A new H2-matrix-based representation of electrodynamic systems with minimized rank and prescribed accuracy

In this work, we generate a new H²-matrix-based representation of the dense system matrix arising from the IE-based analysis of electrodynamic problems. Such a representation features a minimized rank with prescribed accuracy. Instead of using an interpolation based scheme, we develop a new method to construct the nested cluster basis and the coupling matrices, the rank of which is minimized based on the accuracy requirement. Furthermore, the new method has a linear complexity, and hence the computational overhead is minimal for constructing an H²-based representation of the system matrix. The proposed method has been applied to solve large-scale electrodynamic problems. It is shown that a dense matrix-vector multiplication involving over 1 million unknowns can be completed in 20 seconds and 15 GB memory on a single 8222SE AMD Opteron processor.