Implicit numerical multidimensional heat-conduction algorithm parallelization and acceleration on a graphics card

journal article in Web of Science

en

Analytical solutions are much less computationally intensive than numerical ones, and moreover, they are more accurate because they do not contain numerical errors; however, they can only describe a small group of simple heat-conduction prob- lems. A numerical simulation of heat conduction is often used as it is able to describe complex problems, but its computational time is much longer, especially for unsteady multidimensional models with temperature-dependent material properties. After a discretization using the implicit scheme, the heat-conduction problem can be described with N non-linear equations, where N is the large number of the elements of the discretized model. This set of equations can be efficiently solved with an iteration of the line-by-line method, based on the heat-flux superposition, although the computational procedure is strictly serial. This means that no parallel computation can be done, which is strictly required when a graphics card is used to accelerate the computation. This paper describes a multidimensional numerical model of unsteady heat conduction solved with the line-by-line method and a modification of this method for a highly parallel computation. An enormous increase in the speed is demonstrated for the modified line-by-line method accelerated on the graphics card, and the durations of the computations for various mesh sizes are compared with the original line-by-line method.

Analytical solutions are much less computationally intensive than numerical ones, and moreover, they are more accurate because they do not contain numerical errors; however, they can only describe a small group of simple heat-conduction prob- lems. A numerical simulation of heat conduction is often used as it is able to describe complex problems, but its computational time is much longer, especially for unsteady multidimensional models with temperature-dependent material properties. After a discretization using the implicit scheme, the heat-conduction problem can be described with N non-linear equations, where N is the large number of the elements of the discretized model. This set of equations can be efficiently solved with an iteration of the line-by-line method, based on the heat-flux superposition, although the computational procedure is strictly serial. This means that no parallel computation can be done, which is strictly required when a graphics card is used to accelerate the computation. This paper describes a multidimensional numerical model of unsteady heat conduction solved with the line-by-line method and a modification of this method for a highly parallel computation. An enormous increase in the speed is demonstrated for the modified line-by-line method accelerated on the graphics card, and the durations of the computations for various mesh sizes are compared with the original line-by-line method.

heat conduction, numerical simulation, multidimensional numerical model algorithm, acceleration, parallelization, graphics card

01.04.2016

Istitute of Metals and Technology

Ljubljana

1580-2949

50

2

183–187

5