Numerical Techniques for Integral Equations

Finding computationally efficient numerical techniques for simulation of three-dimensional structures has been an important research topic in almost every engineering domain. Surprisingly, the most numerically intractable problem across these various disciplines can be reduced to the problem of solving a three-dimensional potential problem with a problem-specific Greens function. Application examples include: electrostatic analysis of sensors and actuators, electromagnetic analyses of integrated circuit interconnect and packaging, detailed analysis of frequency response and loss in photonic devices, drag force analysis of micromachined structures, and potential flow based aircraft analysis. Over the last fifteen years, we have been developing fast methods for solving these problems, and have developed widely used programs such as FastCap (capacitance), FastHenry (magnetoquasistatics), FastLap (general potential problems), FastImp (full wave impedence extraction),and FastStokes (fast fluid analysis). Our most recent work is in developing higher order methods[1], methods that efficiently discretize curved geometries[2], methods that are more efficient for substrate problems [3], and methods for analyzing rough surfaces [4].