Andrzej Jordan

The Parallel Algorithm of Conjugate Gradient Method

In this paper authors investigate parallel implementation of a conjugate gradient algorithm used for solving a large system of linear algebraic equations. Computations were carried out using a heterogeneous cluster of PCs, working under control of Windows 2000 operating system and an MPI library, as well as a massive parallel processor machine Hitachi SR-2201. The authors implemented two versions of the algorithm in cluster computations: an algorithm with equally distributed data among all processors, and another one with distribution depending on the speed of each PC processor. Speedup in all implementations was investigated and the conclusions were drawn.

A new version of conjugate gradient method parallel implementation

In the article the authors describe an idea of parallel implementation of a conjugate gradient method in a heterogeneous PC cluster and a supercomputer Hitachi SR-2201. The new version of algorithm implementation differs from the one applied earlier (Jordan and Bycul, 2002), because it uses a special method for storing sparse coefficient matrices: only non-zero elements are stored and taken into account during computations, so that the sparsity of the coefficient matrix is taken full advantage of. The article includes a comparison of the two versions. A speedup of the parallel algorithm has been examined for three different cases of coefficient matrices resulting in solving different physical problems. The authors have also investigated a preconditioning method, which uses the inversed diagonal of the coefficient matrix, as a preconditioning matrix.

High Frequency Electromagnetic Fields Analysis with the Use of the Parallel FDTD Method

In the paper the parallel algorithms of the Finite-Difference Time-Domain method are presented. Those algorithms are based on the space domain decomposition. In the presented work, communications among computation nodes in a cluster of PCs and the efficiency of the parallel algorithms are also discussed.

The Modified Speculative Method for the Transient States Analysis

The speculative method is intended to conduct transient states analysis in electrical circuits in which the transient state is described by a system of ordinary differential equations (ODE), linear or non-linear. A general idea of this method is based on the decomposition of the time domain. Computations in subintervals of time are conducted in parallel with the use of one of wellknown sequential numerical methods of solving ODE systems. In the article the modified speculative method, then the analysis of a non-linear model of a DC-motor supplied by a solar generator, as an example of the application of this method, will be presented. The computations were carried out with the use of the cluster of 5 workstations based on Intel Xeon 2.66 GHz processor.

A survey of speculative methods for transient state analysis

The article presents two types of the speculative methods: the speculative method with a fixed integration step, and the speculative method with a variable integration step. These methods are an original approach to the transient states analysis appearing in the physical and electrical systems, in which the transient state is described by a large system of ordinary differential equations, linear or nonlinear. A general idea of these methods is based on decomposition of the total time of transient analysis into subintervals in which computations are conducted in parallel. The application of speculative methods allows one to reduce the time of computations in relation to commonly used sequential algorithms. As an example of the application of speculative methods, the analysis of transient state described by a system of 10 differential equations is presented.

Speculative parallel processing applied to modelling of initial problems in electrical circuits

The paper presents an analysis of the dynamics of an asynchronous motor performed by speculative parallel processing using 41 processors. A simulation of the motor dynamics showed an important speed-up of computation, which depends on the number of parallel processes organised in the analysed time sub-intervals.

Transmittances and frequency characteristics of wave and diffusion heat transfer in the flat slab

Abstract This paper on conduction heat transfer in a slab presents a frequency domain comparison between the usual diffusion model and a wave model which includes the effect of non-instantaneous heat propagation. This is accomplished using a transfer function approach. Additionally, transfer functions relating the temperature distribution to heat flux are presented for various cases. The limit frequency, f li , is developed as that frequency below which the difference between the diffusion model and the wave model is negligible. Above this frequency, the difference between the two models increases rapidly. The work of this paper is an essential generalization of various specific cases found in the previous literature. It also refers to previous papers written by the authors [Int. J. Heat Mass Transfer36, 1709–1713 (1993)].

Optimal Placement of Wind Generators in Medium Voltage Power Grids -- Investigations of Genetic Algorithm

The paper presents investigations of a genetic algorithm for computations of power losses in the MV power grid. In this case, the vector of start population PO0 and mutation likelihood was investigated. Diagrams of power losses in the grid dependent on the value of the mutation operator as well as the vector size of start population p are presented. The construction of the parallel genetic algorithm is presented. Its properties are verified on the cluster of workstations environment using MPI library. The algorithm is validated with a medium sized electrical grid.

Optimal Placement of the Wind Generators in the Medium Voltage Power Grid

The minimization of power losses in the medium voltage (MV) grid requires adjustment of network of power sources. This problem is particularly important for renewable energy sources, for example for the farms of wind generators. Their placement and nominal power should be selected according to the configuration of the network and the largest loads. The implementation of the genetic algorithm (GA) to the presented problem is discussed in this paper. The formulation of the GA algorithm and its performance for different numbers of power sources is analyzed. The optimal placements of wind generators were computed for some case problems.

Application of parallel hybrid algorithm in the optimization technique

The hybrid algorithm presented in the paper illustrates a coupling of the genetic algorithm method with the gradient method without constraints. The parallel implementation of a hybrid algorithm, which consists of the genetic algorithm and Gaussian elimination method is presented.