Refined isogeometric analysis for generalized Hermitian eigenproblems

We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku=λMu). rIGA conserves the desirable properties of maximum-continuity (IGA) while it reduces solution cost by adding zero-continuity basis functions, which decrease matrix connectivity. As a result, enriches approximation space and interconnection between degrees freedom. compare computational costs versus those IGA when employing Lanczos eigensolver with shift-and-invert spectral transformation. When all eigenpairs within given interval [λs,λe] are interest, we select several shifts σk∈[λs,λe] using spectrum slicing technique. For each shift σk, factorization transformation K−σkM controls total eigensolution. Several multiplications operator (K−σkM)−1M vectors follow this factorization. Let p be polynomial degree functions assume that has maximum continuity p−1. rIGA, introduce C0 separators at certain element interfaces minimize cost. setup, our theoretical estimates predict savings compute fixed number up O(p2) in asymptotic regime, is, large problem sizes. Yet, numerical tests show for moderate-size eigenproblems, observed reduction is O(p). In addition, improves accuracy every eigenpair first N0 eigenvalues eigenfunctions, where modes original discretization.