The visualization of power density and temperature distribution of electronic system using elliptic PDE solver

The visualization of power density and temperature are critical in electronic-chip industries. Taking the advantages of mathematical algorithm that is based on elliptic equation of partial differential equation (PDE), the two-dimensional simulation has successfully been generated. The numerical iterative methods that are being used results in efficient elliptic PDE solvers. Numerical analysis is done in terms of execution time, number of iterations and computational complexity of the algorithm being used. The comparison is done between two iterative methods which are Gauss-Seidel and Red-Black Gauss Seidel. The elliptic solver is developed using C language and executed in Linux operating system's environment

Early detection of breast cancer using wave elliptic equation with high performance computing

Breast cancer is the commonest female malignancy in Malaysia and all over the world. The incidence of breast cancer in Malaysia is estimated to be around 27 per 100,000 populations, with close to 3,000 new cases annually. The numerical solution is applied to solve a mathematical model in medicine field. The wave equation can be used as mathematical models in science and engineering fields especially for biological aspects of electromagnetic wave. This paper focuses on the implementation of parallel algorithm for the simulation of breast cancer tumor using two dimensional Helmholtz’s wave equation on a distributed parallel computer system (DPCS). The numerical finite-difference method is chosen as a platform for discretizing the wave equations. The mathematical model of Helmholtz’s model is used to visualize the growth of breast cancer. Parallel Virtual Machine (PVM) is emphasized as communication platform in parallel computer system. The performance of the parallel computing will be analyzed in terms of time execution, speed up, efficiency, effectiveness and temporal performanc

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

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

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

An improved parallel AGE method to solve incomplete blow-up problem through high performance computing system

Incomplete blow-up is a condition under the quasilinear heat equation. The Porous Medium Equation (PME) with power source are admitting incomplete blow-up. It is used as one of the filtration process in the industry. This filtration process has been used globally in the medical and laboratory applications. Previously, the standard numerical procedure was Gauss Seidel method to solve this problem. We propose a new variance of the Alternating Group Explicit Scheme (AGE) algorithms to solve incomplete blow-up problem through High performance computing (HPC). HPC systems include of multiple (usually mass-produced) processors linked together in a single system with commercially available interconnects. This is in contrast to mainframe computers, which are generally monolithic in nature. Four important terms that are, convergent rate by the number of iteration, execution time, computational complexity and stability are considered in this study to evaluate the performances of this approach

High performance computing of thermal control simulation for multilayer full-chip design

The demand on high performance computing is increasing day by day. Large scale of problems needs to be solved computationally fast and accurately without consuming the time. In chip industry, visualizing the thermal simulation involves a large scale of computational complexity and high cost of execution time. Thus, this paper proposes an approach to high performance thermal simulation of multilayer full-chip structure using elliptic Partial Differential Equation (PDE). The prototype of the parallel algorithm is develop using C language and Parallel Virtual Machine and executed on Linux platform. The numerical result and performance analysis will be investigated in terms of execution time, communication cost, speedup, efficiency, effectiveness and temporal performance

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