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Abstract. We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is unconditionally stable with respect to the time step size.

The Immersed Boundary Method (IBM) has been designed by Peskin for the modeling and the numerical approximation of fluid-structure interaction problems, where flexible structures are immersed in a fluid. In this approach, the Navier-Stokes equations are considered everywhere and the presence of the structure is taken into account by means of a source term which depends on the unknown position of the structure. These equations are coupled with the condition that the structure moves at the same velocity of the underlying fluid.Recently, a finite element version of the IBM has been developed, which offers interesting features for both the analysis of the problem under consideration and the robustness and flexibility of the numerical scheme. Initially, we considered structure and fluid with the same density, as it often happens when dealing with biological tissues. Here we study the case of a structure which can have a density higher than that of the fluid. The higher density of the structure is taken into account as an excess of Lagrangian mass located along the structure, and can be dealt with in a variational way in the finite element approach.The numerical procedure to compute the solution is based on a semi-implicit scheme. In fluid-structure simulations, nonimplicit schemes often produce instabilities when the density of the structure is close to that of the fluid. This is not the case for the IBM approach. In fact, we show that the scheme enjoys the same stability properties as in the case of equal densities.

In this paper we discuss the stability of some Stokes finite elements. In particular, we consider a modification of Hood-Taylor and Bercovier-Pironneau schemes which consists in adding piecewise constant functions to the pressure space. This enhancement, which had been already used in the literature, is driven by the goal of achieving an improved mass conservation at element level. The main result consists in proving the inf-sup condition for the enhanced spaces in a general setting and to present some numerical tests which confirm the stability properties. The improvement in the local mass conservation is shown in a forthcoming paper (Boffi et al. In: Papadrakakis, M., Onate, E., Schrefler, B. (eds.) Coupled Problems 2011. Computational Methods for Coupled Problems in Science and Engineering IV, Cimne, 2011) where the presented schemes are used for the solution of a fluid-structure interaction problem.

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Abstract. We present a novel mathematically faithful object oriented design for a general purpose isogeometric library and introduce a high quality open source implementation of it, igatools (http://code.google.com/p/igatools). The library uses advanced programming techniques and supports dimension independent programming. It includes support for manifolds and isogeometric elements of the h-div and h-curl type. To illustrate the flexibility and power of the library we present some example applications including surfaces, fluid and elasticity.

Interdependence between sperm concentration, motility, morphology, and the percentage of aneuploid sperm was explored to test whether oligoasthenoteratospermia (OAT) may have a multiple origin in idiopathic infertile males. A total of 174 men (age, 35.8 +/- 4.3 yr) with idiopathic infertility were studied. Seven patients had nonobstructive azoospermia, 55 had severe OAT, 30 had OAT, 27 had isolated alterations of motility, 45 had alterations of morphology and of motility, and 10 had isolated alterations of morphology. The sperm morphology was assessed with strict criteria. The percentage of aneuploid sperm was assessed with fluorescent in situ hybridization for chromosomes X, Y, 13, 15, 16, 17, 18, 21, and 22. Relationships between sperm features, and the relationship between sperm features and aneuploidies were analyzed with multivariate regression analysis. Statistical analysis did not find any significant relationship between the percentage of typical forms and sperm concentration or between morphology and motility. On the other hand, a positive and significant relationship was found between sperm concentration and motility. The percentage of aneuploid sperm was inversely and significantly related to the percentage of typical forms but not to motility and concentration. Sperm morphology is an independent characteristic with respect to concentration and motility, whereas it showed a significant inverse relationship with respect to the percentage of aneuploid sperm. This means that idiopathic OAT may occur by means of at least two independent pathways, the first affecting concentration and/or motility and the second affecting morphology.

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