Reduced Basis Methods for the Solution of Parametrized PDEs in Repetitive and Complex Networks with Application to CFD
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This thesis addresses the development and implementation of efficient and parallel algorithms for the numerical simulation of Fluid-Structure Interaction (FSI) problems in hemodynamics. Indeed, hemodynamic conditions in large arteries are significantly aff ...
INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Diri ...
In this paper we discuss partial differential equations with multiple scales for which scale resolution are needed in some subregions, while a separation of scale and numerical homogenization is possible in the remaining part of the computational domain. D ...
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...
In this work we introduce a new two-level preconditioner for the efficient solution of large-scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, whi ...
In the strong scaling limit, the performance of conventional spatial domain decomposition techniques for the parallel solution of PDEs saturates. When sub-domains become small, halo-communication and other overheard come to dominate. A potential path beyon ...
The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to ...
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the ...
Eddy current dampers (ECD) can be used to introduce damping in rotordynamic applications. ECD5 are contactless in nature and can be made to introduce negligible drag force, thus being a perfect match for passive magnetic bearings such as permanent magnet b ...
In this paper we discuss partial differential equations with multiple scales for which scale resolution are needed in some subregions, while a separation of scale and numerical homogenization is possible in the remaining part of the computational domain. D ...