nano-optics for solar cell design, and in N/MEMS for Casimir force calculation. In nano-optics, we will discuss the use of surface plasmonics, and plasmonics in nano-particles in enhancing the performace of the solar cell, as will as in spontaneous emission and Purcell effect.

When the frequency is extremely high such that the wavelength is much shorter than the object, we are in the regime of ray optics. In this regime, electromagnetic wave or light behaves like a particle. Different strategies need to be adopted to solve problems in this regime. We will discuss our effort in making the computation load become frequency independent when the frequency is high and the wavelength is short.

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