**Authors:** Wenwen Chai, and Dan Jiao

**Source:**FERMAT,Volume 12,NOV-DEC,2015

**Abstract:** In this paper, we will develop a fast direct integral
equation solver for large-scale electrodynamic analysis. In this
solver, we significantly reduce the cost of an H-matrix-based
computation of electrodynamic problems with prescribed accuracy satisfied, by constructing an efficient matrix algebra-based
method that minimizes the rank of each admissible block based
on accuracy; and by developing a new frequency-dependent Hpartition that minimizes the number of admissible blocks at each
tree level for each frequency point. We will then develop a fast
H-matrix-based LU factorization for directly solving the dense
system matrix resulting from an integral-equation-based analysis
of large-scale electrodynamic problems. The proposed direct
solver successfully solves dense matrices that involve more than
1 million unknowns associated with electrodynamic problems
of 96 wavelengths in fast CPU time (less than 20 hours in
LU factorization, 85 seconds in LU solution), modest memory
consumption, and with the prescribed accuracy satisfied on a
single CPU running at 3 GHz. As an algebraic method, the
underlying fast techniques are kernel independent.

**Index Terms:** Integral-equation based methods, electrodynamic analysis, direct solution, H matrix, large-scale analysis

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