In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems
A wide slot antenna backed by a substrate integrated waveguide (SIW) cavity is presented and investigated for the enhancement of operating bandwidth at 60-GHz band. The 10-dB return loss impedance bandwidth of the antenna increases from 3% to 11.6% with consistent radiation performance as the width to length ratio (WLR) of the rectangular slot cutting from the SIW increases from 0.12 to 0.71. Its dual-resonance operation mechanism is verified by a parametric study. Three 2×4 antenna arrays with different slot WLRs are designed and fabricated with a printed circuit board (PCB) process at the 60-GHz bands. The measured results show that the antenna array with slot WLR of 0.71 achieves the gain of 1012 dBi and the cross-polarization levels of better than 25 dB in both E-and H-planes over the enhanced operating bandwidth of about 11.6%.Index Terms-Cavity-backed antenna, dual-resonance, slot antenna, substrate integrated waveguide (SIW), 60-GHz band.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.