Hessian‐based model reduction for large‐scale systems with initial‐condition inputs

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Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “Second, it may be possible to even further reduce the cost associated with the determination of the largest error bound over Ξtrain (or in fact D) by considering more sophisticated non-ennumerative optimization procedures [32, 20]; however, the error and error bound are highly oscillatory over D, an”
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations (2009, unknown): “…concentration u satisﬁes a homogenous Dirichlet condition u ¼ 0 ; on C D : On the remaining boundary C N ¼ C D n @ X , it satisﬁes a homogenous Neumann condition r u (cid:2) n ¼ 0 ; on C N : We note that a similar contaminant transport problem has been studied in the model reduction context [2].”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, background): “RB-like “snapshot” ideas are also found in some of the many Reduced Order Model (ROM) approaches in the temporal domain [14,38,39,89,116,130,145,155,156]: POD sampling procedures are often invoked, and more recently greedy sampling approaches have also been considered [ 21 ].”