Space decomposition based parallelization solutions for the combined finiteediscrete element method in 2D

The combined finiteediscrete element method （FDEM） belongs to a family of methods of computationalmechanics of discontinua. The method is suitable for problems of discontinua, where particles aredeformable and can fracture or fragment. The applications of FDEM have spread over a number of disciplinesincluding rock mechanics, where problems like mining, mineral processing or rock blasting canbe solved by employing FDEM. In this work, a novel approach for the parallelization of two-dimensional（2D） FDEM aiming at clusters and desktop computers is developed. Dynamic domain decompositionbased parallelization solvers covering all aspects of FDEM have been developed. These have beenimplemented into the open source Y2D software package and have been tested on a PC cluster. Theoverall performance and scalability of the parallel code have been studied using numerical examples. Theresults obtained confirm the suitability of the parallel implementation for solving large scale problems. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

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 development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and 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 have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the 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 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.

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.

Coupling analysis of transmission lines excited by space electromagnetic fields based on time domain hybrid method using parallel technique

We present a time domain hybrid method to realize the fast coupling analysis of transmission lines excited by space electromagnetic fields, in which parallel finite-difference time-domain (FDTD) method, interpolation scheme, and Agrawal model-based transmission line (TL) equations are organically integrated together. Specifically, the Agrawal model is employed to establish the TL equations to describe the coupling effects of space electromagnetic fields on transmission lines. Then, the excitation fields functioning as distribution sources in TL equations are calculated by the parallel FDTD method through using the message passing interface (MPI) library scheme and interpolation scheme. Finally, the TL equations are discretized by the central difference scheme of FDTD and assigned to multiple processors to obtain the transient responses on the terminal loads of these lines. The significant feature of the presented method is embodied in its parallel and synchronous calculations of the space electromagnetic fields and transient responses on the lines. Numerical simulations of ambient wave acting on multi-conductor transmission lines (MTLs), which are located on the PEC ground and in the shielded cavity respectively, are implemented to verify the accuracy and efficiency of the presented method.

Global SH-wave propagation in a 2D whole Moon model using the parallel hybrid PSM/FDM method

We present numerical modeling of SH-wave propagation for the recently proposed whole Moon model and try to improve our understanding of lunar seismic wave propagation. We use a hybrid PSM/FDM method on staggered grids to solve the wave equations and implement the calculation on a parallel PC cluster to improve the computing efficiency. Features of global SH-wave propagation are firstly discussed for a 100-km shallow and900-km deep moonquakes, respectively. Effects of frequency range and lateral variation of crust thickness are then investigated with various models. Our synthetic waveforms are finally compared with observed Apollo data to show the features of wave propagation that were produced by our model and those not reproduced by our models. Our numerical modeling show that the low-velocity upper crust plays significant role in the development of reverberating wave trains. Increasing frequency enhances the strength and duration of the reverberations.Surface multiples dominate wavefields for shallow event.Core–mantle reflections can be clearly identified for deep event at low frequency. The layered whole Moon model and the low-velocity upper crust produce the reverberating wave trains following each phases consistent with observation. However, more realistic Moon model should be considered in order to explain the strong and slow decay scattering between various phases shown on observation data.

Estimates of Convergence Rate of Parallel Multisplitting Itertive Methods

This paper givers an estimated formula of convergence rate for parallel multisplitting iterative method.Using the formula,we can simplify and unify the proof of convergence of PMI_method.

PARALLEL INTERVAL MATRIX MULTISPLITTING AOR METHODS AND THEIR CONVERGENCE

This paper proposes a class of parallel interval matrix multisplitting AOR methods far solving systems of interval linear equations and discusses their convergence properties under the conditions that the coefficient matrices are interval H-matrices.

Dynamic Parallel Method for Eulerian Method of Elastoplastic Hydrodynamics in Three Dimension

Eulerian method is a main numerical simulation method in elastoplastic hydrodynamics, which is suitable for the problems with multi-component and large deformation. As the feature of the problems to be simulated, such as detonation and penetration, the dynamic parallel method （DPM） is designed to adjust the computational domain dynamically to get better load balance. Dynamic parallel method can be separated into two parts： one is division of initial computational domain and location of the data, the other is expansion of the computational domain and adjustment of the data location. DPM program can greatly shorten computational time and be preferable in simulating actual problems. The speedup of the DPM program is linear in parallel test. DPM can be popularized to parallel program of other multi-component high dimension Eulerian methods naturally.

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.

A Class of Real-Time Parallel Combined Methods ofDigital Simulation for Large Systems

In this paper, a class of real-time parallel combined methods (RTPCM) of the digital simulation for a partitioned large system is presented. By means of combination of the parallelism across the system with the parallelism across the method, stiff and non-stiff subsystems are solved in parallel on parallel computer by a parallel Rosenbrock method and a parallel RK method, respectively. Their construction, convergence and numerical stability are discussed, and the digitalsimulation experiments are conducted.

Class of modified parallel combined methods of real-time numerical simulation for a stiff system

A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and relaxing the dependence of stage value computation on sampling time of input function, a class of modified real-time parallel combined methods are constructed. Stiff and nonstiff subsystems are solved in parallel on a parallel computer by a parallel Rosen-brock method and a parallel RK method, respectively. Their order conditions and convergences are discussed. The numerical simulation experiments show that this class of modified algorithms can get high speed and efficiency.

THE PARALLEL MULTISPLITTING METHOD FOR CONSISTENT SYMMETRIC POSITIVE(SEMI-)DEFINITE SYSTEMS

Main resultsTheorem 1 Let A be an n×n symmetric positive semidefinite matrix and let

The Model of Asynchronous Parallel Nonlinear Multisplitting Method on Shared Memory System

Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equations F(x) = 0. We extend the idea of nonlinear multisplitting and consider a new model ill which the iteration is executed asynchronously: Each processor calculate the solution of an individual nonlinear system belong to its nonlinear multisplitting and can update the global approximation residing in the shared memory at any time. A local convergence analysis of this model is presented. Finally, we give a uumerical example which shows a 'strange' property that speedup Sp > p and efficiency Ep > 1.

The Variable Coefficient ABE-I Method and Its Stability

The ABE-I （Alternating Block Explicit-lmplicit） method for diffusion problem is extended to solve the variable coefficient problem and the unconditional stability of the ABE-I method is proved by the energy method.

A DISTRIBUTED LATTICE BOLTZMANN METHOD

In this paper, an overlapping lattice Boltzmann model is introduced and its domain decomposition method, a distributed lattice Boltzmann method is presented. Parallel effectiveness of some programs based on the distributed lattice Boltzmann method are analyzed.

Construction of tree volume equations for Chinese fir plantations in Guizhou Province, southwestern China

Forest volume, the major component of forest biomass, is an important issue in forest resource monitoring.It is estimated from tree volume tables or equations. Based on tree volume data of 1840 sample trees from Chinese fir （Cunninghamia lanceolata） plantations in Guizhou Province in southwestern China, parallel one- and two-variable tree volume tables and tree height curves for central and other areas were constructed using an error-in-variable modeling method. The results show that, although the one-variable tree volume equations and height curves between the central and other areas were significantly different, the two-variable volume equations were sufficiently close, so that a generalized two-variable tree volume equation could be established for the entire province.

Mantle flow beneath the Asian continent and its force to the crust

The mantle unsteady flows, which are in an incompressible and isoviscous spherical shell, are investigated by using algorithms of the parallel Lagrange multiplier dissonant decomposition method (LMDDM) and the parallel Lagrange multiplier discontinuous deformation analyses (LMDDA) in this paper. Some physical fields about mantle flows such as velocity, pressure, temperature, stress and the force to the crust of the Asian continent are calculated on a parallel computer.

ON INCREASING THE PARALLELISM IN NUMERICAL ALGORITHMS

Parallel algorithms have been designed for the past 20 years initially by parallelising existing sequential algorithms for many different parallel architectures. More recently parallel strategies have been identified and utilized 'resulting in many new parallel algorithms. However the analysis of such algorithms reveals that further strategies can be applied to increase the parallelism. One of these, i.e., increasing the computational capacity in each processing node can reduce the congestion/communicgtion for shared memory/distributed memory multiprocessor systems and dramahcally improve the Performance of the algorithm. Two algorithms are identified and studied, i.e., the Cyclic reduction method for solving large tridiagonal linear systems in which the odd/even sequence is increased to a 'stride of 3' or more resulting in an improved algorithm. Similarly the Gaussian Elimination method for solving linear systems in which one element is eliminated at a time can be adapted to parallel form in which two elements are simultaneously eliminated resulting in the Parallel Implicit Elimination (P.I.E.) method. Numerical results are presented to support the analyses.

Role of Parallel Tempering Monte Carlo Simulation in 2D Ising Spin Glass System with Distance Dependent Interaction

Spin glass system is a complex disordered system with a number of local minima separated by entropic barriers. Therefore, parallel tempering Monte Carlo simulation was used in order to get fast thermalisation （to minimize the relaxation time）. Distance dependent interaction coupling in 2D is studied in order to show how a spin glass phase transition occurs when couplings between far away spins are permitted by considering Edwards-Anderson Ising spin glass model. The interaction coupling is a quenched random variable whose probability of being non-zero decays with distance between two spin sites rij = ｜i-j｜mod（L/2）.The interaction coupling is random and its probability distribution is decaying with the distance between the spins （p（Jij） αrij^-ρ）. The model is studied by changing p among three different regimes （p 〉 2D, 4/3 D〈 p 〈 2D, p 〈 4/3D）. A phase transition temperature for p = 2, 3, 4 is obtained.

Study on the Servo Drive of PM-LSM to Be Used in Parallel Synchronous Drive

Recently, linear motors can have high speed control, high acceleration-deceleration. So linear motors are widely used in industrial applications such as precision machine tools. In our laboratory focusing on transport system, we propose parallel synchronous drive of used the PM-LSM （permanent magnet linear synchronous motor）. It can pass luggage without having to stop the working. When you establish ＂parallel synchronous drive＂, a motor follows the other motor. In our laboratory, one of the motors is called ＂master motor＂ and the other motor called ＂slave motor＂. The master motor＇s speed and position pass slave motor then establish parallel synchronous drive. Therefore, slave motor requires high-responsive and precision that follows the master motor. This paper focuses on the control of the slave motor.