查看更多>>摘要：This paper discusses the numerical algorithm and its convergence for solving the time dependent Maxwell-Dirac system with the perfect conductive boundary conditions under the Lorentz gauge. An alternating Crank-Nicolson Galerkin finite element method for solving the problem is presented. This algorithm preserves the conservation of the mass and energy of the system. The sharp error estimates for both the solution and the energy are derived. Numerical test studies are then carried out to confirm the theoretical results. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We investigate the two-dimensional (2-D) perfectly matched layer (PML) models reformulated from the 3-D PML model originally developed by Cohen and Monk in 1999. We propose the discontinuous Galerkin methods for solving both 2-D TMz and TEz models. We establish the proofs of the stability and error estimate for the proposed schemes. Finally, numerical results are presented to demonstrate the accuracy and performance of our method. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper presents a new technique based on a collocation method using cubic splines for second order elliptic equation with irregularities in one dimension and two dimensions. The differential equation is first collocated at the two smooth sub domains divided by the interface. We extend the sub domains from the interior of the domain and then the scheme at the interface is developed by patching them up. The scheme obtained gives the second order accurate solution at the interface as well as at the regular points. Second order accuracy for the approximations of the first order and the second order derivative of the solution can also be seen from the experiments performed. Numerical experiments for 2D problems also demonstrate the second order accuracy of the present scheme for the solution u and the derivatives u(x), u(xx) and the mixed derivative u(xy). The approach to derive the interface relations, established in this paper for elliptic interface problems, can be helpful to derive high order accurate numerical methods. Numerical tests exhibit the super convergent properties of the scheme. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
Bultheel, AdhemarCruz-Barroso, RuymanMendoza, Carlos Diaz
22页
查看更多>>摘要：In this paper we illustrate that paraorthogonality on the unit circle T is the counterpart to orthogonality on R when we are interested in the spectral properties. We characterize quasi-paraorthogonal polynomials on the unit circle as the analogues of the quasi orthogonal polynomials on R. We analyse the possibilities of preselecting some of its zeros, in order to build positive quadrature formulas with prefixed nodes and maximal domain of validity. These quadrature formulas on the unit circle are illustrated numerically. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
Krotz, JohannesSweeney, Matthew R.Gable, Carl W.Hyman, Jeffrey D....
20页
查看更多>>摘要：We present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high quality balanced mesh is produced. (C)2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We present a new class of neural networks for solving nonlinear complementarity problems (NCPs) based on some family of real-valued functions (denoted by ") that can be used to construct smooth perturbations of the level curve defined by phi(NR)(x, y) = 0, where phi(NR) is the natural residual function (also called the "min "function). We introduce two important subclasses of ", which deserve particular attention because of their significantly different theoretical and numerical properties. One of these subfamilies yields a smoothing function for phi(NR), while the other subfamily only yields a smoothing curve for phi(NR) (x, y) = 0. We also propose a simple framework for generating functions from these subclasses. Using the smoothing approach, we build two types of neural networks and provide sufficient conditions to guarantee asymptotic and exponential stability of equilibrium solutions. Finally, we present extensive numerical experiments to validate the theoretical results and to illustrate the difference in numerical performance of functions from the two subclasses. Numerical comparisons with existing neural networks for NCPs are also demonstrated. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Linear multiplicative programming (LMP) problems have many applications, although their solving can be difficult. To solve LMPs, we propose a convex approximation approach with a standard partition in intervals. First, a novel convex relaxation strategy is designed, which is used to obtain a convex relaxation problem, and provides a lower bound for LMPs. Then, through solving a sequence of convex relaxation programming problems, we can obtain an approximate optimal solution of LMPs. The main calculation of the algorithm focuses on solving these convex programming problems, which can be completed by a convex optimization software. Furthermore, the convergence and the complexity of the algorithm are discussed theoretically. Finally, numerical experiments show the effectiveness of the designed algorithm in terms of running time and the number of iterations. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：With the rapid development of digital currencies such as Bitcoin, it is difficult to extract the effective information from massive data and quantify the value of digital assets using current methods. As a key underlying technology, blockchain technology can no longer meet most of the needs of digital currency transactions. Based on this, the digital asset is taken as the research object and an analysis model for digital asset value is established with the deep learning technology in this study. Then, the authorization mechanism in the distributed position and orientation system (DPOS) algorithm is extracted and applied to the precise backward error tracking (PBET) algorithm based on the existing consensus algorithm in blockchain technology. Thus, a dynamic delegated practical byzantine fault tolerance (DDPBFT) algorithm that can be applied to the blockchain is proposed. Finally, a supervisable digital currency system is constructed based on the improved blockchain technology. After specific analysis, it is found that the analysis model for digital asset value based on the deep learning proposed in this study shows good stability and accuracy, and can help enterprises to analyze the value of digital assets. Compared with the existing consensus mechanism algorithms, the proposed DDPBFT algorithm shows better results in terms of throughput and delay. Finally, the supervisable digital currency model based on the improved blockchain technology can unite the public chains, alliance chains, and user wallets, and realize the traceability of transaction information. In short, the quantitative analysis of the value of digital assets has been realized and the supervision of digital currency transactions has been achieved by using the improved blockchain technology. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We propose unconditionally energy stable Runge-Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift- Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipation remains preserved for arbitrary time steps and spatial meshes. The method integrates a penalty free DG method for spatial discretization with a multi-stage algebraically stable RK method for temporal discretization by the energy quadratiztion (EQ) strategy. The resulting fully discrete DG method is proven to be unconditionally energy stable. By numerical tests on several benchmark problems we demonstrate the high order accuracy, energy stability, and simplicity of the proposed algorithm. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Cubature schemes, in this case for uniformly weighted integration over the unit disk, enable exact evaluation of numerical integrals of polynomials but have been explicitly constructed for only low or moderate degrees. In this paper, cubature formulae are discovered for a wider range of degrees by leveraging numerical optimization. These results include a degree-17 cubature scheme with fewer points than existing solutions and up to a degree-77 solution with 1021 cubature points. Optimization heuristics and patterns in the distributions of cubature points are discussed, which serve as vital guides in this work. For example, these heuristics leverage a connection to circle-packing configurations to facilitate the discovery of fully symmetric cubature schemes. (C)& nbsp;2022 The Authors. Published by Elsevier B.V.& nbsp; & nbsp;
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