We present a time-parallelization method that enables to accelerate the computation of quantum optimal control algorithms. We show that this approach is approximately fully efficient when based on a gradient method as optimization solver: the computational time is approximately divided by the number of available processors. The control of spin systems, molecular orientation and BoseEinstein condensates are used as illustrative examples to highlight the wide range of application of this numerical scheme.
We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of classical impedance boundary conditions, as well as the case of transmission impedance conditions wherein the impedances are certain coercive operators. The latter type of problems is instrumental in the speed up of the convergence of Domain Decomposition Methods for Helmholtz problems. Our regularized formulations use as unknowns the Dirichlet traces of the solution on the boundary of the domain. Taking advantage of the increased regularity of the unknowns in our formulations, we show through a variety of numerical results that a graded-mesh based Nyström discretization of these regularized formulations leads to efficient and accurate solutions of interior and exterior Helmholtz problems with impedance boundary conditions.
Abstract. This work is motivated by the monitoring of conductive clogging deposits in steam generator at the level of support plates. One would like to use monoaxial coils measurements to obtain estimates on the clogging volume. We propose a 3D shape optimization technique based on simplified parametrization of the geometry adapted to the measurement nature and resolution. The direct problem is modeled by the eddy current approximation of time-harmonic Maxwell's equations in the low frequency regime. A potential formulation is adopted in order to easily handle the complex topology of the industrial problem setting. We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each coil vertical position which is excessively time and memory consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a fixed and invariant triangulation. Numerical experiments are presented to illustrate the convergence and the efficiency of the method.
Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the flow patterns better, and estimate reservoir petrophysical properties such as porosity and permeability. This study introduces multifractals as descriptors for rock samples' heterogeneity at the pore scale. We analyzed twenty rock samples from sandstone and carbonate reservoirs using their 3D X-ray micro-computed tomography images. In addition, we simulated porosity and permeability properties and examined their correlation with multifractal parameters. The results show that the capacity dimension D 0 and the information dimension D 1 correlate with porosity and permeability simulated from images, respectively. Finally, we calculated several multifractal parameters such as the width of the spectrum, the asymmetry degree of the spectrum in the horizontal direction and the value of the vertical difference between the two branches of the spectrum. Results illustrate the ability of multifractal parameters to classify groups of rock samples according to their degree of heterogeneity.INDEX TERMS Heterogeneity, micro computed tomography, multifractals.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.