Global optimization of multilevel electricity market models including network design and graph partitioning

We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal network expansion and the optimal zonal configuration of zonal pricing electricity markets, which is an extension of the model discussed in Grimm et al. (2019) that does not include a network design problem. The two classical discrete optimization problems of network design and graph partitioning together with nonlinearities due to economic modeling yield extremely challenging mixed-integer nonlinear multilevel models for which we develop two problem-tailored solution techniques. The first approach relies on an equivalent bilevel formulation and a standard KKT transformation thereof including novel primal-dual bound tightening techniques, whereas the second is a tailored generalized Benders decomposition. For the latter, we strengthen the Benders cuts of Grimm et al. (2019) by using the structure of the newly introduced network design subproblem. We prove for both methods that they yield global optimal solutions. Afterward, we compare the approaches in a numerical study and show that the tailored Benders approach clearly outperforms the standard KKT transformation. Finally, we present a case study that illustrates the economic effects that are captured in our model.     

Application of multilevel analysis in animal sciences

Multilevel modeling is considerably useful way to analyze hierarchical data sets. The main purpose of this paper is to apply multilevel analysis in animal science and also show that this modeling technique is appropriate to analyze this kind of data. Thus multilevel modeling technique is used to analyze the milk yield data which has hierarchical structures, sires nested within cows. As a result of the analysis done in this paper, it is obvious that multilevel modeling is needed to use for analyzing this data. This illustrates that it is a convenient way to use multilevel analysis for the data which obtained from animals when the data have hierarchies.     

A unified framework for the construction of various algebraic multilevel preconditioning methods

1.IntroductionThediscretizationofmanysecondorderselfadjointellipticboundaryvalueproblemsbythefiniteelementmethodleadstolargesparsesystemsoflinearequationswithsymmetricpositivedefinite(SPD)coefficientmatrices.Fortheselinearsystems,algebraicmultilevelp...     

Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains

In this paper, we study the order reduced finite element method for the fourth order eigenvalue problems on multi-connected planar domains. Particularly, we take the biharmonic and the Helmholtz transmission eigenvalue problems as model problems, present for each an equivalent order reduced formulation and a corresponding stable discretization scheme, and present rigorous theoretical analysis. The schemes are readily fit for multilevel correction algorithms with optimal computational costs. Numerical experiments are given for verifications.     

Parallel multilevel solvers for the cardiac electro-mechanical coupling

We develop a parallel solver for the cardiac electro-mechanical coupling. The electric model consists of two non-linear parabolic partial differential equations (PDEs), the so-called Bidomain model, which describes the spread of the electric impulse in the heart muscle. The two PDEs are coupled with a non-linear elastic model, where the myocardium is considered as a nearly-incompressible transversely isotropic hyperelastic material. The discretization of the whole electro-mechanical model is performed by Q1 finite elements in space and a semi-implicit finite difference scheme in time. This approximation strategy yields at each time step the solution of a large scale ill-conditioned linear system deriving from the discretization of the Bidomain model and a non-linear system deriving from the discretization of the finite elasticity model. The parallel solver developed consists of solving the linear system with the Conjugate Gradient method, preconditioned by a Multilevel Schwarz preconditioner, and the non-linear system with a Newton–Krylov-Algebraic Multigrid solver. Three-dimensional parallel numerical tests on a Linux cluster show that the parallel solver proposed is scalable and robust with respect to the domain deformations induced by the cardiac contraction.     

M/G/1/MLPS compared to M/G/1/PS

Multilevel processor sharing scheduling disciplines have recently been resurrected in papers that focus on the differentiation between short and long TCP flows in the Internet. We prove that, for M/G/1 queues, such disciplines are better than the processor sharing discipline with respect to the mean delay whenever the hazard rate of the service time distribution is decreasing.     

MULTILEVEL AUGMENTATION METHODS FOR SOLVING OPERATOR EQUATIONS

We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstra     

Giga-bit optical receiver for plastic optical fibre

An optical receiver with high sensitivity and linearity specially designed for Giga-bit communications over small-bandwidth high-attenuation multimode plastic optical fiber is presented. An automatic gain control transimpedance amplifier and linear post amplifiers are used to maintain a good performance with multilevel modulation. Using multilevel signaling and large-diameter integrated photodiodes make the presented optical receiver suitable for large core plastic optical fiber. For a wavelength of 675 nm, a sensitivity of −26.3 dB m (BER = 10⁻⁹) at 500 Mb/s is presented by a binary signal. A data rate of 1 Gb/s and a sensitivity of −19.8 dB m (BER = 10⁻⁹) are achieved with four-level pulse amplitude modulation.     

Upper bound of the constant in the strengthened C.B.S. inequality for FEM 2D elasticity equations

The basic theory of the strengthened Cauchy–Buniakowskii–Schwarz (C.B.S.) inequality is the main tool in the convergence analysis of the recently proposed algebraic multilevel iterative methods. An upper bound of the constant γ in the strengthened C.B.S. inequality for the case of the finite element solution of 2D elasticity problems is obtained. It is assumed that linear triangle finite elements are used, the initial mesh consisting of right isosceles triangles and the mesh refinement procedure being uniform. For the resulting linear algebraic systems we have proved that γ²<0.75 uniformly on the mesh parameter and on Poisson's ratio ν ? (0, 1/2). Furthermore, the presented numerical tests show that the same relation holds for arbitrary initial right triangulations, even in the case of degeneracy of triangles. The theoretical results obtained are practically important for successful implementation of the finite element method to large-scale modeling of complicated structures. They allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real–life elasticity problems.     

Aircraft noise annoyance modeling: Consideration of noise sensitivity and of different annoying acoustical characteristics

Noise annoyance due to aircraft flyover noise was assessed under laboratory conditions. The main objectives of the study were: (i) to identify influential acoustical features of noise annoyance, (ii) to propose noise indices to characterize these acoustical features and (iii) to enhance annoyance models including influential acoustical and non-acoustical variables. Therefore, a verbalization task was performed by the participants of the experiment to collect their whole impression concerning the aircraft flyover noises for which they rated annoyance. This verbalization task highlights that noise annoyance was influenced by three main acoustical features: (i) the spectral content, (ii) the temporal variation and (iii) the perceived sound intensity. Four combinations of noise indices were used to propose multilevel annoyance models, in combination with the individual noise sensitivity. Noise sensitivity was found to highly contribute to annoyance models and should therefore be considered in future studies dealing with noise annoyance due to aircraft noise. Different combinations of noise indices coupled with noise sensitivity were found to be promising for future studies that aim to enhance current annoyance models.