Fast Direct Error-Controlled Solution of Scattering Problems via ℋ-matrix Acceleration of Locally Corrected Nyström Method

The fast direct high-order solution of radiation problems in the presence of perfect electrically conducting (PEC) sphere with the Locally Corrected Nystrom (LCN) method is presented. Accelerated solution is obtained using error-controlled hierarchical (ℋ)-matrix framework. Matrix fill time and direct solution time are shown to be substantially reduced compared to those needed by conventional LCN. The error of solution is computed via comparison against the analytical Mie series solution. Developed computational framework is shown to produce the higher order solution while preserving high compressibility of the corresponding ℋ-matrix blocks. The memory cost and CPU time complexity scaling with the size of the problem is analyzed.