Computational Physics

Most electromagnetic wave propagation problems of practical interest cannot be solved analytically. When one is computing scattering or radiation from bodies from around one to several wavelengths in size existing approximate techniques for solving the problem fail: multipole expansions diverge and diffraction is significant enough that geometric or physical optics approaches are also inadequate. Numerical integral and differential equation solutions are possible, but their simple implementations require extraordinary amounts of computer time and memory for some problems. My collaborators at Hughes Research Laboratories and Yale University and I have developed techniques for numerically solving these problems in an economical fashion. We expect to be able to solve problems on a work station using our techniques that are not possible on the largest supercomputers using less sophisticated techniques. I am looking for undergraduate and graduate students interested in improving, implementing, and testing these algorithms. Our current research directions include

  • testing currently implemented algorithms
  • developing efficient techniques for modelling induced currents in wire structures
  • applying the techniques developed for scattering and radiation for waveguide propagation and high frequency circuits
  • applying electromagnetic tecniques to scattering and radiation of scalar (acoustic) waves

These techniques have many practical applications in the areas of radar and antenna design, modelling of high density and high speed circuits, submarine detection, and acoustic modelling.

The problems were are currently working on in this area involve correctly accounting for surface roughness during reflection from thin films in the extreme ultraviolet. Greg Hart and I received a best paper award for this work in 2013 from the Utah Academy of Sciences, Arts and Letters. An earlier Utah Academy paper by Elise Martin describes some of our work in describing rough surfaces.