Toward a more robust and accurate fast integral equation solver for microchip applications

Summary form only given. In this talk, we review fast integral equation solvers for low frequencies and high frequencies. We discuss some of the current problems and suggest possible solutions. We also describe the use of fast solvers for layered media. When applied to low frequencies, fast solvers usually have a low-frequency breakdown. Methods to overcome this low frequency breakdown are discussed. Moreover, a general method of moments encounters low frequency breakdown problems, and a remedy for this is also given. Many of the low frequency problems can be tackled by setting the frequency identically to zero, hence solving an electrostatic or a magnetostatic problem. Such a solution technique is also presented. For layered structures, we need a special Green's function. A closed form Green's function can be used to solve some of the complicated layered medium problems. Also, some applications of fast solvers to solve the lithography problem are demonstrated.