Fernandes, Luis M.Judice, Joaquim J.Kostreva, Michael M.Ebiefung, Aniekan A....
15页
查看更多>>摘要：The Vertical Generalized Linear Complementarity Problem (VGLCP) is an extension of the well-known Linear Complementarity Problem (LCP) that has been discussed in the literature and has found many interesting applications in the past several years. A Block Principal Pivoting (BPP) algorithm was designed for finding the unique solution of the LCP when the matrix of this problem is a P-matrix and shown to be quite efficient for solving large-scale LCPs. In this paper, we introduce an extension of this BPP algorithm for finding the unique solution of the VGLCP when its matrix is a vertical block P-matrix. A Least-Index Single Principal Pivoting (LISPP) algorithm is used as a safeguard to guarantee convergence for the BPP algorithm in a finite number of iterations. Computational experiments with a number of VGLCP test problems indicate that the new BPP algorithm is quite efficient for computing the unique solution of large-scale VGLCPs with vertical block P-matrices in practice. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Asa derivative-free algorithm, the multivariate quadrature rule has been widely used to calculate statistical moments of the output of a system with uncertain inputs. In this paper, by using Rosenblatt transformation and copula method, the system inputs are related to an independent standard normal random vector U; then, a multivariate polynomial model is introduced to relate the system outputs to U, whereby a set of moment matching equations are derived to define quadrature weights and points. After reviewing the tensor product (TP) based quadrature rule and sparse grid method (SGM), the univariate dimension reduction (UDR) method is reformulated by Kronecker product. Following this routine, a new multivariate quadrature rule is derived by combining a Hadamard matrix based quadrature rule and discrete sine transformation matrix (DSTM). Compared with TP and SGM, the proposed quadrature rule can significantly alleviate the curse of dimensionality, its computational burden increases linearly with respect to the number of uncertain inputs. Besides, the proposed algorithms can match moment matching equations neglected by the UDR method, and thus perform more robustly in the uncertainty quantification problem. Finally, numerical examples are performed to check the proposed quadrature rule. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper establishes the precise second order convergence rates of the continuous time Markov chain (CTMC) approximation method for pricing options under the general framework of stochastic local volatility (SLV) models. The stochastic local volatility models studied in this paper include Heston model, 4/2 model, alpha-Hypergeometric model, stochastic alpha beta rho (SABR) model, Heston-SABR model and quadratic SLV model. Using the stochastic flow theorem, the closed-form CTMC approximation formula for the Greeks are obtained and the second order convergence rates are proved. Numerical examples confirm the theoretical findings. (C) 2021 Elsevier B.V. All rights reserved.
Liu, XiaodongMorgan, Nathaniel R.Lieberman, Evan J.Burton, Donald E....
26页
查看更多>>摘要：The existing high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic methods are restricted to using quadratic meshes with quadratic polynomials (P2), which in turn, yield up to third-order accuracy. These existing DG hydrodynamic schemes, when extended to work with cubic meshes and cubic polynomials (P3), can be unstable on strong-shock problems. Therefore, this paper presents a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method to simulate compressible material dynamics (e.g., gasses, fluids, and solids) with strong-shocks using cubic meshes and cubic polynomials, and delivers up to fourth-order accuracy on smooth flows. The stability on shock problems is achieved using new hierarchical orthogonal basis functions and a new subcell mesh stabilization (SMS) scheme for cubic meshes. The accuracy and robustness of the new high-order accurate Lagrangian DG hydrodynamic method is demonstrated by simulating a diverse suite of challenging test problems covering gas and solid dynamic problems on curvilinear meshes. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper is devoted to recovering a time-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation with the time Caputo derivative from an additional integral condition. The uniqueness and a conditional stability for such an inverse problem are proved. Then the two-point gradient method is used to solve the inverse zeroth-order coefficient problem numerically. Some properties of the forward operator are obtained, such as the Frechet differentiability, the Lipschitz continuity and the tangential cone condition to guarantee the convergence of the proposed algorithm. Four numerical examples in one-dimensional and two-dimensional spaces are provided to show the effectiveness and stability of the suggested algorithm. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, the stochastic interface for diffraction grating is considered and the model is formulated as the Helmholtz interface problems (HIPs). In order to have more accuracy simulation, PML boundary is used to describe the stochastic interface. Then we develop shape-Taylor expansion for the solution of HIPs, through perturbation method, we obtain the approximate simulations of second and third order. Error estimation and efficient computation of solutions by low-rank approximation are given. Finally, we illustrate these results with numerical simulations. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We investigate the performance of a unified finite element method for the numerical solution of moving fronts in porous media under non-isothermal flow conditions. The governing equations consist of coupling the Darcy equation for the pressure to two convection-diffusion-reaction equations for the temperature and depth of conversion. The aim is to develop a non-oscillatory unified Galerkin-characteristic method for efficient simulation of moving fronts in porous media. The method is based on combining the modified method of characteristics with a Galerkin finite element discretization of the governing equations. The main feature of the proposed unified finite element method is that the same finite element space is used for all solutions to the problem including the pressure, velocity, temperature and concentration. Analysis of convergence and stability is also presented in this study and error estimates in the L-2-norm are established for the numerical solutions. In addition, due to the Lagrangian treatment of convection terms, the standard Courant-Friedrichs-Lewy condition is relaxed and the time truncation errors are reduced in the diffusion-reaction part. We verify the method for the benchmark problem of moving fronts around an array of cylinders. The numerical results obtained demonstrate the ability of the proposed method to capture the main flow features. (c) 2020 Elsevier B.V. All rights reserved.
Ojeda-Hernandez, ManuelCabrera, Inma P.Cordero, Pablo
9页
查看更多>>摘要：We generalize the notion of quasi-closed element to fuzzy posets in two stages: First, in the crisp style in which each element in a given universe either is quasi-closed or not. Second, in the graded style by defining degrees to which an element is quasi-closed. We discuss the different possible definitions and comparing them with each other. Finally, we show that the most general one has good properties to be used when we have a complete fuzzy lattice as a frame. (C)& nbsp;2021 The Authors. Published by Elsevier B.V.& nbsp;
查看更多>>摘要：Fractal interpolation functions (FIFs) supplement and subsume all classical interpolants. The major advantage by the use of fractal functions is that they can capture either the irregularity or the smoothness associated with a function. This work proposes the use of cubic spline FIFs through moments for the solutions of a two-point boundary value problem (BVP) involving a complicated non-smooth function in the non-homogeneous second order differential equation. In particular, we have taken a second order linear BVP: y'(x) + Q(x)y'(x) + P(x)y(x) = R(x) with the Dirichlet's boundary conditions, where P(x) and Q(x) are smooth, but R(x) may be a continuous nowhere differentiable function. Using the discretized version of the differential equation, the moments are computed through a tridiagonal system obtained from the continuity conditions at the internal grids and endpoint conditions by the derivative function. These moments are then used to construct the cubic fractal spline solution of the BVP, where the non-smooth nature of y' can be captured by fractal methodology. When the scaling factors associated with the fractal spline are taken as zero, the fractal solution reduces to the classical cubic spline solution of the BVP. We prove that the proposed method is convergent based on its truncation error analysis at grid points. Numerical examples are given to support the advantage of the fractal methodology. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：This manuscript proposes an implicit two-step hybrid block method which incorporates fourth derivatives, for solving linear and non-linear third-order boundary value problems in ODEs. The derivation of the present method is based on collocation and interpolation techniques, and the convergence analysis of the new strategy is proved to be seventh-order convergent. The proposed approach produces discrete approximations at the grid points, obtained after solving an algebraic system of equations. Numerical experiments are studied to show the performance and viability of the proposed approach. The numerical results demonstrated that the new technique gives accurate approximations, which are better than some existing strategies in the available literature and also found to be in good agreement with known analytical solutions. (C)& nbsp;2021 The Authors. Published by Elsevier B.V.
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