查看更多>>摘要：In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. While intrusive methods inherit certain advantages such as adaptivity and an improved accuracy, they suffer from two key issues. First, intrusive methods tend to show oscillations, especially at shock structures and second, standard intrusive methods can lose hyperbolicity. The aim of this work is to tackle these challenges with the help of two different strategies. First, we combine filters with the multi-element approach for the hyperbolicity-preserving stochastic Galerkin (hSG) scheme. While the limiter used in the hSG scheme ensures hyperbolicity, the filter as well as the multi-element ansatz mitigate oscillations. Second, we derive a multi-element approach for the intrusive polynomial moment (IPM) method. Even though the IPM method is inherently hyperbolic, it suffers from oscillations while requiring the solution of an optimization problem in every spatial cell and every time step. The proposed multi-element IPM method leads to a decoupling of the optimization problem in every multi-element. Thus, we are able to significantly decrease computational costs while improving parallelizability. Both proposed strategies are extended to adaptivity, allowing to adapt the number of basis functions in each multi-element to the smoothness of the solution. We finally evaluate and compare both approaches on various numerical examples such as a NACA airfoil and a nozzle test case for the two-dimensional Euler equations. In our numerical experiments, we observe the mitigation of spurious artifacts. Furthermore, using the multi-element ansatz for IPM significantly reduces computational costs. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We study efficient implicit methods to denoise low-field MR images using a nonlinear diffusion operator as a regularizer. This problem can be formulated as solving a nonlinear reaction-diffusion equation. After discretization, a lagged-diffusion approach is used which requires a linear system solve in every nonlinear iteration. The choice of diffusion model determines the denoising properties, but it also influences the conditioning of the linear systems. As a solution method, we use Conjugate Gradient (CG) in combination with a suitable preconditioner and deflation technique. We consider four different preconditioners in combination with subdomain deflation. We evaluate the methods for four commonly used denoising operators: standard Laplace operator, two Perona-Malik type operators, and the Total Variation (TV) operator. We show that a Discrete Cosine Transform (DCT) preconditioner works best for problems with a slowly varying diffusion coefficient, while Jacobi preconditioning with subdomain deflation works best for a strongly varying diffusion, as happens for the TV operator. This research is part of a larger effort that aims to provide low-cost MR imaging capabilities for low-resource settings. We have evaluated the algorithms on low-field MRI images using inexpensive commodity hardware. With a suitable preconditioner for the chosen diffusion model, we are able to limit the time to denoise three-dimensional images of more than 2 million pixels to less than 15 s, which is fast enough to be used in practice. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we consider multidimensional diffusion-reaction equations with time fractional partial derivatives of the Caputo type and orders of differentiation in (0, 1). The models are extensions of various well-known equations from mathematical physics, biology, and chemistry. In the present manuscript, we will impose initial-boundary data on a closed and bounded spatial multidimensional domain. Single-term and multi term fractional systems are considered in this work. In the first stage, we show that the fractional models possess energy-like functionals which are dissipated in L-2(Omega) with respect to time. The systems are investigated rigorously from the analytical point of view, and dissipative numerical models to approximate their solutions are proposed and rigorously analyzed. Our discretizations will make use of the uniform L1 approximation scheme to estimate the time-fractional derivatives, and the usual central difference operators to approximate the spatial Laplacian. To that end, various results of the literature will be crucial, including some useful discrete forms of Paley-Wiener inequalities. Some numerical examples are included to show the asymptotic behavior of the numerical methods and, ultimately, their dissipative character. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The supply chain network model is constructed in this study based on comparison of traditional supply chain and the modern supply chain so as to solve the poor communication effect, uncirculated information, and unbalanced supply and demand in enterprises. After three algorithms and three commodity predication models are compared, a model combining with the network neural commodity demand predication method and the particle swarm optimization (PSO) algorithm is used to comprehensively evaluate the predication effect and algorithm performance by using the supply chain data of the enterprises, coming up with an optimal model. Results of the study show that: on national warehouses and regional warehouses, the difference between the predicted value and the actual value of autoregressive integrated (AR) mixture density networks (MDN) (AR-MDN) is 15%, the average outlier is between 450 and 150, the score of root mean square error (RMSE) and mean absolute percentage error (MAPE) is 117.342 and 2.334, respectively. It indicates that the fitting trend, prediction accuracy, and stability of the model are better than those of the autoregressive integrated moving average model (ARIMA) and multilayer perceptron-long short term memory (MLP-LSTM) model. Regarding determination of the stochastic requirements, the average optimal solution of the improved PSO (IPSO) is 0.45, indicating that performance of the algorithm is significantly stronger than that of the PSO algorithm and the artificial bee colony (ABC) algorithm; the comprehensive evaluation score of the combination model for the IPSO algorithm and the AR-MDN commodity prediction model is 67.41 with the optimal effect. The supply chain network model constructed in this study can provide enterprises with a good commodity demand predication method and improve their ability to respond to risks in the supply chain. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Many classical synchronization problems such as the assembly line crew scheduling problem (ALCS), some data association problems or multisensor tracking problems can be formulated as finding intra-column rearrangements for a single matrix repre-senting costs, distances, similarities or time requirements. In this paper, we consider an extension of these problems to the case of multiple matrices, reflecting various possible instances (scenarios). To approximate optimal rearrangements, we introduce the Block Swapping Algorithm (BSA) and a further customization of it that we call the customized Block Swapping Algorithm (Cust BSA). A numerical study shows that the two algorithms we propose - in particular Cust BSA - yield high-quality solutions and also deal efficiently with high-dimensional set-ups. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper the problem of Synthetic Aperture Radar (SAR) and optical satellite images co-registration is considered. Because of the distinct natures of SAR and optical images, there exist huge radiometric and geometric differences between such images. As a result, the traditional registration approaches are no longer applicable in this case and it makes the registration process challenging. Mostly motivated by the crop field monitoring problem, we propose a new variational approach to the co-registration of SAR and optical images. The core idea of our approach is to involve into consideration a constrained optimization problem on the set of affine transformations for which the cost functional is the L-p-cross-correlation between sustainable parts of two fattened skeletons for the selectively smoothed SAR image and the luma component of an optical image, respectively. We discuss the consistency of the proposed statement of this problem, propose the scheme for its regularization, derive the corresponding optimality system, and describe in detail the algorithm for the practical implementation of co-registration procedure. To evaluate the performance of the proposed approach, we illustrate its crucial steps with the help of several numerical experiments and real satellite images. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The Arnoldi method is a commonly used technique for finding a few eigenpairs of large, sparse and nonsymmetric matrices. Recently, a new variant of Arnoldi method (NVRA) was proposed. In NVRA, the modified Ritz vector is used to take the place of the Ritz vector by solving a minimization problem. Moreover, it was shown that if the refined Arnoldi method converges, then the NVRA method also converges. The contribution of this work is as follows. First, we point out that the convergence theory of the NVRA method is incomplete. More precisely, the cosine of the angle between the refined Ritz vector and the Ritz vector may not be uniformly lower-bounded, and it can be arbitrarily close to zero in theory. Consequently, the modified Ritz vector may fail to converge even when the search subspace is good enough. A remedy to the convergence of the NVRA method is given. Second, we show that the linear system for solving the modified Ritz vector in the NVRA method will become more and more ill-conditioned as the refined Ritz vector converges. If the Ritz vector also tends to converge as the refined Ritz vector does so, the ill-conditioning of the linear system will have little influence on the convergence of the modified Ritz vector, and the modified Ritz vector can improve the Ritz vector substantially. Otherwise, the ill-conditioning may have significant influence on the convergence of the modified Ritz vector. Third, to fix the NVRA method, we propose an improved refined Arnoldi method that uses improved refined Ritz vector to take the place of the modified Ritz vector. Theoretical results indicate that the improved refined Ritz method is often better than the refined Ritz method. Numerical experiments illustrate the numerical behavior of the improved refined Ritz method, and demonstrate the effectiveness of our theoretical analysis. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The main purpose of this work is to study the numerical solution of a time fractional partial integro-differential equation of Volterra type, where the time derivative is defined in Caputo sense. Our method is a combination of the classical L1 scheme for temporal derivative, the general second order central difference approximation for spatial derivative and the repeated quadrature rule for integral part. The error analysis is carried out and it is shown that the approximate solution converges to the exact solution. Several examples are given in support of the theoretical findings. In addition, we have shown that the order of convergence is more high on any subdomain away from the origin compared to the entire domain. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Discontinuous Galerkin composite finite element methods (DGCFEM) are designed to tackle approximation problems on complicated domains. Partial differential equations posed on complicated domain are common when there are mesoscopic or local phenomena which need to be modelled at the same time as macroscopic phenomena. In this paper, an optical lattice will be used to illustrate the performance of the approximation algorithm for the ground state computation of a Gross-Pitaevskii equation, which is an eigenvalue problem with eigenvector nonlinearity. We will adapt the convergence results of Marcati and Maday 2018 to this particular class of discontinuous approximation spaces and benchmark the performance of the classic symmetric interior penalty hp-adaptive algorithm against the performance of the hp-DGCFEM. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We present a novel approach to the study of singular components for the family of shock induced copulas which is of great importance in many applications. We concentrate on three most known families of these copulas, Marshall (also called Marshall-Olkin), reflected maxmin (RMM for short), and maxmin. Although it is generally believed that "all"shock model copulas are singular, both RMM and maxmin contain nontrivial cases of members that are absolutely continuous. It seems that for the latter family this is observed for the first time. (C) 2021 Elsevier B.V. All rights reserved.
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