Abstract-NERSC has partnered with 20 representative application teams to evaluate performance on the Xeon-Phi Knights Landing architecture and develop an application-optimization strategy for the greater NERSC workload on the recently installed Cori system. In this article, we present early case studies and summarized results from a subset of the 20 applications highlighting the impact of important architecture differences between the Xeon-Phi and traditional Xeon processors. We summarize the status of the applications and describe the greater optimization strategy that has formed.
Φ tr (x, 0) = Φ 0 (x) and W (x, 0) = W 0 (x) for a. a. x ∈ Ω (1.10)arising as a special case of (1.1) − (1.6) if the conductivity tensors satisfy M e = λ M i with a constant parameter λ > 0, thus allowing to eliminate Φ e as an independent variable. In a series of papers, 02) the authors investigated optimal control problems related to the dynamics (1.1) − (1.6) and (1.7) − (1.10) together with standard two-variable ionic models, namely the Rogers-McCulloch, FitzHugh-Nagumo and the linearized Aliev-Panfilov model (see Subsection 2.a) below). Using I e as control variable while I i = o, 03) and relying on a weak solution concept for the monodomain as well as for the bidomain system, the authors studied existence of minimizers and derived first-order necessary optimality conditions. 01) The bidomain model has been considered first in [ Tung 78 ] . A detailed introduction may be found e. g. in [ Sundnes/ Lines/Cai/Nielsen/Mardal/Tveito 06 ] , pp. 21 − 56. 02) [ Kunisch/Wagner 12 ] , [ Kunisch/Wagner 13a ] and [ Kunisch/Wagner 13b ] . 03) This setting is due to physiological reasons. 11) [ Simon 87 ] , p. 90, Corollary 8. 12) [ FitzHugh 61 ] , together with [ Nagumo/Arimoto/Yoshizawa 62 ] . 13) [ Rogers/McCulloch 94 ] . 14) This model is taken from [ Bourgault/Coudière/Pierre 09 ] , p. 480. Instead, the original model from [ Aliev/ Panfilov 96 ] contains a Riccati equation for the gating variable. * , (2.62)
This work addresses an optimal control approach for a model problem in cardiac electrophysiology. A rather complete treatment including the analysis of the model equations, derivation of the optimality system, description of its discretization and a numerical feasibility study in a parallel environment is provided.
Abstract.Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function f with a convex body K ⊂ R nm instead of the whole space R nm as the range of definition. In the present paper, we trace the consequences of an infinite extension of f outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the lower semicontinuous quasiconvex envelopeOur main result is a representation theorem for f (qc) which generalizes Dacorogna's well-known theorem on the representation of the quasiconvex envelope of a finite function. The paper will be completed by the calculation of f (qc) in two examples.Mathematics Subject Classification. 26B25, 26B40, 49J45, 52A20.
We provide an example of a convex infinite horizon problem with a linear objective functional where the different interpretations of the improper integral ∞ 0 f (t, x(t), u(t)) dt in either Lebesgue or Riemann sense lead to different but finite optimal values.
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