This work presents a multi-physics model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of fundamental effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. The capillaries are considered as one-dimensional concentrated source with arbitrary configuration, possibly curved. This model describes the variation of flow rate and velocity as local differential formulation of mass and momentum conservation along the capillary axis. The second part of this work aims to find a new iterative strategy to solve the system arising from the finite element discretization, using a GMRES method. The iterative solver is accelerated by a block preconditioner based on the Schur complements of the pressure problems. Therefore, different preconditioners for the stand alone vessel, tissue and uncoupled problem are derived. Two options are considered to solve the residual system: an Incomplete LU factorization and an Algebraic Multigrid Method. The second approach required the use of a library, called SAMG, developed at the Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), which contains the Algebraic Multigrid solver used.
Questo lavoro presenta un modello multi-fisica per la microcircolazione che descrive l'interazione del plasma con i globuli rossi. Il modello tiene conto degli effetti fondamentali che caratterizzano la microcircolazione, come l'effetto Fahraeus-Lindqvist ed il plasma skimming. I capillari sono considerati come una sorgente monodimensionale concentrata sull'asse del vaso con configurazione arbitraria, possibilmente curva. Questo modello descrive la variazione di portata e velocità come formulazione differenziale locale della conservazione della massa e del momento lungo l'asse del capillare. La seconda parte di questo lavoro mira a trovare una nuova strategia per risolvere il sistema derivante dalla discretizzazione ad elementi finiti, utilizzando un metodo GMRES. Il risolutore iterativo viene accelerato da un precondizionatore a blocchi basato sul complemento di Schur del problema in pressione. Pertanto, vengono derivati diversi precondizionatori per il problema nel solo vaso, nel tessuto e per quello globale non accoppiato. Vengono considerate due opzioni per precondizionare i residui: una fattorizzazione LU incompleta ed un metodo Multigrid Algebrico. Il secondo approccio richiede l'uso di una libreria, chiamata SAMG, sviluppata presso il Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), che contiene i risolutori Multigrid Algebrici utilizzati.
Mixed finite element method and preconditioning for 3D-1D problems
GEROSA, FANNIE MARIA
2016/2017
Abstract
This work presents a multi-physics model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of fundamental effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. The capillaries are considered as one-dimensional concentrated source with arbitrary configuration, possibly curved. This model describes the variation of flow rate and velocity as local differential formulation of mass and momentum conservation along the capillary axis. The second part of this work aims to find a new iterative strategy to solve the system arising from the finite element discretization, using a GMRES method. The iterative solver is accelerated by a block preconditioner based on the Schur complements of the pressure problems. Therefore, different preconditioners for the stand alone vessel, tissue and uncoupled problem are derived. Two options are considered to solve the residual system: an Incomplete LU factorization and an Algebraic Multigrid Method. The second approach required the use of a library, called SAMG, developed at the Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), which contains the Algebraic Multigrid solver used.File | Dimensione | Formato | |
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https://hdl.handle.net/10589/137287