Two-sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS(2024)

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摘要
In this paper, new fast computing methods for partial differential equations with variable coefficients are studied and analyzed. They are two kinds of two-sided Krylov enhanced proper orthogonal decomposition (KPOD) methods. First, the spatial discrete scheme of an advection-diffusion equation is obtained by Galerkin approximation. Then, an algorithm based on a two-sided KPOD approach involving the block Arnoldi and block Lanczos processes for the obtained time-varying equations is put forward. Moreover, another type of two-sided KPOD algorithm based on Laguerre orthogonal polynomials in frequency domain is provided. For the two kinds of two-sided KPOD methods, we present a theoretical analysis for the moment matching of the discrete time-invariant transfer function in time domain and give the error bound caused by the reduced-order projection between the Galerkin finite element solution and the approximate solution of the two-sided KPOD method. Finally, the feasibility of four two-sided KPOD algorithms is verified by several numerical results with different inputs and setting parameters.
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关键词
model order reduction,partial differential equations,two-sided Krylov enhanced proper orthogonal decomposition
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