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In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent. The RBHM is applied to Stokes equations in domains wh ...
The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned so ...
The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized. State variables are solutions ...
A lumped parameter, state space model for a tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. I ...
The objective of this work is to develop a numerical framework to perform rapid and reliable simulations for solving parametric problems in domains represented by networks and to extend the classical reduced basis method. Aimed at this scope, we propose tw ...
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
In this work we consider quasi-optimal versions of the Stochastic Galerkin Method for solving linear elliptic PDEs with stochastic coeffcients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solu ...
We present a new fully first-order strongly hyperbolic representation of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyp ...
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by mu ...
The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of num ...