The reduced basis method for initial value problems
SIAM Journal on Numerical Analysis
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
A fast solver for Fokker--Planck equation applied to viscoelastic flows calculations: 2D FENE model
Journal of Computational Physics
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Multiscale simulations for suspensions of rod-like molecules
Journal of Computational Physics
libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
Engineering with Computers
Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
SIAM Journal on Scientific Computing
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In this paper we present a reduced basis method for the parametrized Fokker-Planck equation associated with evolution of finitely extensible nonlinear elastic (FENE) dumbbells in a Newtonian solvent for a (prescribed) extensional macroscale flow. We apply a proper orthogonal decomposition (POD)-greedy sampling procedure for the stable identification of optimal reduced basis spaces, and we develop a rigorous finite-time a posteriori bound for the error in the reduced basis prediction of the two outputs of interest—the optical anisotropy and the first normal stress difference. We present numerical results for stress-conformation hysteresis as a function of Weissenberg number and final time that demonstrate the rapid convergence of the reduced basis approximation and the effectiveness of the a posteriori error bounds.