000013473 001__ 13473
000013473 005__ 20161114165555.0
000013473 04107 $$aeng
000013473 046__ $$k2011-05-25
000013473 100__ $$aBecache, E.
000013473 24500 $$aA Reflection-Transmission Analysis of a Fictitious Domain Method  for Wave Scattering by a Sound-Hard Obstacle

000013473 24630 $$n3.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013473 260__ $$bNational Technical University of Athens, 2011
000013473 506__ $$arestricted
000013473 520__ $$2eng$$aWe consider the wave scattering by a sound-hard obstacle in a fluid. In previous works, we had proposed a method based on a first order in time mixed variational formulation allowing to use regular meshes for most of the computations. The boundary condition was weakly taken into account by the fictitious domain method. The resulting system was discretized with two families of finite elements compatible with mass lumping. Through some numerical examples we showed that the first family (which provides optimal rate of convergence in absence of boundary [1]; pure propagation) does not always take into account correctly the boundary condition. To overcome this problem, we had introduced a second family of finite elements for which we have obtained a convergence proof [2]. Inspired on this work we had extended this mixed finite element to the more complex case of elastodynamic equations with a free surface boundary condition [3]. Several numerical experiments as well as a numerical convergence analysis show that the numerical method computes a good approximate solution. The resulting numerical scheme has the following properties: allows rapid computations, leads to quasi-explicit schemes after time discretization, permits to control the CFL number and accounts complex geometries avoiding the staircase phenomena. In this study we present a plane wave reflection-transmission analysis of the method with both families of finite elements for the scalar case that confirms most of the previous results and provides the quantitative behavior of the numerical error with respect to the discretization parameters (in some particular situations). We consider several configurations where the geometry and the meshes present a periodicity in one direction. This allows to study the interaction of numerical plane waves with the obstacle and to compare them with the continuous case. Some ideas on the extension of this study to elastodynamics will be given. 

000013473 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013473 653__ $$a

000013473 7112_ $$aCOMPDYN 2011 - 3rd International Thematic Conference$$cIsland of Corfu (GR)$$d2011-05-25 / 2011-05-28$$gCOMPDYN2011
000013473 720__ $$aBecache, E.$$iRodriguez, J.$$iTsogka, Ch.
000013473 8560_ $$ffischerc@itam.cas.cz
000013473 8564_ $$s10639$$uhttps://invenio.itam.cas.cz/record/13473/files/159.pdf$$yOriginal version of the author's contribution as presented on CD, section: MS 32 Waves and Computation.
000013473 962__ $$r13401
000013473 980__ $$aPAPER