Related papers: Simultaneous Reduced Basis Approximation of Parame…

In this article we apply reduced order techniques for the approximation of parametric eigenvalue problems. The effect of the choice of sampling points is investigated. Here we use the standard proper orthogonal decomposition technique to…

We present reduced basis approximations and rigorous a posteriori error bounds for the instationary Stokes equations. We shall discuss both a method based on the standard formulation as well as a method based on a penalty approach, which…

In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the…

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…

This work focuses on assessing the information-theoretic limits of scene parameter estimation in plenoptic imaging systems. A general framework to compute lower bounds on the parameter estimation error from noisy plenoptic observations is…

Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be…

In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems,…

We provide two new methods for computing lower bounds of eigenvalues of symmetric elliptic second-order differential operators with mixed boundary conditions of Dirichlet, Neumann, and Robin type. The methods generalize ideas of Weinstein's…

We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and…

This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…

In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal…

A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…

The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…

In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new…