Port reduction in parametrized component static condensation: approximation and a posteriori error estimation

By Jens L. Eftang, Anthony T. Patera. 2013

82 citations recorded by the source corpus.

We introduce a port (interface) approximation and a posteriori error bound framework for a general component‐based static condensation method in the context of parameter‐dependent linear elliptic partial differential equations. The key ingredients are as follows: (i) efficient empirical port approximation spaces—the dimensions of these spaces may be chosen small to reduce the computational cost associated with formation and solution of the static condensation system; and (ii) a computationally tractable a posteriori error bound realized through a non‐conforming approximation and associated conditioner—the error in the global system approximation, or in a scalar output quantity, may be bounded relatively sharply with respect to the underlying finite element discretization.

Subfields: Computational Mechanics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/db9e98e6c93ab05126925627d5999c55e26c6578

Citations in the corpus

• On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “…been successfully pursued to mitigate the modal deformation of the POD basis by partitioning the state space, 164–167 time domain, 157,168–175 physical domain, 176–179 or parameter space 180–182 using multiple local, piecewise affine subspace approximations instead of a single global approximation.”