New High-Order Compact ADI Algorithms for 3D Nonlinear Time-Fractional Convection-Diffusion Equation

Numerical approximations of the three-dimensional (3D) nonlinear time-fractional convection-diffusion equation is studied, which is firstly transformed to a time-fractional diffusion equation and then is solved by linearization method combined with alternating direction implicit (ADI) method. By using fourth-order Padé approximation for spatial derivatives and classical backward differentiation method for time derivative, two new high-order compact ADI algorithms with orders O(τmin(1+α,2−α)+h4) and O(τ2−α+h4) are presented. The resulting schemes in each ADI solution step corresponding to a tridiagonal matrix equation can be solved by the Thomas algorithm which makes the computation cost effective. Numerical experiments are shown to demonstrate the high accuracy and robustness of two new schemes

Identification and classification of high risk groups for Coal Workers' Pneumoconiosis using an artificial neural network based on occupational histories: a retrospective cohort study

<p>Abstract</p> <p>Background</p> <p>Coal workers' pneumoconiosis (CWP) is a preventable, but not fully curable occupational lung disease. More and more coal miners are likely to be at risk of developing CWP owing to an increase in coal production and utilization, especially in developing countries. Coal miners with different occupational categories and durations of dust exposure may be at different levels of risk for CWP. It is necessary to identify and classify different levels of risk for CWP in coal miners with different work histories. In this way, we can recommend different intervals for medical examinations according to different levels of risk for CWP. Our findings may provide a basis for further emending the measures of CWP prevention and control.</p> <p>Methods</p> <p>The study was performed using longitudinal retrospective data in the Tiefa Colliery in China. A three-layer artificial neural network with 6 input variables, 15 neurons in the hidden layer, and 1 output neuron was developed in conjunction with coal miners' occupational exposure data. Sensitivity and ROC analyses were adapted to explain the importance of input variables and the performance of the neural network. The occupational characteristics and the probability values predicted were used to categorize coal miners for their levels of risk for CWP.</p> <p>Results</p> <p>The sensitivity analysis showed that influence of the duration of dust exposure and occupational category on CWP was 65% and 67%, respectively. The area under the ROC in 3 sets was 0.981, 0.969, and 0.992. There were 7959 coal miners with a probability value < 0.001. The average duration of dust exposure was 15.35 years. The average duration of ex-dust exposure was 0.69 years. Of the coal miners, 79.27% worked in helping and mining. Most of the coal miners were born after 1950 and were first exposed to dust after 1970. One hundred forty-four coal miners had a probability value ≥0.1. The average durations of dust exposure and ex-dust exposure were 25.70 and 16.30 years, respectively. Most of the coal miners were born before 1950 and began to be exposed to dust before 1980. Of the coal miners, 90.28% worked in tunneling.</p> <p>Conclusion</p> <p>The duration of dust exposure and occupational category were the two most important factors for CWP. Coal miners at different levels of risk for CWP could be classified by the three-layer neural network analysis based on occupational history.</p

An Efficient Algorithm with Stabilized Finite Element Method for the Stokes Eigenvalue Problem

This paper provides a two-space stabilized mixed finite element scheme for the Stokes eigenvalue problem based on local Gauss integration. The two-space strategy contains solving one Stokes eigenvalue problem using the P1-P1 finite element pair and then solving an additional Stokes problem using the P2-P2 finite element pair. The postprocessing technique which increases the order of mixed finite element space by using the same mesh can accelerate the convergence rate of the eigenpair approximations. Moreover, our method can save a large amount of computational time and the corresponding convergence analysis is given. Finally, numerical results are presented to confirm the theoretical analysis

A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation

In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank–Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method

Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem

summary:This paper provides an accelerated two-grid stabilized mixed finite element scheme for the Stokes eigenvalue problem based on the pressure projection. With the scheme, the solution of the Stokes eigenvalue problem on a fine grid is reduced to the solution of the Stokes eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. By solving a slightly different linear problem on the fine grid, the new algorithm significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate. Finally, numerical experiments are shown to verify the high efficiency and the theoretical results of the new method

Numerical Approximation of the Space Fractional Cahn-Hilliard Equation

In this paper, a second-order accurate (in time) energy stable Fourier spectral scheme for the fractional-in-space Cahn-Hilliard (CH) equation is considered. The time is discretized by the implicit backward differentiation formula (BDF), along with a linear stabilized term which represents a second-order Douglas-Dupont-type regularization. The semidiscrete schemes are shown to be energy stable and to be mass conservative. Then we further use Fourier-spectral methods to discretize the space. Some numerical examples are included to testify the effectiveness of our proposed method. In addition, it shows that the fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case

Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem

In this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite element with the interior penalty discontinuous Galerkin formulation. Optimal a priori error estimates are derived for both semidiscrete and fully discrete schemes

Error estimates for an augmented method for one-dimensional elliptic interface problems

Abstract Elliptic interface problems have many important scientific and engineering applications. Interface problems are encountered when the computational domain involves multi-materials with different conductivities, densities, or permeability. The solution or its gradient often has a jump across the interface due to discontinuous coefficients or singular sources. In this paper, optimal convergence of an augmented method is derived for one-dimensional interface problems. The dependence of the discontinuous coefficient in the error analysis is also considered. Numerical examples are presented to confirm the theoretical analysis and show that the estimate is sharp