Overlapping schwarz methods for isogeometric analysis

We construct and analyze an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis. The preconditioner is based on partitioning the domain of the problem into overlapping subdomains, solving local isogeometric problems on these subdomains, and solving an additional coarse isogeometric problem associated with the subdomain mesh. We develop an $h$-analysis of the preconditioner, showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and \u201eoverlap sizes\u201d for fixed polynomial degree $p$ and regularity $k$ of the basis functions. Numerical results in two- and three-dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters $h, p, k$, number of subdomains $N$, overlap size, and also jumps in the coefficients of the elliptic operator

Comparison of single- and multistage strategies during fenestrated-branched endovascular aortic repair of thoracoabdominal aortic aneurysms

Objective: The aim of this study was to compare outcomes of single or multistage approach during fenestrated-branched endovascular aortic repair (FB-EVAR) of extensive thoracoabdominal aortic aneurysms (TAAAs). Methods: We reviewed the clinical data of consecutive patients treated by FB-EVAR for extent I to III TAAAs in 24 centers (2006-2021). All patients received a single brand manufactured patient-specific or off-the-shelf fenestrated-branched stent grafts. Staging strategies included proximal thoracic aortic repair, minimally invasive segmental artery coil embolization, temporary aneurysm sac perfusion and combinations of these techniques. Endpoints were analyzed for elective repair in patients who had a single- or multistage approach before and after propensity score adjustment for baseline differences, including the composite 30-day/in-hospital mortality and/or permanent paraplegia, major adverse event, patient survival, and freedom from aortic-related mortality. Results: A total of 1947 patients (65% male; mean age, 71 ± 8 years) underwent FB-EVAR of 155 extent I (10%), 729 extent II (46%), and 713 extent III TAAAs (44%). A single-stage approach was used in 939 patients (48%) and a multistage approach in 1008 patients (52%). A multistage approach was more frequently used in patients undergoing elective compared with non-elective repair (55% vs 35%; P < .001). Staging strategies were proximal thoracic aortic repair in 743 patients (74%), temporary aneurysm sac perfusion in 128 (13%), minimally invasive segmental artery coil embolization in 10 (1%), and combinations in 127 (12%). Among patients undergoing elective repair (n = 1597), the composite endpoint of 30-day/in-hospital mortality and/or permanent paraplegia rate occurred in 14% of single-stage and 6% of multistage approach patients (P < .001). After adjustment with a propensity score, multistage approach was associated with lower rates of 30-day/in-hospital mortality and/or permanent paraplegia (odds ratio, 0.466; 95% confidence interval, 0.271-0.801; P = .006) and higher patient survival at 1 year (86.9±1.3% vs 79.6±1.7%) and 3 years (72.7±2.1% vs 64.2±2.3%; adjusted hazard ratio, 0.714; 95% confidence interval, 0.528-0.966; P = .029), compared with a single stage approach. Conclusions: Staging elective FB-EVAR of extent I to III TAAAs was associated with decreased risk of mortality and/or permanent paraplegia at 30 days or within hospital stay, and with higher patient survival at 1 and 3 years

Iterative ilu preconditioners for linear systems and eigenproblems

Iterative ILU factorizations are constructed, analyzed and applied as preconditioners to solve both linear systems and eigenproblems. The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications, which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes. We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations. The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems