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The present paper is devoted to the construction and study of numerical methods for solving an initial boundary value problem for a differential equation containing several terms with fractional time derivatives in the sense of Caputo. This equation is suitable for describing the process of fluid flow in fractured porous media under some physical assumptions, and has an important applied significance in petroleum engineering. Two different approaches to constructing numerical schemes depending on orders of the fractional derivatives are proposed. The semi-discrete and fully discrete numerical schemes for solving the problem are analyzed. The construction of a fully discrete scheme is based on applying the finite difference approximation to time derivatives and the finite element method in the spatial direction. The approximation of the fractional derivatives in the sense of Caputo is carried out using the L1-method. The convergence of both numerical schemes is rigorously proved. The results of numerical tests conducted for model problems are provided to confirm the theoretical analysis. In addition, the proposed computational method is applied to study the flow of oil in a fractured porous medium within the framework of the considered model. Based on the results of the numerical tests, it was concluded that the model reproduces the characteristic features of the fluid flow process in the medium under consideration. [ABSTRACT FROM AUTHOR]

In this paper, we address an inventory system where the demand rate multiplicatively combines the effects of time and selling price. It is assumed that the demand rate is the product of two power functions, one depending on the selling price and the other on the time elapsed since the last inventory replenishment. Shortages are allowed and fully backlogged. The aim is to obtain the lot sizing, the inventory cycle and the unit selling price that maximize the profit per unit time. To achieve this, two efficient algorithms are proposed to obtain the optimal solution to the inventory problem for all possible parameter values of the system. We solve several numerical examples to illustrate the theoretical results and the solution methodology. We also develop a numerical sensitivity analysis of the optimal inventory policy and the maximum profit with respect to the parameters of the demand function. [ABSTRACT FROM AUTHOR]

This paper deals with the design and implementation of cross-platform, D2Q9-BGK and D3Q27-MRT, lattice Boltzmann method solver for 2D and 3D flows developed with ArrayFire library for high-performance computing. The solver leverages ArrayFire's just-in-time compilation engine for compiling high-level code into optimized kernels for both CUDA and OpenCL GPU backends. We also provide C++ and Rust implementations and show that it is possible to produce fast cross-platform lattice Boltzmann method simulations with minimal code, effectively less than 90 lines of code. An illustrative benchmarks (lid-driven cavity and Kármán vortex street) for single and double precision floating-point simulations on 4 different GPUs are provided. Data Set License: MIT [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis of the influence of mechanical properties and the thickness of viscoelastic materials on the transient dynamic behavior of free layer damping beams. Specifically, the beams consist of cantilever metal sheets with surface viscoelastic treatment, and two different configurations are analyzed: symmetric and asymmetric. The viscoelastic material is characterized by a five-parameter fractional derivative model, which requires specific numerical methods to solve for the transverse displacement of the free edge of the beam when a load is applied. Concretely, a homogenized finite element formulation is performed to reduce computation time, and the Newmark method is applied together with the Grünwald–Letnikov method to accomplish the time discretization of the fractional derivative equations. Amplitudes and response time are evaluated to study the transient dynamic behavior and results indicate that, in general, asymmetrical configurations present more vibration attenuation than the symmetrical ones. Additionally, it is deduced that a compromise between response time and amplitudes has to be reached, and in addition, the most influential parameters have been determined to achieve greater vibration reduction. [ABSTRACT FROM AUTHOR]