Non-Intrusive Reduced-Order Modeling of Parameterized Electromagnetic Scattering Problems using Cubic Spline Interpolation

• Published in: Journal of scientific computing Vol. 87; no. 2; p. 52
• Main Authors: Li, Kun, Huang, Ting-Zhu, Li, Liang, Lanteri, Stéphane
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-05-2021; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Basis functions; Coefficients; Computational Mathematics and Numerical Analysis; Computer Science; Datasets; Decomposition; Electromagnetic scattering; Finite element method; Galerkin method; Interpolation; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical models; Mathematics; Mathematics and Statistics; Methods; Model reduction; Modeling and Simulation; Multilayers; Parameterization; Parameters; Partial differential equations; Plane waves; Proper Orthogonal Decomposition; Reduced order models; Singular value decomposition; Theoretical; Non-intrusive reduced-order modeling; Parameterized electromagnetic scattering problems; Discontinuous Galerkin method; Proper orthogonal decomposition; Cubic spline interpolation; Reduced basis method
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-021-01467-2

This paper presents a non-intrusive model order reduction (MOR) for the solution of parameterized electromagnetic scattering problems, which needs to prepare a database offline of full-order solution samples (snapshots) at some different parameter locations. The snapshot vectors are produced by a high order discontinuous Galerkin time-domain (DGTD) solver formulated on an unstructured simplicial mesh. Because the second dimension of snapshots matrix is large, a two-step or nested proper orthogonal decomposition (POD) method is employed to extract time- and parameter-independent POD basis functions. By using the singular value decomposition (SVD) method, the principal components of the projection coefficient matrices (also referred to as the reduced coefficient matrices) of full-order solutions onto the RB subspace are extracted. A cubic spline interpolation-based (CSI) approach is proposed to approximate the dominating time- and parameter-modes of the reduced coefficient matrices without resorting to Galerkin projection. The generation of snapshot vectors, the construction of POD basis functions and the approximation of reduced coefficient matrices based on the CSI method are completed during the offline stage. The RB solutions for new time and parameter values can be rapidly recovered via outputs from the interpolation models in the online stage. In particular, the offline and online stages of the proposed RB method, termed as the POD-CSI method, are completely decoupled, which ensures the computational validity of the method. Moreover, a surrogate error model is constructed as an efficient error estimator for the POD-CSI method. Numerical experiments for the scattering of plane wave by a 2-D dielectric cylinder and a multi-layer heterogeneous medium nicely illustrate the performance of POD-CSI method.