An efficient BEM for numerical solution of the biharmonic boundary value problem

This paper presents an efficient BEM for solving biharmonic equations. All boundary values including geometries are approximated by the universal high order radial basis function networks (RBFNs) rather than the usual low order interpolations. Numerical results show that the proposed BEM is considerably superior to the linear/quadratic-BEM in terms of both accuracy and convergence rate

Solving high-order partial differential equations with indirect radial basis function networks

This paper reports a new numerical method based on radial basis function networks (RBFNs) for solving high-order partial differential equations (PDEs). The variables and their derivatives in the governing equations are represented by integrated RBFNs. The use of integration in constructing neural networks allows the straightforward implementation of multiple boundary conditions and the accurate approximation of high-order derivatives. The proposed RBFN method is verified successfully through the solution of thin-plate bending and viscous flow problems which are governed by biharmonic equations. For thermally driven cavity flows, the solutions are obtained up to a high Rayleigh number

A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark problems including the lid-driven triangular-cavity flow are employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

This paper presents a new effective radial basis function (RBF) collocation technique for the free vibration analysis of laminated composite plates using the first order shear deformation theory (FSDT). The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids. Instead of using conventional differentiated RBF networks, one-dimensional integrated RBF networks (1D-IRBFN) are employed on grid lines to approximate the field variables. A number of examples concerning various thickness-to-span ratios, material properties and boundary conditions are considered. Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method

Neural Network-Optimized Channel Estimator and Training Signal Design for MIMO Systems with Few-Bit ADCs

This paper is concerned with channel estimation in MIMO systems with few-bit ADCs. In these systems, a linear minimum mean-squared error (MMSE) channel estimator obtained in closed-form is not an optimal solution. We first consider a deep neural network (DNN) and train it as a non-linear MMSE channel estimator for few-bit MIMO systems. We then present a first attempt to use DNN in optimizing the training signal and the MMSE channel estimator concurrently. Specifically, we propose an autoencoder with a specialized first layer, whose weights embed the training signal matrix. Consequently, the trained autoencoder prompts a new training signal design that is customized for the MIMO channel model under consideration.Comment: 5 pages, 3 figures, to appear in IEEE Signal Processing Letter

A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows

A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is demonstrated with the solution of the start-up Couette flow of the Hookean and FENE dumbbell model fluids

Multi-source in DF cooperative networks with the PSR protocol based full-duplex energy harvesting over a Rayleigh fading channel: performance analysis

Due to the tremendous energy consumption growth with ever-increasing connected devices, alternative wireless information and power transfer techniques are important not only for theoretical research but also for saving operational costs and for a sustainable growth of wireless communications. In this paper, we investigate the multi-source in decode-and-forward cooperative networks with the power splitting protocol based full-duplex energy harvesting relaying network over a Rayleigh fading channel. In this system model, the multi-source and the destination communicate with each other by both the direct link and an intermediate helping relay. First, we investigate source selection for the best system performance. Then, the closed-form expression of the outage probability and the symbol error ratio are derived. Finally, the Monte Carlo simulation is used for validating the analytical expressions in connection with all main possible system parameters. The research results show that the analytical and simulation results matched well with each other.Web of Science68327526