The value of continuity: Refined isogeometric analysis and fast direct solvers

We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce . C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method "refined Isogeometric Analysis (rIGA)". To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing the Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between . p2 and . p3, with . p being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to . p2. In a . 2D mesh with four million elements and . p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a . 3D mesh with one million elements and . p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.

The principles of chemistry

vol. 2, part

The principles of chemistry.

Mode of access: Internet

Compressible flows on moving domains: Stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling

A novel stabilized formulation for 3D compressible viscous flows on moving domains is developed. New weak imposition of essential boundary conditions and sliding-interface formulations are also proposed in the context of moving-domain compressible flows. The new formulation is successfully tested on a set of examples spanning a wide range of Reynolds and Mach numbers showing its superior robustness. Experimental validation of the new formulation is also carried out with good success. In addition, the formulation is applied to simulate flow inside a gas turbine stage, illustrating its potential to support design of real engineering systems through high-fidelity aerodynamic analysis.This article is published as Xu, Fei, George Moutsanidis, David Kamensky, Ming-Chen Hsu, Muthuvel Murugan, Anindya Ghoshal, and Yuri Bazilevs. "Compressible flows on moving domains: Stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling." Computers & Fluids 158 (2017): 201-220. DOI: 10.1016/j.compfluid.2017.02.006.</p