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In this Note we derive a posteriori error estimates for a multiscale method, the so-called heterogeneous multiscale method, applied to elliptic homogenization problems. The multiscale method is based on a macro-to-micro formulation. The macroscopic method ...
In this work we apply reduced basis methods to parametrized airfoils configurations to study inviscid potential, thermal and viscous flows. Parametrization includes geometry, ground effect and airfoils interaction. ...
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces. ...
This work deals with the development and application of reduction strategies for real-time and many query problems arising in fluid dynamics, such as shape optimization, shape registration (reconstruction), and shape parametrization. The proposed strategy ...
A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh re ...
A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined w ...
In previous work, we defined the category of functors F-quad, associated to F-2-vector spaces equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category F-quad, named the mixed functors. We give the c ...
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at diff ...
In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a low dimensional s ...
Reduced basis approximations for geometrically parametrized advection- diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized ...
