Wideband Fast Kernel-Independent Modeling of Large Multiscale Structures Via Nested Equivalent Source Approximation

We propose a wideband fast kernel-independent modeling of large multiscale structures; we employ a nested equivalent source approximation (NESA) to compress the dense system matrix. The NESA was introduced by these authors for low and moderate frequency problems (smaller than a few wavelengths); here, we introduce a high-frequency NESA algorithm, and propose a hybrid version with extreme wideband properties. The equivalent sources of the wideband NESA (WNESA) are obtained by an inverse-source process, enforcing equivalence of radiated fields on suitably defined testing surfaces. In the low-frequency region, the NESA is used unmodified, with a complexity of mathcal{O}(N) . In the high-frequency region, in order to obtain a fixed rank matrix compression, we hierarchically divide the far coupling space into pyramids with angles related to the peer coupling group size, and the NESA testing surfaces are defined as the boundaries of the pyramids. This results in a directional nested low-rank (fixed rank) approximation with mathcal{O}(Nlog {N}) computational complexity that is kernel independent; overall, the approach yields wideband fast solver for the modeling of large structures that inherits the efficiency and accuracy of low-frequency NESA for multiscale problems. Numerical results and discussions demonstrate the validity of the proposed work.