Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber

International audienceIt is well known in the literature that standard hierarchical matrix (H-matrix) based methods, although very efficient for asymptotically smooth kernels, are not optimal for oscillatory kernels. In a previous paper, we have shown that the method should nevertheless be used in the mechanical engineering community due to its still important data-compression rate and its straightforward implementation compared to H 2-matrix, or directional, approaches. Since in practice, not all materials are purely elastic it is important to be able to consider visco-elastic cases. In this context, we study the effect of the introduction of a complex wavenumber on the accuracy and efficiency of H-matrix based fast methods for solving dense linear systems arising from the discretization of the elastodynamic (and Helmholtz) Green's tensors. Interestingly, such configurations are also encountered in the context of the solution of transient purely elastic problems with the convolution quadrature method. Relying on the theory proposed in [12] for H 2-matrices for Helmholtz problems, we study the influence of the introduction of damping on the data compression rate of standard H-matrices. We propose an improvement of H-matrix based fast methods for this kind of configuration. This work is complementary to the recent work [12]. Here, in addition to addressing another physical problem, we consider standard H-matrices, derive a simple criterion to introduce additional compression and we perform extensive numerical experiments

Association Between Early Invasive Mechanical Ventilation and Day-60 Mortality in Acute Hypoxemic Respiratory Failure Related to Coronavirus Disease-2019 Pneumonia

Objectives:. About 5% of patients with coronavirus disease-2019 are admitted to the ICU for acute hypoxemic respiratory failure. Opinions differ on whether invasive mechanical ventilation should be used as first-line therapy over noninvasive oxygen support. The aim of the study was to assess the effect of early invasive mechanical ventilation in coronavirus disease-2019 with acute hypoxemic respiratory failure on day-60 mortality. Design:. Multicenter prospective French observational study. Setting:. Eleven ICUs of the French OutcomeRea network. Patients:. Coronavirus disease-2019 patients with acute hypoxemic respiratory failure (Pao2/Fio2 ≤ 300 mm Hg), without shock or neurologic failure on ICU admission, and not referred from another ICU or intermediate care unit were included. Intervention:. We compared day-60 mortality in patients who were on invasive mechanical ventilation within the first 2 calendar days of the ICU stay (early invasive mechanical ventilation group) and those who were not (nonearly invasive mechanical ventilation group). We used a Cox proportional-hazard model weighted by inverse probability of early invasive mechanical ventilation to determine the risk of death at day 60. Measurement and Main Results:. The 245 patients included had a median (interquartile range) age of 61 years (52–69 yr), a Simplified Acute Physiology Score II score of 34 mm Hg (26–44 mm Hg), and a Pao2/Fio2 of 121 mm Hg (90–174 mm Hg). The rates of ICU-acquired pneumonia, bacteremia, and the ICU length of stay were significantly higher in the early (n = 117 [48%]) than in the nonearly invasive mechanical ventilation group (n = 128 [52%]), p < 0.01. Day-60 mortality was 42.7% and 21.9% in the early and nonearly invasive mechanical ventilation groups, respectively. The weighted model showed that early invasive mechanical ventilation increased the risk for day-60 mortality (weighted hazard ratio =1.74; 95% CI, 1.07–2.83, p=0.03). Conclusions:. In ICU patients admitted with coronavirus disease-2019-induced acute hypoxemic respiratory failure, early invasive mechanical ventilation was associated with an increased risk of day-60 mortality. This result needs to be confirmed