Sparse factorizations for fast local mode computations

Integral equation-based numerical models provide an important tool for the analysis and design in a variety of application areas. Traditional implementations of IE-based models lead to dense matrices, and this significantly limits the range of problems that can be addressed using such approaches. To treat more complex problems, it is necessary to use more sophisticated methods which rely on compressed representations of the underlying integral operators. Unfortunately, maintaining the advantages provided by such sparse representations of the underlying operators in turn requires the use of either fast iterative solution methods, or more complicated fast direct solution methods. The purpose of this paper is to contribute to the latter class of solution methods. In particular, we present a fast decomposition algorithm for sparse representations of integral operators and demonstrate how the proposed decompositions can be used within the fast direct solution framework previously discussed in (Adams et al., 2006) for low-to-moderate frequency EM phenomena.