A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model

This theses deals with a parallel Cartesian method to solve elliptic problems with complex interfaces and its application to elliptic irregular domain problems in the framework of a tumor growth model. This method is based on a finite differences scheme and is second order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express the interface transmission conditions. The method is described and the details of its parallelization, performed with the PETSc library, are provided. Numerical validations of the method follow with comparisons to other related methods in literature. A numerical study of the parallelized method is also given. Then, the method is applied to solve elliptic irregular domain problems appearing in a three-dimensional continuous tumor growth model, the two-species Darcy model. The approach used in this application is based on the penalization of the interface transmission conditions, in order to impose homogeneous Neumann boundary conditions on the border of an irregular domain. The simulations of model are provided and they show the ability of the method to impose a good approximation of the considered boundary conditions.

Grantor dc:publisher

Politecnico di Torino

Year dc:date

2012

Author dc:creator

• CISTERNINO, MARCO

• problema ellittico con interfaccia
• metodo cartesiano
• schema al secondo ordine
• incognite sull'interfaccia
• metodo parallelo
• crescita tumorale
• metodo di penalizzazione
• problema ellittico in dominio irregolare
• condizioni al bordo di Neumann omogenee.
• elliptic interface problem
• Cartesian method
• second order scheme
• interface unknown
• parallel method
• tumor growth
• penalty method
• elliptic irregular domain problem
• homogeneous Neumann boundary conditions
• Settore MAT/08 - Analisi Numerica

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Creative commons
• license uri:http://creativecommons.org/licenses/by/3.0/it/

Language dc:language

ita, fre, eng

Identifier

10.6092/polito/porto/2497156

OAI identifier oai:identifier

oai:iris.polito.it:11583/2497156