查看更多>>摘要：We developed and analyzed the multiblock mortar expanded mixed method for second order parabolic partial differential equations. This is a domain decomposition method in which the computational domain is expressed as the union of non-overlapping subdomains separated by interfaces. An auxiliary variable is introduced on the interface which represents the pressure and serves as Dirichlet boundary condition for local subdomain problems. The interface variable also plays the part of Lagrange multiplier to enforce flux matching condition on the interfaces. We explored the expanded mixed method to discretize each subdomain. We propose the semi-discrete formulation and address the solvability of the discrete problem. The optimal order convergence is provided for the continuous time case. We also investigate the fully discrete formulation and derived corresponding error estimates. The numerical experiments are conducted to demonstrate the theory developed in the paper.(c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Vibrations of structures subjected to concentrated point loads have many applications in mechanical engineering. Experiments are expensive and numerical methods are often used for simulations. In this paper, we consider the plate vibration with nonlinear dependence on the eigen-parameter. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function. The Bogner-Fox-Schmit element is used for discretization and the spectral indicator method is employed to compute the eigenvalues. The convergence is proved using the abstract approximation theory of Karma (1996a; 1996b). Numerical examples are presented for validations. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Stability has been an elusive issue for high-order time integration of two fluids coupled across an interface. Iteration between fluid domains can be used to enforce stability, but then there can be time step restrictions for the iterations to converge. The design of methods is complicated by additional properties like conservation of fluxes between fluids and multirate time stepping that are needed for applications. We propose and investigate an iterative approach that has no time step restriction to achieve a stable, multirate, flux-conservative and high-order accurate method for the fluid-fluid problem. Computational examples also illustrate a clear advantage for computing with large time steps, compared to another recent method.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we present a unified finite difference framework to efficiently compute band structures of three dimensional linear non-dispersive isotropic photonic crystals with any of 14 Bravais lattice structures to a reasonable accuracy. Specifically, we redefine a suitable orthogonal coordinate system, and meticulously reformulate the Bloch condition for oblique Bravais lattices, and clearly identify the hierarchical companion matrix structure of the resulting discretized partial derivative operators. As a result, eigen-decompositions of discretized partial derivative operators and notably the discretized double-curl operator of any size, become trivial, and more importantly, the nullspace free method for the Maxwell's equations holds naturally in all 14 Bravais lattices. Thus, the great difficulty arising from high multiplicity of zero eigenvalues has been completely overcome. On the basis of these results, we perform calculations of band structures of several typical photonic crystals to demonstrate the efficiency and accuracy of our algorithm.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Accurate spatio-temporal traffic data is crucial to intelligent transportation systems. Missing traffic data is an important problem to solve. Low-rank matrix completion provides an effective way to find the missing data. The completion aims to obtain a low-rank matrix that can approximate the known entries as far as possible. Meanwhile, some linear constraint marginal information of the matrix can also be observed in the real application. In this paper, we utilize such marginal information to largely improve the performance of common matrix completion algorithms and propose an alternating direction method of multipliers (ADMM) and conjugate gradient descent method (CGD) based SoftImpute alternative least square (ALS) algorithm. We analyze their convergence rates and prove that the model can always converge to a first-order stationary point. We also utilize ADMM and CGD to largely accelerate the subproblem and make its complexity of each iteration at the same level as the popular SoftImpute-ALS matrix completion algorithm. Furthermore, this algorithm can be used in distributed computation, suitable for large-scale problems. In the numerical experiments, we demonstrate its outstanding matrix completion performance and high speed in several traffic matrix datasets. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A concordance measure is often a better way to model dependence than Pearson's correlation coefficient since it is invariant with respect to monotone increasing transformations of the random variables. In this paper, we focus on the relationships between Gini's gamma and Spearman's footrule. We establish the exact region determined by them. We also present copulas where the bounds of the region are attained. We introduce the concordance similarity measure and compute it for all pairs of (weak) concordance measures for which the exact regions determined by them are known. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider an exterior linear elastodynamics problem with vanishing initial conditions and Dirichlet datum on the scatterer. We convert the Navier Equation, governing the wave behaviour, into two space-time Boundary Integral Equations (BIEs) whose solution is approximated by the energetic Boundary Element Method (BEM). To apply this technique, we have to set the BIEs in a weak form related to the energy of the differential problem solution at the final time instant of analysis. After the space-time discretization of the weak formulation, we have to deal with double space-time integrals, with a weakly singular kernel depending on primary and secondary wave speeds and multiplied by Heaviside functions. The main purpose of this work is the analysis of these peculiar integrals and the study of suitable quadrature schemes for their approximation. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we study the low-tubal-rank tensor completion problem, i.e., the problem of recovering a third-order tensor by observing a subset of its entries, when these entries are selected uniformly at random. We propose a mathematical analysis of an extension of the Burer-Monteiro factorisation approach to this problem. We then illustrate the use of the Burer-Monteiro approach on a challenging OCT reconstruction problem on both synthetic and real world data, using an alternating minimisation algorithm.(c) 2022 Published by Elsevier B.V.
查看更多>>摘要：A Local discontinuous Galerkin (LDG) finite element method on triangular mesh was introduced and analyzed in Castillo et al. (2000) for elliptic problem with suboptimal order of convergence for the flux variable. The purpose of this work is to develop a LDG finite element method on polytopal mesh that achieves optimal convergence rate for both unknowns, potential u and its gradient q. In our new LDG method, u and q are approximated by polynomials of degree k and k - 1 respectively. Optimal order of convergence are obtained for both unknowns. Numerical results in 2d and 3d are presented to confirm the theory.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The paper develops a first-order random coefficient mixed-thinning integer-valued autoregressive time series model (RCMTINAR(1)) to deal with the data related to the counting of elements of variable character. Moments and autocovariance functions for this model are studied as the distribution of the innovation sequence is unknown. The conditional least squares and modified quasi-likelihood are adopted to estimate the model parameters. Asymptotic properties of the obtained estimators are established. The performances of these estimators are investigated and compared with false mod-ified quasi-likelihood via simulations. Finally, the practical relevance of the model is illustrated by using two applications to a SIMpass data set and a burglary data set with a comparison with relevant models that exist so far in the literature. (c) 2022 Elsevier B.V. All rights reserved.
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