Model Order Reduction for Parametric Hermitian Eigenvalue Problems: Local Acceleration with Taylor-Reduced Basis Method
This work addresses model order reduction for eigenvalue problems in computational science and engineering, offering a local acceleration technique that is incremental, building on existing perturbation theory.
The paper tackles the efficient approximation of eigenspaces for large-scale parametric Hermitian matrices by introducing the Taylor-reduced basis method (Taylor-RBM), which constructs an approximation space using derivative information of the spectral projector at a reference point, and provides error analysis and computational procedures to justify and implement the method.
This paper is concerned with the Taylor-reduced basis method (Taylor-RBM) for the efficient approximation of eigenspaces of large scale parametric Hermitian matrices. The Taylor-RBM is a local model order reduction method, which constructs an approximation space by capturing derivatives information of the spectral projector at a reference point in the parameter domain. We perform a concise error analysis to justify the Taylor-RBM for eigenvalue problems, and we present a computationally efficient procedure to assemble the Taylor-reduced basis space. Since this method is tightly connected to the classical multivariate analytic perturbation theory, we also provide a detailed analysis of the spectral approximation using the truncated power series of the eigenprojector, and compare this with the approximation obtained from the Taylor-RBM.