A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators
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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 ...
We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...
Building simulation requires a large number of uncertain inputs and parameters. These include quantities that may be known with reasonable confidence, like the thermal properties of materials and building dimensions, but also inputs whose correct values ca ...
In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in affinely parametrized geometries, focusing on the role played by the Brezzi's and Babuska's stability constants. The crucial ...
Models of vegetation dynamics that are designed for application at spatial scales larger than individual forest gaps suffer from several limitations. Typically, either a population average approximation is used that results in unrealistic tree allometry an ...
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are o ...
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 ...
This thesis is concerned with the development, analysis and implementation of efficient reduced order models (ROMs) for the simulation and optimization of parametrized partial differential equations (PDEs). Indeed, since the high-fidelity approximation of ...
[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 ...
Rocket and gas turbine combustion dynamics involves a confluence of diverse physics and interaction across a number of system components. Any comprehensive, self-consistent numerical model is burdened by a very large computational mesh, stiff unsteady proc ...
American Institute of Aeronautics and Astronautics2014