1,721,014 research outputs found
On the Effect of Boundary Conditions on the Scalability of Schwarz Methods
No full textIt is well known that one-level Schwarz methods are not weakly scalable, if the number of subdomains increases and the whole domain Ω is fixed. However, the recent work [2], published in the field of implicit solvation models used in computational chemistry, has drawn attention to the opposite case in which the number of subdomains increases, but their size remains unchanged, and, as a result, the size of the whole domain Ω increases
Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems
No full textThis paper is concerned with a novel convergence analysis of the optimized Schwarz waveform relaxation method (OSWRM) for the solution of optimal control problems governed by periodic parabolic partial differential equations (PDEs). The new analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition. This leads to a precise characterization of the convergence factor of the method at the semidiscrete level. Using this characterization, the optimal transmission condition parameter is obtained at the semidiscrete level and its asymptotic behavior as the time discretization converges to zero is analyzed in detail
An Overlapping Waveform Relaxation Preconditioner for Economic Optimal Control Problems With State Constraints
No full textAs shown in [8], the semismooth Newton method lacks of convergence if the parameter is not sufficiently large. This is, however, in contrast with typical applications, where a sufficiently small is required [6, 8]. The goal of this paper is to tackle this problem by using a nonlinear preconditioning technique based on an overlapping optimized waveform-relaxation method (WRM) characterized by Robin transmission conditions [2, 3]
Insulinoma of presumed pamcreatic origin diagnosed in the liver and lymph node of a Chianina cow
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