Parallel hybrid PSO with CUDA for lD heat conduction equation

• A new method for solving the one-dimensional heat conduction equation is constructed.
• We also obtain a new method to deal with the nonlocal boundary conditions.
• We design a parallel hybrid algorithm by hybridizing the PSO and CGM with CUDA.
• PHPSO algorithm can speed up the computing of general linear equations.

Objectives: We propose a parallel hybrid particle swarm optimization (PHPSO) algorithm to reduce the computation cost because solving the one-dimensional (1D) heat conduction equation requires large computational cost which imposes a great challenge to both common hardware and software equipments.Background: Over the past few years, GPUs have quickly emerged as inexpensive parallel processors due to their high computation power and low price, The CUDA library can be used by Fortran, C, C++, and by other languages and it is easily programmed. Using GPU and CUDA can efficiently reduce the computation time of solving heat conduction equation.Methods: Firstly, a spline difference method is used to discrete 1D heat conduction equation into the form of linear equation systems, secondly, the system of linear equations is transformed into an unconstrained optimization problem, finally, it is solved by using the PHPSO algorithm. The PHPSO is based on CUDA by hybridizing the PSO and conjugate gradient method (CGM).Results: A numerical case is given to illustrate the effectiveness and efficiency of our proposed method. Comparison of three parallel algorithms shows that the PHPSO is competitive in terms of speedup and standard deviation. The results also show that using PHPSO to solve the one-dimensional heat conduction equation can outperform two parallel algorithms as well as HPSO itself.Conclusions: It is concluded that the PHPSO is an efficient and effective approach towards the 1D heat conduction equation, as it is shown to be with strong robustness and high speedup.