查看更多>>摘要：In this paper, a backward problem for a time-space fractional diffusion equation is considered, which is to determine the initial data from a noisy final data. To deal with this ill-posed problem, combined the ideas of the Tikhonov regularization in Hilbert Schales proposed by Natterer in 1984 and the fractional Tikhonov method given by Hochstenbach-Reichel in 2011, a Tikhonov regularization method is constructed. Based on the Fourier transform, an a-priori and an a-posteriori regularization parameter choice rules are used to guarantee the order optimal convergence rates. By the finite difference methods and the Discrete Fourier transform, numerical examples in one-dimensional and two-dimensional cases are given for the a-posteriori regularization parameter choice rule. Theoretical and numerical results show that the proposed method works well for both the smooth and the non-smooth functions. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We present an algorithm for generating approximations for the logarithm of Barnes G- function in the half-plane Re(z) >= 3/2. These approximations involve only elementary functions and are easy to implement. The algorithm is based on a two-point Pade approximation and we use it to provide two approximations to ln(G(z)), accurate to 3 x 10(-16 )and 3 x 10(-31) in the half-plane Re(z) >= 3/2; a reflection formula is then used to compute Barnes G-function in the entire complex plane. A by-product of our algorithm is that it also produces accurate approximations to the gamma function. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper presents a high order all-speed semi-implicit weighted compact nonlinear scheme (WCNS) for the isentropic Navier-Stokes system. To avoid the severe CFL stability restriction, the pressure and viscous terms are treated implicitly in time, while the other terms are treated explicitly in time. The third-order IMEX Runge- Kutta methods and the fifth-order WCNS are used for time discretization and spatial discretization, respectively. The generated linear equations of velocity components are solved by the GMRES iterative algorithm. Numerical results in one, two and three dimensions in both compressible and incompressible regimes are presented to show the performance of the designed scheme. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Projection depth (PD), one of the prevailing location depth notions, is a powerful and favored tool for multivariate nonparametric analysis. It permits the extension of the univariate median and weighted means to a multivariate setting. The multidimensional projection depth median (PM) and depth weighted means, including the Stahel-Donoho (SD) estimator are highly robust and affine equivariant. PM has the highest finite sample breakdown point robustness among affine equivariant location estimators. However, the computation of PD remains a challenge because its exact computation is only feasible for a data set with a dimension that is theoretically no higher than eight but practically no higher than three. Approximate algorithms such as random direction procedure or simulated annealing (SA) algorithm, are time-consuming in high dimensional cases. Here, we present an efficient SA algorithm and its extension for the computation of PD. Simulated and real data examples indicate that the proposed algorithms outperform their competitors, including the Nelder-Mead method, and the SA algorithm, in high-dimensional cases and can obtain highly accurate results compared with those of the exact algorithm in low-dimensional cases.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper is concerned with an inverse problem of recovering the space-dependent advection coefficient and the fractional order in a one-dimensional time-fractional reaction-advection-diffusion-wave equation. Based on a transformation, the original equation can be changed into a new form without an advection term. Then we show the uniqueness of recovering the fractional order and the zeroth-order coefficient which contains the information of the "original "advection coefficient by the observation data at two end points. Under the theory of the first-order ordinary differential equation, we obtain the uniqueness result of the advection coefficient. Lastly, we solve the inverse problem numerically from Bayesian perspective by using the iterative regularizing ensemble Kalman method, and numerical examples are presented to show the effectiveness of the proposed method. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our results provide algorithms for detecting affine equivalence of these surfaces, and therefore, in particular, the symmetries of a surface of translation or a minimal surface of the considered types. Additionally, we apply our results to designing surfaces of translation and minimal surfaces with symmetries, and to computing the symmetries of the higher-order Enneper surfaces. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. With the sampling time step arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sample size tends to infinity. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：There exists the inconsistency among the design model, the analysis model, and the optimization model for the fluid cooling channel, as well as the numerical difficulty and the high computational cost caused by solving the problem of forced convection heat transfer. Our method overcomes these issues by three steps. Firstly, the seamless conversion among the three models is achieved through volume parametric reconstruction. The initial fluid cooling channel model is obtained based on some topological optimization methods, then a suitable model for isogeometric analysis (IGA) is reconstructed. Secondly, the IGA of the heat flux coupling problem is realized. To get a low-cost but sufficiently accurate analysis results, the Darcy reduced-order model is introduced when applying the IGA method, and the method is called DRIGA. After derivation of formulas for DRIGA, and applying the material properties and the boundary conditions, the problem of forced convection heat transfer is solved. With the same Darcy's reduced-order model, the calculation is finished by the finite element method (FEM), and the method is called DRFEM. Solution accuracy is studied by comparing with the solution results from the COMSOL, DRFEM and DRIGA to verify the precision and effectiveness of DRIGA. Finally, the shape optimization is realized by taking the control points on the boundary of the solid and liquid as design variables and the average temperature as objective function. After optimization, not only the average temperature is reduced, but also the boundary is continuous and smooth. The given examples show that high solution accuracy and efficient convergence can be obtained with the condition of fewer computing elements in our method. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we discuss the convergence of the modulus-based matrix splitting iteration methods for solving implicit complementarity problems. We simplify the iteration form of the modulus-based matrix splitting (MMS) iteration method, then propose the convergence conditions for both the simplified MMS iteration method and the modified MMS iteration method in terms of spectral radius and matrix norm. Besides, we provide the concrete convergence domains of the parameter matrix for the special case of the two methods. The corresponding numerical experiments are illustrated to show the presented results. (C) 2022 Elsevier B.V. All rights reserved.
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