A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems

Detrimental hemodynamic and inflammatory effects of microparticles originating from septic rats

Objective: Microparticles (MPs) are membrane vesicles with procoagulant and proinflammatory properties released during cell activation and might be potentially involved in the pathophysiology of septic shock. This study was designed to assess the effects of MPs from septic origin on the systemic hemodynamics as well as on the inflammatory, oxidative, and nitrosative stresses.Design: A prospective, randomized, controlled experimental study with repeated measurements. Setting: Investigational animal laboratory. Subjects: Forty healthy rats were randomly allocated to three groups: 10 animals inoculated with MPs isolated from control rats (cMPs), 15 animals inoculated with MPs isolated from sham rats (shMPs), and 15 animals inoculated with MPs isolated from rats with peritonitis (sMPs). Interventions: Rats were anesthetized, mechanically ventilated, and infused with the same amount of cMPs, shMPs, or sMPs. We measured the heart rate, mean arterial pressure, carotid artery, and portal vein blood flows. Hemodynamic parameters were recorded during 7 hours, and then animals were killed. Aorta and heart were harvested for further in vitro tissue analyses. Measurements and Main Results: 1) The cellular origin (phenotype) but not the circulating concentration of MPs was different in septic rats, characterized by a significant increase in leukocyte-derived MPs. 2) sMPs but not cMPs or shMPs decreased mean arterial pressure without any effect on carotid artery and portal vein blood flows. 3) Rats inoculated with sMPs exhibited an increase in superoxide ion production and nuclear factor kappa B activity, overexpression of inducible nitric oxide synthase with subsequent nitric oxide overproduction and decrease in endothelial nitric oxide synthase activation. Conclusions: Rats with sepsis induced by peritonitis exhibited a specific phenotype of MPs. Inoculation of sMPs in healthy rats reproduced hemodynamic, septic inflammatory patterns, associated with oxidative and nitrosative stresses

Effects of hydrogen sulfide on hemodynamics, inflammatory response and oxidative stress during resuscitated hemorrhagic shock in rats

Introduction Hydrogen sulfide (H2S) has been shown to improve survival in rodent models of lethal hemorrhage. Conversely, other authors have reported that inhibition of endogenous H2S production improves hemodynamics and reduces organ injury after hemorrhagic shock. Since all of these data originate from unresuscitated models and/or the use of a pre-treatment design, we therefore tested the hypothesis that the H2S donor, sodium hydrosulfide (NaHS), may improve hemodynamics in resuscitated hemorrhagic shock and attenuate oxidative and nitrosative stresses. Methods Thirty-two rats were mechanically ventilated and instrumented to measure mean arterial pressure (MAP) and carotid blood flow (CBF). Animals were bled during 60 minutes in order to maintain MAP at 40 ± 2 mm Hg. Ten minutes prior to retransfusion of shed blood, rats randomly received either an intravenous bolus of NaHS (0.2 mg/kg) or vehicle (0.9% NaCl). At the end of the experiment (T = 300 minutes), blood, aorta and heart were harvested for Western blot (inductible Nitric Oxyde Synthase (iNOS), Nuclear factor-κB (NF-κB), phosphorylated Inhibitor κB (P-IκB), Inter-Cellular Adhesion Molecule (I-CAM), Heme oxygenase 1(HO-1), Heme oxygenase 2(HO-2), as well as nuclear respiratory factor 2 (Nrf2)). Nitric oxide (NO) and superoxide anion (O2 -) were also measured by electron paramagnetic resonance. Results At the end of the experiment, control rats exhibited a decrease in MAP which was attenuated by NaHS (65 ± 32 versus 101 ± 17 mmHg, P < 0.05). CBF was better maintained in NaHS-treated rats (1.9 ± 1.6 versus 4.4 ± 1.9 ml/minute P < 0.05). NaHS significantly limited shock-induced metabolic acidosis. NaHS also prevented iNOS expression and NO production in the heart and aorta while significantly reducing NF-kB, P-IκB and I-CAM in the aorta. Compared to the control group, NaHS significantly increased Nrf2, HO-1 and HO-2 and limited O2 - release in both aorta and heart (P < 0.05). Conclusions NaHS is protective against the effects of ischemia reperfusion induced by controlled hemorrhage in rats. NaHS also improves hemodynamics in the early resuscitation phase after hemorrhagic shock, most likely as a result of attenuated oxidative stress. The use of NaHS hence appears promising in limiting the consequences of ischemia reperfusion (IR)

A method of finite element tearing and interconnecting for the Helmholtz problem

International audienc

A non Overlapping Domain Decomposition Method for the Exterior Helmholtz Problem

In this paper, we first show that the domain decomposition methods that are usually efficient for solving elliptic problems typically fail when applied to acoustics problems.Next, we present an alternative domain decomposition algorithm that is better suited for the exterior Helmholtz problem. We describe it in a formalism that can use either one or two Lagrange multiplier fields for solving the corresponding interface problem by a Krylov method. In order to improve convergence and ensure scalability with respect the number of subdomains, we propose two complementary preconditioning techniques. The first preconditioner is based on a spectral analysis of the resulting interface operator and targets the high frequency components of the error. The second preconditioner is based on a coarsening technique, employs plane waves, and addresses the low frequency components of the error. Finally, we show numerically that, using both preconditioners, the convergence rate of the proposed domain decomposition method is quasi independent of the number of elements in the mesh, the number of subdomains, and depends only weakly on the wavenumber, which makes this method uniquely suitable for solving large-scale high frequency exterior acoustics problems

Parallel computing for electromagnetism at ONERA

Communication to : 11th annual review of progress in applied computational electromagnetics, Naval postgraduate school, Monterey, CA (USA), March 20-25, 1995SIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 22419, issue : a.1995 n.113 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc