MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems
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This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...
In this paper we present an a posteriori error analysis for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. Unlike standard finite element methods, our discretization scheme relies on macro- and microfini ...
We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the paramete ...
We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the paramete ...
We propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline-online decomposition when the problem is solved for many different parametric config ...
We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over Q to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of Q. The proof is based ...
An adaptive reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is proposed for elliptic problems with multiple scales. The multiscale method is based on the RB-FE-HMM introduced in [A. Abdulle, Y. Bai, Reduced basis finite element het ...
Integral observers are useful tools for estimating the plant states in the presence of non-vanishing disturbances resulting from plant-model mismatch and exogenous disturbances. It is well known that these observers can eliminate bias in all states, given ...
Saddlepoint techniques have been used successfully in many applications, owing to the high accuracy with which they can approximate intractable densities and tail probabilities. This article concerns their use for the estimation of high-order integer-value ...
[B. Fares et al., J. Comput. Phys., 230 (2011), pp. 5532-5555], a reduced basis method (RBM) for the electric field integral equation (EFIE) using the boundary element method (BEM) is developed, based on a simplified a posteriori error estimator for the gr ...