PARALLEL ALGORITHMS OF ONE-LEG METHOD AND ITERATED DEFECT CORRECTION METHODS

The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.

AN ITERATIVE PARALLEL ALGORITHM OF FINITE ELEMENT METHOD

In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.

Review of the algebraic linear methods and parallel implementation in numerical simulation of groundwater flow

The desire to increase spatial and temporal resolution in modeling groundwater system has led to the requirement for intensive computational ability and large memory space. In the course of satisfying such requirement, parallel computing has played a core role over the past several decades. This paper reviews the parallel algebraic linear solution methods and the parallel implementation technologies for groundwater simulation. This work is carried out to provide guidance to enable modelers of groundwater systems to make sensible choices when developing solution methods based upon the current state of knowledge in parallel computing.

A Class of Parallel Runge-Kutta Methods for Differential-Algebraic Systems of Index 2

A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.

ON THE CONVERGENCE OF PARALLEL BFGS METHOD

According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, which are divided-into two groups, the first group has p processors, the second group has q processors, the two groups are asynchronous. parallel, If we assume the objective function is twice continuously differentiable and uniformly convex, we prove the iteration converge globally to the solution, and under some additional conditions we show the method is superlinearly convergent. Finally, we show the numerical results of this algorithm.

GPU-Based Simulation of Dynamic Characteristics of Ballasted Railway Track with Coupled Discrete-Finite Element Method

Considering the interaction between a sleeper,ballast layer,and substructure,a three-dimensional coupled discrete-finite element method for a ballasted railway track is proposed in this study.Ballast granules with irregular shapes are constructed using a clump model using the discrete element method.Meanwhile,concrete sleepers,embankments,and foundations are modelled using 20-node hexahedron solid elements using the finite element method.To improve computational efficiency,a GPU-based(Graphics Processing Unit)parallel framework is applied in the discrete element simulation.Additionally,an algorithm containing contact search and transfer parameters at the contact interface of discrete particles and finite elements is developed in the GPU parallel environment accordingly.A benchmark case is selected to verify the accuracy of the coupling algorithm.The dynamic response of the ballasted rail track is analysed under different train speeds and loads.Meanwhile,the dynamic stress on the substructure surface obtained by the established DEM-FEM model is compared with the in situ experimental results.Finally,stress and displacement contours in the cross-section of the model are constructed to further visualise the response of the ballasted railway.This proposed coupling model can provide important insights into high-performance coupling algorithms and the dynamic characteristics of full scale ballasted rail tracks.

A GPU-Based Parallel Algorithm for 2D Large Deformation Contact Problems Using the Finite Particle Method

Large deformation contact problems generally involve highly nonlinear behaviors,which are very time-consuming and may lead to convergence issues.The finite particle method(FPM)effectively separates pure deformation from total motion in large deformation problems.In addition,the decoupled procedures of the FPM make it suitable for parallel computing,which may provide an approach to solve time-consuming issues.In this study,a graphics processing unit(GPU)-based parallel algorithm is proposed for two-dimensional large deformation contact problems.The fundamentals of the FPM for planar solids are first briefly introduced,including the equations of motion of particles and the internal forces of quadrilateral elements.Subsequently,a linked-list data structure suitable for parallel processing is built,and parallel global and local search algorithms are presented for contact detection.The contact forces are then derived and directly exerted on particles.The proposed method is implemented with main solution procedures executed in parallel on a GPU.Two verification problems comprising large deformation frictional contacts are presented,and the accuracy of the proposed algorithm is validated.Furthermore,the algorithm’s performance is investigated via a large-scale contact problem,and the maximum speedups of total computational time and contact calculation reach 28.5 and 77.4,respectively,relative to commercial finite element software Abaqus/Explicit running on a single-core central processing unit(CPU).The contact calculation time percentage of the total calculation time is only 18%with the FPM,much smaller than that(50%)with Abaqus/Explicit,demonstrating the efficiency of the proposed method.

Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.

The Parallel Calculation of the Ground-State Correlation Energy of Helium Atom

When we use Modified Configuration Interaction method(MCI) to calculate the correlation energy of double electron systems, for obtaining the higher precision, we always need huge calculations. In order to handle this problem, which will cost much CPU time and memory room if only using a single computer to do it, we now adopt the parallel multisection recurrence algorithm. Thus we can use several CPUs to get the ground state energy of a Helium atom at the same time.

The parallel 3D magnetotelluric forward modeling algorithm

The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the data in the frequency domain, which is very suitable for parallel computation. With the advantage of MPI and based on an analysis of the flow of the 3D magnetotelluric serial forward algorithm, we suggest the idea of parallel computation and apply it. Three theoretical models are tested and the execution efficiency is compared in different situations. The results indicate that the parallel 3D forward modeling computation is correct and the efficiency is greatly improved. This method is suitable for large size geophysical computations.

An Approach of Distributed Joint Optimization for Cluster-based Wireless Sensor Networks

Wireless sensor networks (WSNs) are energyconstrained, so energy saving is one of the most important issues in typical applications. The clustered WSN topology is considered in this paper. To achieve the balance of energy consumption and utility of network resources, we explicitly model and factor the effect of power and rate. A novel joint optimization model is proposed with the protection for cluster head. By the mean of a choice of two appropriate sub-utility functions, the distributed iterative algorithm is obtained. The convergence of the proposed iterative algorithm is proved analytically. We consider general dual decomposition method to realize variable separation and distributed computation, which is practical in large-scale sensor networks. Numerical results show that the proposed joint optimal algorithm converges to the optimal power allocation and rate transmission, and validate the performance in terms of prolonging of network lifetime and improvement of throughput. © 2014 Chinese Association of Automation.

CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.

LOCAL AND PARALLEL FINITE ELEMENT METHOD FOR THE MIXED NAVIER-STOKES/DARCY MODEL WITH BEAVERS-JOSEPH INTERFACE CONDITIONS

In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.

EXPANDABLE PARALLEL FINITE ELEMENT METHODS FOR LINEAR ELLIPTIC PROBLEMS

In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element methods,there are two attractive features of the methods shown in this article:1)a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous;2)the computational domain of each local subproblem is contained in a ball with radius of O(H)(H is the coarse mesh parameter),which means methods in this article are more suitable for parallel computing in a large parallel computer system.Some a priori error estimation are obtained and optimal error bounds in both H^1-normal and L^2-normal are derived.Finally,numerical results are reported to test and verify the feasibility and validity of our methods.

A parallel two-level finite element method for the Navier-Stokes equations

Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.

Parallel Region－Preserving Multisection Method for Solving Generalized Eigenproblem

The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the developing of the parallel computers, but all the research work is limited in standard eigenproblem of symmetric tridiagonal matrix. The multisection method for solving generalized eigenproblem applied significantly in many secience and engineering domains has not been studied. The parallel region--preserving multisection method (PRM for shotr) for solving generalized eigenproblem of large sparse real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We tested the method on the YH--1 vector computer,and compared with the parallel region-preserving determinant search method (parallel region--preserving bisection method)(PRB for short). The numerical results show that PRM has a higher speed-up, for instance it attains the speed-up of 7.7 when the scale of the problem is 2114 and the eigenpair found is 3; and PRM is superior to PRB when scale of the problem is large.

Fast Parallel Method for Polynomial Evaluation at Points in Arithmetic Progression

We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.

Local and parallel finite element algorithms for time-dependent convection-diffusion equations

Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel proce- dures. Hence, these local and parallel algorithms only involve one small original problem on the coarse mesh and some correction problems on the local fine grid. One technical tool for the analysis is the local a priori estimates that are also obtained. Some numerical examples are given to support our theoretical analvsis.

Extraction of pipeline defect feature based on variational mode and optimal singular value decomposition

Because the magnetic signal information of pipeline defects obtained by magnetic flux leakage detection contains interference signals, it is difficult to accurately extract the features. Therefore, a novel pipeline defect feature extraction method based on VMD-OSVD (variational modal decomposition - optimal singular value decomposition) is proposed to promote the signal to noise ratio (SNR) and reduce aliasing in the frequency domain. By using the VMD method, the sampled magnetic signal is decomposed, and the optimal variational mode is selected according to the rate of relative change (VMK) of Shannon entropy (SE) to reconstruct the signal. After that, SVD algorithm is used to filter the reconstructed signal again, in which the H-matrix is optimized with the phase-space matrix to enhance SNR and decrease the frequency domain aliasing. The results show that the method has excellent denoising ability for defect magnetic signals, and SNR is increased by 21.01%, 24.04%, 0.96%, 32.14%, and 20.91%, respectively. The improved method has the best denoising effect on transverse mechanical scratches, but a poor denoising effect on spiral welding position. In the frequency domain, the characteristics of different defects are varied, and their corresponding frequency responses are spiral weld corrosion > transverse mechanical cracking > girth weld > deep hole > normal pipe. The high-frequency band is the spiral weld corrosion with f1 = 153.37 Hz. The low-frequency band is normal with f2 = 1 Hz. In general, the VMD-OSVD method is able to improve the SNR of the signal and characterize different pipe defects. And it has a certain guiding significance to the application of pipeline inspection in the field of safety in the future.

Ship Appearance Optimal Design on RCS Reduction Using Response Surface Method and Genetic Algorithms

Radar cross section (RCS) reduction technologies are very important in survivability of the military naval vessels. Ship appearance shaping as an effective countermeasure of RCS reduction redirects the scattered energy from one angular region of interest in space to another region of little interest. To decrease the scattering electromagnetic signals from ship scientifically, optimization methods should be introduced in shaping design. Based on the assumption of the characteristic section design method, mathematical formulations for optimal shaping design were established. Because of the computation-intensive analysis and singularity in shaping optimization, the response surface method (RSM) combined genetic algorithm (GA) was proposed. The poly-nomial response surface method was adopted in model approximation. Then genetic algorithms were employed to solve the surrogate optimization problem. By comparison RCS of the conventional and the optimal design, the superiority and effectiveness of proposed design methodology were verified.