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arXiv · 1509.05705

A Computationally Optimal Randomized Proper Orthogonal Decomposition Technique

Dan Yu·Suman Chakravorty
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Abstract

In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal decomposition (RPOD*) technique to obtain the reduced order model by perturbing the primal and adjoint system using Gaussian white noise. We show that the computations required by the RPOD* algorithm is orders of magnitude cheaper when compared to the balanced proper orthogonal decomposition (BPOD) algorithm and BPOD output projection algorithm while the performance of the RPOD* algorithm is much better than BPOD output projection algorithm. It is optimal in the sense that a minimal number of snapshots is needed. We also relate the RPOD* algorithm to random projection algorithms. The method is tested on two advection-diffusion equations.

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Dan Yu, Suman Chakravorty. 2016-05-03. A Computationally Optimal Randomized Proper Orthogonal Decomposition Technique. https://arxiv.org/abs/1509.05705

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