A Novel Mask-Vectorized Matrix Assembly Method for ACA-Nyström Analysis of Electrically Large Electromagnetic Scattering

The Nyström discretization of boundary integral equations produces dense impedance matrices that are prohibitive for two-dimensional electrically large electromagnetic scattering problems. Fast algorithms like adaptive cross approximation (ACA) reduce far-field complexity, but matrix assembly remains a bottleneck due to numerous conditional branches hindering vectorization. We propose a novel mask-vectorized matrix assembly method integrated with an ACA-accelerated Nyström method for the two-dimensional electric-field integral equation. By constructing a Boolean mask, the self-singular, near-singular, and regular entries within each densely assembled near-field block are classified, thereby enabling branch-free SIMD computation. Self-singular terms are evaluated using closed-form expressions, near-singular terms are computed with 32-point Gauss–Legendre quadrature, and regular terms are evaluated directly by a one-point Nyström scheme. The same branch-free SIMD evaluation is also applied to regular far-field blocks. Finally, we combine single-thread SIMD with OpenMP multi-threading, distributing independent blocks across threads. Far-field compression uses partially pivoted ACA, and the system is solved by preconditioned GMRES. Numerical results show speedup over the standard ACA-Nyström baseline with full accuracy preservation.