A non-intrusive model order reduction approach for parameterized time-domain Maxwell's equations

<p style='text-indent:20px;'>We present a non-intrusive model order reduction (NIMOR) approach with an offline-online decoupling for the solution of parameterized time-domain Maxwell's equations. During offline stage, training parameters are chosen by using Smolyak sparse grid method approximation level <inline-formula><tex-math id="M1">\begin{document}$ L $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M2">\begin{document}$ L\geq1 $\end{document}</tex-math></inline-formula>) over target space. For each selected parameter, snapshot vectors first produced high discontinuous Galerkin (DGTD) solver formulated on unstructured simplicial mesh. In to minimize overall computational cost in stage and improve accuracy NIMOR method, radial basis function (RBF) interpolation is then used construct more at id="M3">\begin{document}$ L+1 $\end{document}</tex-math></inline-formula>, which includes grids from id="M4">\begin{document}$ $\end{document}</tex-math></inline-formula>. A nested proper orthogonal decomposition (POD) employed extract time- parameter-independent POD functions. By singular value (SVD) principal components reduced coefficient matrices high-fidelity solutions onto reduced-order subspace spaned functions extracted. Moreover, Gaussian process regression (GPR) proposed approximate dominating parameter-modes matrices. online new time parameter values can be rapidly recovered via outputs models without DGTD method. Numerical experiments scattering plane wave 2-D dielectric cylinder multi-layer heterogeneous medium nicely illustrate performance method.</p>