000013120 001__ 13120
000013120 005__ 20161114160328.0
000013120 04107 $$aeng
000013120 046__ $$k2009-06-22
000013120 100__ $$aBecache, E.
000013120 24500 $$aThe fictitious domain method and applications in wave propagation - part i

000013120 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013120 260__ $$bNational Technical University of Athens, 2009
000013120 506__ $$arestricted
000013120 520__ $$2eng$$aThis paper deals with the convergence analysis of the fictitious domain method used for taking into account the Neumann boundary condition on the surface of a crack (or more generally an object) in the context of acoustic and elastic wave propagation. For both types of waves we consider the first order in time formulation of the problem known as mixed velocitypressure formulation for acoustics and velocity-stress formulation for elastodynamics. The convergence analysis for the discrete problem depends on the mixed finite elements used. We consider here two families of mixed finite elements that are compatible with mass lumping. When using the first one which is less expensive and corresponds to the choice made in a previous paper, it is shown that the fictitious domain method does not always converge. For the second one a theoretical convergence analysis was carried out in [7] for the acoustic case. Here we present numerical results that illustrate the convergence of the method both for acoustic and elastic waves (for more details see also [6]).

000013120 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013120 653__ $$afictitious domain method, mixed finite elements, cracks, elastic waves, acoustic waves Abstract. This paper deals with the convergence analysis of the fictitious domain method used for taking into account the Neumann boundary condition on the surface of a crack (or more generally an object) in the context of acoustic and elastic wave propagation. For both types of waves we consider the first order in time formulation of the problem known as mixed velocitypressure formulation for acoustics and velocity-stress formulation for elastodynamics. The convergence analysis for the discrete problem depends on the mixed finite elements used. We consider here two families of mixed finite elements that are compatible with mass lumping. When using the first one which is less expensive and corresponds to the choice made in a previous paper, it is shown that the fictitious domain method does not always converge. For the second one a theoretical convergence analysis was carried out in [7] for the acoustic case. Here we present numerical results that illustrate the convergence of the method both for acoustic and elastic waves (for more details see also [6]).

000013120 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013120 720__ $$aBecache, E.$$iRodriguez, J.$$iTsogka, C.
000013120 8560_ $$ffischerc@itam.cas.cz
000013120 8564_ $$s724026$$uhttps://invenio.itam.cas.cz/record/13120/files/CD160.pdf$$yOriginal version of the author's contribution as presented on CD, section: Computational methods for waves - ii (MS).
000013120 962__ $$r13074
000013120 980__ $$aPAPER