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Abstract: Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly in situations where the vehicle power demands are too high (during acceleration), the solution of the studied problem may not exist. To deal with such cases, we introduce a numerical method which seeks maximal suppliable power demands for which the solution exists. This corresponds to introducing a scaling parameter to reduce the demanded power. The interpretation of the scaling parameter is the amount of energy which is absent in the system, and which needs to be provided by external sources such as on-board batteries. We propose an efficient two-stage algorithm to find the optimal scaling parameter and the resulting potentials in the overhead wire network. We perform a comparison with a naive approach and present a real-world simulation in the part of the Pilsen city in the Czech Republic. These simulations are performed in the traffic micro-simulator SUMO, a popular open-source traffic simulation platform. PubDate: 2021-12-01

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Abstract: Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction, applying the dynamical approach using the Kelvin viscoelastic model and cohesive interface properties. The existence and convergence results rely on the semilinear computational scheme coming from the method of discretization in time, using several types of Rothe sequences, coupled with the extended finite element method (XFEM) for practical calculations. Numerical examples refer to cementitious samples reinforced by short steel fibres, with increasing number of applications as constructive parts in civil engineering. PubDate: 2021-12-01

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Abstract: Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on finding the inverse forms of van der Grinten projections I-IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations. Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy to implement and are applicable to the coordinate transformations. PubDate: 2021-12-01

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Abstract: The paper presents a discontinuous Galerkin method for solving partial integrodifferential equations arising from the European as well as American option pricing when the underlying asset follows an exponential variance gamma process. For practical purposes of numerical solving we introduce the modified option pricing problem resulting from a localization to a bounded domain and an approximation of small jumps, and we discuss the related error estimates. Then we employ a robust numerical procedure based on piecewise polynomial generally discontinuous approximations in the spatial domain. This technique enables a simple treatment of the American early exercise constraint by a direct encompassing it as an additional nonlinear source term to the governing equation. Special attention is paid to the proper discretization of non-local jump integral components, which is based on splitting integrals with respect to the domain according to the size of the jumps. Moreover, to preserve sparsity of resulting linear algebraic systems the pricing equation is integrated in the temporal variable by a semi-implicit Euler scheme. Finally, the numerical results demonstrate the capability of the numerical scheme presented within the reference benchmarks. PubDate: 2021-12-01

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Abstract: This article deals with the solvability of the boundary-value problem for the Navier-Stokes equations with a direction-dependent Navier type slip boundary condition in a bounded domain. Such problems arise when steady flows of fluids in domains with rough boundaries are approximated as flows in domains with smooth boundaries. It is proved by means of the Galerkin method that the boundary-value problem has a unique weak solution when the body force and the variability of the surface friction are sufficiently small compared to the viscosity and the surface friction. PubDate: 2021-11-30

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Abstract: We study the axisymmetric Navier-Stokes equations. In 2010, Loftus-Zhang used a refined test function and re-scaling scheme, and showed that $$\left {{\omega ^r}(x,t)} \right + \left {{\omega ^z}(r,t)} \right \leqslant {C \over {{r^{10}}}},\,\,\,\,\,0 < r \leqslant {1 \over 2}.$$ By employing the dimension reduction technique by Lei-Navas-Zhang, and analyzing ωr, ωz and ωθ/r on different hollow cylinders, we are able to improve it and obtain $$\left {{\omega ^r}(x,t)} \right + \left {{\omega ^z}(r,t)} \right \leqslant {{C\left {\ln \,r} \right } \over {{r^{17/2}}}},\,\,\,\,\,0 < r \leqslant {1 \over 2}.$$ PubDate: 2021-11-22

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Abstract: In this paper, we present a new iterative method for solving a linear system, whose coefficient matrix is an M-matrix. This method includes four parameters that are obtained by the accelerated overrelaxation (AOR) splitting and using the Taylor approximation. First, under some standard assumptions, we establish the convergence properties of the new method. Then, by minimizing the Frobenius norm of the iteration matrix, we find the optimal parameters. Meanwhile, numerical results on test examples show the efficiency of the new proposed method in contrast with the Hermitian and skew-Hermitian splitting (HSS), AOR methods and a modified version of the AOR (QAOR) iteration. PubDate: 2021-11-22

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Abstract: Distance metrics are at the core of many processing and machine learning algorithms. In many contexts, it is useful to compute the distance between data using multiple criteria. This naturally leads to consider vector-valued metrics, in which the distance is no longer a real positive number but a vector. In this paper, we propose a principled way to combine several metrics into either a scalar-valued or vector-valued metric. We illustrate our framework by reformulating the popular structural similarity (SSIM) index and a simple case of the Wasserstein distance used for optimal transport. PubDate: 2021-11-22

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Abstract: In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary condition. This boundary condition is given by a second order spatial differential operator imposed on the boundary. A generalized impedance boundary condition can be used to model corrosion and delimitation. The well-posedness for the direct problem is established where the Laplace transform is used to study the time dependent boundary value problem. The inverse impedance problem of determining the parameters from the Cauchy data is also studied provided the boundary of the subregion is known. The uniqueness of recovering the boundary parameters from the Neumann to Dirichlet mapping is proven. PubDate: 2021-11-16

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Abstract: A method for the detection of the initial stress tensor is proposed. The method is based on measuring distances between pairs of points located on the wall of underground opening in the excavation process. This methods is based on solving twelve auxiliary problems in the theory of elasticity with force boundary conditions, which is done using the least squares method. The optimal location of the pairs of points on the wall of underground openings is studied. The pairs must be located so that the condition number of the least square matrix has the minimal value, which guarantees a reliable estimation of initial stress tensor. PubDate: 2021-11-16

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Abstract: Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations Ax — x = b, where A ∈ ℝn×n is an M-matrix or strictly diagonally dominant matrix, b ∈ ℝn and x ∈ ℝn is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness of our methods. PubDate: 2021-11-11

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Abstract: We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface implicitly, which supports natural implementation of topology changes, such as merging and splitting, and makes the approach attractive for applications in material science. The main tool in the new scheme are convolution kernels developed in previous studies that approximate the given anisotropy in a nonlocal way. We provide a detailed report on the numerical properties of the proposed algorithm. PubDate: 2021-11-01

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Abstract: Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the proposed iterative methods. Then, we study upper bounds for the spectral radius of iteration matrices and give upper bounds for the extrapolation parameter of the methods. Moreover, the optimal parameters which minimize upper bounds of the spectral radius are obtained. Finally, several numerical examples are given to show the efficiency of the presented method. PubDate: 2021-10-25

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Abstract: We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter β which defines the size of the neighborhood of the central-path and of the parameter θ which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined and converges to the optimal solution of SDLS. Moreover, we obtain the currently best known iteration bound for the algorithm with a short-update method, namely, \({\cal O}(\sqrt n \log (n/\varepsilon))\) . Finally, we report some numerical results to illustrate the efficiency of our proposed algorithm. PubDate: 2021-10-20

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Abstract: In this paper, we consider an initial boundary value problem for the two-dimensional primitive equations of large scale oceanic dynamics. Assuming that the depth of the ocean is a positive constant, we establish rigorous a priori bounds of the solution to problem. With the aid of these a priori bounds, the continuous dependence of the solution on changes in the boundary terms is obtained. PubDate: 2021-10-20

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Abstract: We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value u0 ∈ H1(Ω)is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when u0 ∈ L2 (Ω) and the integral kernel in the nonlocal boundary condition is symmetric. PubDate: 2021-10-19

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Abstract: In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of m different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia method for establishing equalities and inequalities. We also give an extensive approach for seemingly unrelated regression models (SURMs) by applying the results obtained for SULMMs to SURMs. PubDate: 2021-10-18

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Abstract: We consider the boundary value problem $$\begin{array}{*{20}{c}} {u'''(t) = f(t,u(t),u'(t),u''(t)),}&{0 < t < 1,} \end{array}$$ $$\begin{array}{*{20}{c}} {u(0) = u'(0) = 0,}&{u(1) = \int_0^1 {g(s)u(s)\text{d}s,} } \end{array}$$ where f: [0, 1] × ℝ3 → ℝ+, g: [0, 1] → ℝ+ are continuous functions. The case when f = f (u(t)) was studied in 2018 by Guendouz et al. Using the fixed-point theory on cones they established the existence of positive solutions. Here, by the method developed by ourselves very recently, we establish the existence, uniqueness and positivity of the solution under easily verified conditions and propose an iterative method for finding the solution. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the iterative method. PubDate: 2021-10-01

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Abstract: In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions with regular Lagrange multipliers are derived for a penalized-regularized version. The performance of the overall approach is illustrated by numerical examples. PubDate: 2021-10-01