Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization
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The Navier–Stokes equations play a key role in the modeling of blood flows in the vascular sys- tem. The cost for solving the 3D linear system obtained by Finite Element (FE) discretization of the equations, using tetrahedral unstructured meshes and time a ...
In this work we provide a convergence analysis for the quasi-optimal version of the Stochastic Sparse Grid Collocation method we had presented in our previous work \On the optimal polynomial approximation of Stochastic PDEs by Galerkin and Collocation meth ...
Obtaining a reliable gradient estimate for an unknown function when given only its discrete measurements is a common problem in many engineering disciplines. While there are many approaches to obtaining an estimate of a gradient, obtaining lower and upper ...
We discuss in this thesis the numerical approximation of fluid-structure interaction (FSI) problems with a particular concern (albeit not exclusive) on hemodynamics applications. Firstly, we model the blood as an incompressible fluid and the artery wall as ...
This paper examines the computational complexity certification of the fast gradient method for the solution of the dual of a parametric con- vex program. To this end, a lower iteration bound is derived such that for all parameters from a compact set a solu ...
The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a d-dimensional hypercube. Linear systems with tensor product struc ...
Society for Industrial and Applied Mathematics2009
We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method. In our analysis we deal with unstruc ...
The purpose of this thesis is to investigate methods for the solution of multiscale problems both from the mathematical and numerical point of view, with a particular concern on applications to flows through heterogeneous porous media. After an overview of ...
We consider a Galerkin Finite Element approximation of the Stokes–Darcy problem which models the coupling between surface and groundwater flows. Then we propose an iterative subdomain method for its solution, inspired to the domain decomposition theory. Th ...
We are interested in the numerical solution of the unsteady Navier-Stokes equations on large scale parallel architectures. We consider efficient preconditioners, such as the Pressure Convection-Diffusion (PCD), the Yosida preconditioner, the SIMPLE precond ...