This paper proposed a data-driven non-intrusive model order reduction (NIMOR) approach for parameterized time-domain Maxwell's equations. The NIMOR method consisted of fully decoupled offline and online stages. Initially, the high-fidelity (HF) solutions for some training time and parameter sets were obtained by using a discontinuous Galerkin time-domain (DGTD) method. Subsequently, a two-step or nested proper orthogonal decomposition (POD) technique was used to generate the reduced basis (RB) functions and the corresponding projection coefficients within the RB space. The high-order dynamic mode decomposition (HODMD) method leveraged these corresponding coefficients to predict the projection coefficients at all training parameters over a time region beyond the training domain. Instead of direct regression and interpolating new parameters, the predicted projection coefficients were reorganized into a three-dimensional tensor, which was then decomposed into time- and parameter-dependent components through the canonical polyadic decomposition (CPD) method. Gaussian process regression (GPR) was then used to approximate the relationship between the time/parameter values and the above components. Finally, the reduced-order solutions at new time/parameter values were quickly obtained through a linear combination of the POD modes and the approximated projection coefficients. Numerical experiments were presented to evaluate the performance of the method in the case of plane wave scattering.
Citation: Mengjun Yu, Kun Li. A data-driven reduced-order modeling approach for parameterized time-domain Maxwell's equations[J]. Networks and Heterogeneous Media, 2024, 19(3): 1309-1335. doi: 10.3934/nhm.2024056
This paper proposed a data-driven non-intrusive model order reduction (NIMOR) approach for parameterized time-domain Maxwell's equations. The NIMOR method consisted of fully decoupled offline and online stages. Initially, the high-fidelity (HF) solutions for some training time and parameter sets were obtained by using a discontinuous Galerkin time-domain (DGTD) method. Subsequently, a two-step or nested proper orthogonal decomposition (POD) technique was used to generate the reduced basis (RB) functions and the corresponding projection coefficients within the RB space. The high-order dynamic mode decomposition (HODMD) method leveraged these corresponding coefficients to predict the projection coefficients at all training parameters over a time region beyond the training domain. Instead of direct regression and interpolating new parameters, the predicted projection coefficients were reorganized into a three-dimensional tensor, which was then decomposed into time- and parameter-dependent components through the canonical polyadic decomposition (CPD) method. Gaussian process regression (GPR) was then used to approximate the relationship between the time/parameter values and the above components. Finally, the reduced-order solutions at new time/parameter values were quickly obtained through a linear combination of the POD modes and the approximated projection coefficients. Numerical experiments were presented to evaluate the performance of the method in the case of plane wave scattering.
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Mengjun Yu, Kun Li. A data-driven reduced-order modeling approach for parameterized time-domain Maxwell's equations[J]. Networks and Heterogeneous Media, 2024, 19(3): 1309-1335. doi: 10.3934/nhm.2024056
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