Adaptive reduced basis finite element heterogeneous multiscale method
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In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on n is an element of N a priori known, separated microscopic length scales, are considered. The convergence of multileve ...
Frequently, we use the Moore-Penrose pseudoinverse (MPP) even in cases when we do not require all of its defining properties. But if the running time and the storage size are critical, we can do better. By discarding some constraints needed for the MPP, we ...
The goal of this thesis is to study an anisotropic adaptive algorithm for transonic compressible viscous flow around an airwing. A convection-diffusion model problem is considered, an anisotropic a posteriori error estimator for the H1 semi-norm of the err ...
[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 ...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the "reduced basis". The purpose of th ...
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 ...
Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods, in scientic computing may become crucial in applications of increasing complexity. In this paper we review the reduced basis method (built upon a high-delity "truth" f ...
We introduce an a posteriori modeling error estimator for the effective computation of electric potential propagation in the heart. Starting from the Bidomain problem and an extended formulation of the simplified Monodomain system, we build a hybrid model, ...
We propose the reduced basis method for the solution of parametrized optimal control problems described by parabolic partial differential equations in the unconstrained case. The method, which is based on an off-line–on-line decomposition procedure, allows ...
We present a fast algorithm for image restoration in the presence of Poisson noise. Our approach is based on (1) the minimization of an unbiased estimate of the MSE for Poisson noise, (2) a linear parametrization of the denoising process and (3) the preser ...