Some parallel numerical methods in solving partial differential equations

This paper will discuss the solution of twodimensional partial differential equations (PDEs) using some parallel numerical methods namely Gauss Seidel and Red Black Gauss Seidel. The selected two-dimensional PDE to solve in this paper are of parabolic and elliptic type. Parallel Virtual Machine (PVM) is used in support of the communication among all microprocessors of Parallel Computing System. PVM is well known as a software system that enables a collection of heterogeneous computers to be used as coherent and flexible concurrent computational resource. The numerical results will be presented graphically and parallel performance measurement by Gauss Seidel and Red Gauss Seidel methods will be evaluated in terms of execution time, speedup, efficiency, effectiveness and temporal performance. Performance evaluations are critical as this paper aimed to fabricate an efficient Two-Dimensional PDE Solver (TDPDES). This new well-organized TDPDES technique will enhance the research and analysis procedure of many engineering and mathematic fields

Temperature behavior visualization on rubber material involving phase change simulation

Material engineers are excited with the design of a new rubber product through the development of a new composite of rubber product. Our research contributes in developing the mathematical simulation based on Gauss-Seidel Red-Black and Gauss-Seidel method to solve the temperature behavior of the rubber elasticity, strength, entropy and classical experiments through reference publications and stimulating rubber physics research elsewhere. The temperature behavior leads to the partial differential equation of heat transfer problem involving phase change simulation. The prototype of the algorithm implement on Linux operating system using C language.Roziha Darwis, Norma Alias, Nazeeruddin Yaacob, Mohamed Othman, Nurashikin Abdullah, Teh Yuan Yin

Mathematical simulation for 3-dimensional temperature visualization on open source-based grid computing platform

New Iterative Alternating Group Explicit (NAGE) is a powerful parallel numerical algorithm for multidimensional temperature prediction. The discretization is based on finite difference method of partial differential equation (PDE) with parabolic type. This paper proposed the NAGE method as a straight forward transformation from sequential to parallel algorithm using domain decomposition and splitting strategies. The processes involving the scheduling of communication, algometric and mapping the sub domain into a number of processors. The critical 3-Dimensional temperature visualization involves large scale of computational complexity. This computational challenge inspiring us to utilize the power of advanced high performance computing resources. By the means of higher performance computing, the computation cannot be relying on just one single set of cluster. Therefore, this research takes the advantage of utilizing multiple set of clusters from geographically different location which is known as grid computing. In realizing this concept, we consider the advantages of data passing between two web services which each are connected with one or multiple set of clusters. For this kind of relationship, we choose service-oriented architecture (SOA) style. Each web services are easily maintainable since there is loose coupling between interacting nodes. The development of this architecture is based on several programming language as it involves algorithm implementation on C, parallelization using Parallel Virtual Machine (PVM) and Java for web services development. As the conclusions, this leading grid-based application platform has a bright potential in managing highly scalable and reliable temperature prediction visualization. The efficiency of this application will be measured based on the results of numerical analysis and parallel performance

The parallelization of the direct and iterative schemes for solving boundary layer problem on heterogeneous cluster systems

In this paper, we present iterative schemes, specifically the iterative schemes: conjugate gradient, and Gauss-Seidel as well as direct schemes: LU factorization and Gauss elimination for solving boundary layer problem. The aim of this paper is to offer reasonable assessments and contrasts on behalf of the numerical experiments of these two schemes. The sequential and parallel programming is developed using a C programming language under Linux environment, while the parallel programming is running using the Parallel Virtual Machine (PVM) on a heterogeneous cluster systems. The analysis of the results are conducted in terms of numerical and parallel performance evaluations namely execution time, speedup, efficiency, effectiveness and temporal performance. The results prove that the iterative methods of conjugate gradient and Gauss-Seidel method are the alternatives scheme for solving the large scale computation

Parallelization of temperature distribution simulations for semiconductor and polymer composite material on distributed memory architecture

The implementations of parallel algorithms in solving partial differential equations (PDEs) for heat transfer problems are based on the high performance computing using distributed memory architecture. In this paper, the parallel algorithms are exploited finite difference method in solving multidimensional heat transfer problem for semiconductor components and polymer composite materials. Parallel Virtual Machine (PVM) and C language based on Linux operating system are the platform to run the parallel algorithms. This research focused on Red-Black Gauss Seidel (RBGS) iterative method. Parallel performance evaluations in terms of speedup, efficiency, effectiveness, temporal performance and communication cost are analyzed

Parallel iterative block and direct block methods for 2-space dimension problems on distributed memory architecture

In numerical simulations of partial differential equations, it is often the case that we have to solve the matrix equations accrued from finite difference models of the equations. For computational purposes, we can iterate the solution system in such a way that the resulting matrices on the left hand side become easy to handle such as diagonal matrices or small matrices, for example the block systems. This indicates that we can apply various group computational molecules to simulate the partial differential equations numerically. In this paper, we present two problems of group schemes, specifically the Alternating Group Explicit (AGE) method and the Crack Propagation. We offer reasonable assessments and contrasts on behalf of the numerical experiments of these two methods ported to run through Parallel Virtual Machine (PVM) on distributed memory architecture

Parallel system for abnormal cell growth prediction based on fast numerical simulation

The paper focuses on a numerical method for detecting, visualizing and monitoring abnormal cell growth using large-scale mathematical simulations. The discretization of multi-dimensional partial differential equation (PDE) is based on finite difference method. The predictor system depending on users input data via a user interface, generating the initial and boundary condition generated from parabolic or elliptic type of PDE. The processing large sparse matrixes are based on multiprocessor computer systems for abnormal growth visualization. The multi-dimensional abnormal cell has produced the numerical analysis and understanding results at the target area for the potential improvement of detection and monitoring the growth. The development of the prediction system is the combinations of the parallel algorithms, open source software on Linux environment and distributed multiprocessor system. The paper ends with a concluding remark on the parallel performance evaluations and numerical analysis in reducing the execution time, communication cost and computational complexity

Parallelization of iterative and direct schemes for Keller-Box method on distributed memory platform

In this paper, we present iterative schemes, specifically the conjugate gradient, and Gauss seidel red-black (GSRB) and direct schemes namely LU factorization and Gauss elimination for Keller-box scheme. The aim of this paper is to offer reasonable assessments and contrasts on behalf of the numerical experiments of these two schemes ported to run through Parallel Virtual Machine (PVM) on distributed memory platform. The computational complexity also presented for the comparison purpose, and the graphs of parallel evaluation in terms of speedup, efficiency, effectiveness and temporal performance are presented as well

Performance evaluation of multidimensional parabolic type problems on distributed computing systems

Parabolic Partial Differential Equations (PDE) are well suited to multiprocessor implementation. However, the performance of a parallel program can be damaged by the mismatches between the parallelism available in the application and that available in the architecture. Communication cost, memory requirements, execution time, implementation cost, and others from a problem specific function should be considered to estimate a parallel program. In this paper, we present an optimizing technique called granularity analysis to evaluate the parallel algorithms particularly AGE families without degrading the performances. The resultant granularity analysis scheme is appropriate for developing adaptive parallelism of declarative programming languages on multiprocessors. The results recommend that the proposed method can be used for performance estimation of parallel programs. Red Black Gauss Seidel (GSRB) is selected as the benchmark for the differences numerical methods

Efficient 3D temperature propagation for laser glass interaction

A new algorithm in the class of the AGE method is for developed to solve the heat equation in 3 space dimensions laser glass model problem. AGE method is one of the iterative, convergent, stable and second order accurate with respect to space and time. All the parallel strategies were developed on a CPUs. The distributed parallel computer system was run on the homogeneous cluster of 20 Intel Pentium IV PCs, each with a storage of 20GB and speed of 1.6 MHz. where data decomposition is run asynchronously and concurrently at every time level. The performance evaluations of the algorithm are increasing in terms of speed-up, efficiency and effectiveness