Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 1: models and algorithms

The article presents a method of computing the step response of an air floor heater. The method implements parallel algorithms on a graphics processing unit. In the analyzed concrete slab heating ducts are placed. Hot air is transferred through them, thanks to which the heat penetrates into the slab. Heat transfer into the environment takes place on the top surface of the floor by natural convection and radiation. The bottom surface of the slab is thermally insulated. A two-dimensional heat equation was discretized with the use of the implicit finite difference method. In order to solve the obtained system of equations, the conjugate gradient method was used. Moreover, in order to examine the possibility of shortening the computations time, the algorithm of this method was implemented on a graphics processing unit. A computer program, using the CUDA parallel computing platform and linear algebra libraries CUBLAS and CUSPARSE, was developed.