Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 2: results and their evaluation

Using models and algorithms presented in the first part of the article, a spatio-temporal distribution of the step response of a floor heater was determined. The results have been presented in the form of heating curves and temperature profiles of the heater in the selected time moments. The computations results were verified through comparing them with the solution obtained with the use of a commercial program NISA. Additionally, the distribution of the average time constant of thermal processes occurring in the heater was determined. The analysis of the use of a graphics processing unit in numerical computations based on the conjugate gradient method was done. It was proved that the use of a graphics processing unit is profitable in the case of solving linear systems of equations with dense coefficient matrices. In the case of a sparse matrix, the speed-up depends on the number of its non-zero elements.

[1]  Jack J. Dongarra,et al.  Basic Linear Algebra Subprograms Technical (Blast) Forum Standard (1) , 2002, Int. J. High Perform. Comput. Appl..

[2]  Wolfgang Straßer,et al.  A Parallel Preconditioned Conjugate Gradient Solver for the Poisson Problem on a Multi-GPU Platform , 2010, 2010 18th Euromicro Conference on Parallel, Distributed and Network-based Processing.

[3]  Claude Brezinski,et al.  Numerical Methods for Engineers and Scientists , 1992 .

[4]  G.J.M. Smit,et al.  Implementing the conjugate gradient algorithm on multi-core systems , 2007, 2007 International Symposium on System-on-Chip.

[5]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[6]  J. Gołębiowski,et al.  Thermal analysis of short-circuit and cooling states in a DC cable with the use of parallel computations , 2009 .

[7]  Satoshi Matsuoka,et al.  Fast Conjugate Gradients with Multiple GPUs , 2009, ICCS.

[8]  J. Forenc Determination of the initial conditions in the parallel method for the state equation solving , 2008 .

[9]  Stanislaw Rosloniec Fundamental Numerical Methods for Electrical Engineering , 2008, Lecture Notes in Electrical Engineering.

[10]  J. Shewchuk An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[11]  Jonas Koko,et al.  Parallel preconditioned conjugate gradient algorithm on GPU , 2012, J. Comput. Appl. Math..

[12]  Jie Cheng,et al.  Programming Massively Parallel Processors. A Hands-on Approach , 2010, Scalable Comput. Pract. Exp..

[13]  Guillaume Caumon,et al.  Concurrent number cruncher: a GPU implementation of a general sparse linear solver , 2009, Int. J. Parallel Emergent Distributed Syst..

[14]  Maxim Naumov,et al.  Incomplete-LU and Cholesky Preconditioned Iterative Methods Using CUSPARSE and CUBLAS , 2012 .

[15]  J. Forenc,et al.  Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 1: models and algorithms , 2013 .

[16]  Venkata Dinavahi,et al.  SIMD-Based Large-Scale Transient Stability Simulation on the Graphics Processing Unit , 2010, IEEE Transactions on Power Systems.

[17]  Jerzy Gołȩbiowski,et al.  Dynamics of three-dimensional temperature field in electrical system of floor heating , 2002 .