Using CUDA architecture for computer simulations of thermomechanical phenomena

Abstract

Abstract. This paper presents a simulation of the casting solidification process performed on graphics processors compatible with nVidia CUDA architecture. Indispensable for the parallel implementation of a computer simulation of the solidification process, it was necessary to modify the numerical model. The new approach shown in this paper allows the process of matrix building to be divided into two independent phases. The first is independent from the nodal temperature values computed in successive time-steps. The second is performed on the basis of nodal temperature values, but does not require a description of the finite element mesh. This phase is performed in each time step of the simulation of the casting solidification process. The separation of these two phases permits an effective implementation of the simulation software of the casting solidification process on the nVidia CUDA architecture or any other multi-/manycore architecture. The use of GPUs nVidia for the implementation of a computer simulation of the solidification process significantly reduced the waiting time for results. In the course of computer simulations important speedup of the computations was observed.Keywords: numerical modeling, solidification, distributed and parallel processing, CUDA General informationProblems faced by engineers and scientists often require carry out the complicated and time-consuming computer simulations, on the basis of which changes can be incorporated into the analyzed object (its geometric model). Such tasks require the most modern solutions in the field of computer science, the most popular solution is parallel processing. Over the last few years the dynamic development of multicore processors has had a direct impact on the availability of advanced high performance solutions for scientists and engineers. Graphic processors (GPUsGraphics Processing Unit) are increasingly being used in high performance computations. A single GPU has a theoretical computational power several times higher than the fastest available CPU. Figure 1 shows the increase in the theoretical computational power of graphic processors and general purpose processors since 2003.

A Sequential Approach to Numerical Simulations of Solidification with Domain and Time Decomposition

“…Boundary condition given by Equation (2) is the Newton boundary condition, where the exchange of heat on Γ 1 with the environment takes place with heat transfer coefficient α. T |Γ 1 is the temperature on the Γ 1 boundary of the domain and T env is the environment temperature. Boundary condition given by Equation 3is the continuity boundary condition on the Γ 2 boundary separating Ω 1 and Ω 2 domains with temperature T (1) and T (2) , respectively. The thermal conductivity coefficient of the material in the separating layer is given by β, and δ is the thickness of this layer and n is the normal vector to the boundary.…”

“…In both cases, improving computational efficiency, while providing high accuracy, is of utmost importance, with several remedies already available. For instance, one option is to harness large computing clusters either based on CPUs or accelerated architectures such as GPUs [1][2][3][4][5]. However, these require at least minimal expertise in high-performance computing, although they are feasible, they may not be easily available.…”

A computer simulation of solidification taking into account the movement of the liquid phase

“…However, increasing complexity of models, present problem in their implementation. Nowadays, complex models must be implemented with use of technologies like parallel computers [4], accelerated architectures like GPU [5], or using special organization of calculations [6].…”

Use of the distributed computing at the castings solidification simulation

“…They are presented in works [3][4][5], however, they are complicated because they require to use the special equipment.…”