Approximate optimal projection for reduced-order models

作者：Oberai Assad A^*; Jagalur Mohan Jayanth

来源：International Journal for Numerical Methods in Engineering, 2016, 105(1): 63-80.

DOI：10.1002/nme.4963

• reduced-order models
• optimal projections
• variational multiscale Method

A critical component of a reduced-order model is the projection that maps the original high-fidelity system on to the reduced-order basis. In this manuscript, we develop a projection for linear systems that is optimal in an operator-independent norm. We derive an expression for this projection as a Galerkin projection plus another component that is interpreted as the effect of the scales that live outside the reduced-order basis. We note that the exact form of this projection does not lead to a viable computational method because it involves the inverse of the original high-fidelity operator. We approximate this inverse by an inexpensive preconditioner and create a practical method whose costs are of the same order as the Galerkin method. We test the performance of this method on heat conduction and advection-diffusion problems while using the incomplete LU preconditioner as an approximate to the inverse of the original operator, and conclude that it provides more accurate results than the Galerkin projection.

• 出版日期2016-1-6
• 单位MIT