Multilevel fast multipole method for modeling permeable structures using conformal finite elements.

Abstract

The analysis of penetrable structures has traditionally been carried out using partial differential equation methods due to the large computation time and memory requirements of integral equation methods. To reduce this computational bottle neck, this thesis focuses on fast integral equation methods for modeling penetrable geometries with both dielectric and magnetic material properties. Previous works have employed the multilevel fast multipole method for impenetrable targets in the context of flat-triangular geometry approximations. In this thesis, we integrate the multilevel fast multipole method with surface and volume integral equation techniques to accurately analyze arbitrarily curved inhomogeneous targets. It is demonstrated that conformal geometry modeling using curvilinear elements achieve higher accuracy at lower sampling rates. Also, the combined use of curvilinear elements and the multilevel fast multipole method allows for significantly faster and more efficient numerical methods. The proposed method reduces the traditional <italic>O</italic>(<italic> N</italic><super>2</super>) computational cost down to <italic>O</italic>(<italic> N</italic> log <italic>N</italic>) and thus practical size geometries can be analyzed. Several example calculations are given in the thesis along with comparisons with partial differential equation methods.