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作者:A. Rezazadeh , M. Mahmoudi , M. Darehmiraki
来源:[J].Computational and Applied Mathematics, 2020, Vol.39 (24), pp.3432-3456
摘要:Abstract(#br)In this paper, we employ a reduced basis method for solving PDE constrained optimization problem governed by a fractional parabolic equation with the fractional derivative in time. The fractional derivative used in this paper is Caputo fractional derivative whos...
作者:R. Chakir , J.K. Hammond
来源:[J].Journal of Computational and Applied Mathematics(IF 0.989), 2018, Vol.337, pp.1-17
摘要:Abstract(#br)This work aims at investigating the use of reduced basis (RB) methods to diminish the cost of numerical simulation of elastoplasticity problems arising from geotechnics modeling, and involving parameter-dependent partial differential equations (PDEs). Computation tim...
作者:Yanlai Chen , Jiahua Jiang , Akil Narayan
来源:[J].Computers and Mathematics with Applications(IF 2.069), 2019, Vol.77 (7), pp.1963-1979
摘要:Abstract(#br)The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parameterizedpartial differential equations. It identifies a low-dimensional subspace for approximation of the parametric solution manifold that is embedded in high-dimensional space. A...
作者:Yanlai Chen , Jan S. Hesthaven , Yvon Maday ...
来源:[J].Computer Methods in Applied Mechanics and Engineering(IF 2.617), 2012, Vol.233-236, pp.92-108
摘要:Abstract(#br)We study nontrivial applications of the reduced basis method (RBM) for electromagnetic applications with an emphasis on scattering and the estimation of radar cross section (RCS). The method and several extensions are explained with two examples with different charac...
作者:Jiahua Jiang , Yanlai Chen , Akil Narayan
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.73 (2-3), pp.853-875
摘要:The reduced basis method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the offline portion of the algorithm is a greedy algorithm, requiring maximization of an error estimate over parameter sp...
作者:Mazen Ali , Kristina Steih , Karsten Urban
来源:[J].Advances in Computational Mathematics(IF 1.468), 2017, Vol.43 (2), pp.257-294
摘要:We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot (i.e., parameter-dependent) do not permit the sta...
作者:Giuseppe Pitton , Gianluigi Rozza
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.73 (1), pp.157-177
摘要:In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams....
作者:N. Dal Santo , S. Deparis , A. Manzoni ...
来源:[J].Computer Methods in Applied Mechanics and Engineering(IF 2.617), 2018, Vol.344
摘要:Abstract(#br)In this paper we propose a new, purely algebraic, Petrov–Galerkin reduced basis (RB) method to solve the parametrized Stokes equations, where parameters serve to identify the (variable) domain geometry. Our method is obtained as an algebraic least squares reduced basis...
作者:Stefano Pagani , Andrea Manzoni , Alfio Quarteroni
来源:[J].Computer Methods in Applied Mechanics and Engineering(IF 2.617), 2018, Vol.340, pp.530-558
摘要:... This poses significant challenges to reduced order modeling (ROM) techniques –such as the reduced basis method –traditionally employed when dealing with the repeated solution of parameter dependent differential equations. Indeed, the nonlinear nature of the problem, the...
作者:M. Fares , J.S. Hesthaven , Y. Maday ...
来源:[J].Journal of Computational Physics(IF 2.138), 2011, Vol.230 (14), pp.5532-5555
摘要:Abstract(#br)We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field ...

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