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Modern graphics accelerators (GPUs) can significantly speed up the execution of numerical problems. However, porting programs to graphics accelerators is not an easy task, sometimes requiring their almost complete rewriting. CUDA graphics accelerators, thanks to technology developed by NVIDIA, allow one to have a single source code for both conventional processors (CPUs) and CUDA. However, parallelization on shared memory is still done differently and should be specified explicitly. The use of a functional programming library developed by the authors makes it possible to hide the use of one or another parallelization mechanism on shared memory within the library and make the user's source code completely independent of the computing device used (CPU or CUDA). This article shows how this can be done. [ABSTRACT FROM AUTHOR]

In this paper, we present results of the development of certain parallel numerical methods for solving three-dimensional evolutionary and stationary problems of diffusion and heat transfer. We present a detailed description of a special, explicit iteration scheme for parabolic equations and discuss a multigrid technology used for solving elliptic equations and implicit schemes for parabolic equations. [ABSTRACT FROM AUTHOR]

A method for calculating the nonstationary thermal interaction between a viscous gas flow and a solid body is presented. The method consists in direct joint integration over time of the equations of gas dynamics of a multicomponent mixture and the heat equation in a solid on multi-block unstructured meshes. To calculate one time step, the system of governing equations is split into hyperbolic and parabolic subsystems. The numerical method provides approximation of the matching condition (continuity of temperature and the normal component of the heat flux) at the interface between gas and solid and is efficient for nonstationary calculations. The comparison with the analytical solution of the model problem of the interaction of a high-speed flow and a heated plate confirm the efficiency of the method. [ABSTRACT FROM AUTHOR]

A method for constructing a quasi-isometric parametrization of a plane curvilinear quadrilateral is described. The parametrization is defined using a generalized Dirichlet variational functional. Based on its minimization, an algorithm for generating grids that implement a quasi-isometric parametrization of quadrilaterals with curved, but sufficiently smooth boundaries is developed. Primary attention is given to the numerical features of the proposed approach. [ABSTRACT FROM AUTHOR]

An approach to the time integration of the Navier–Stokes equations for a compressible heat-conducting gas is developed. According to this approach, the solution algorithm is split into a convective and a diffusion stage. The convective stage represents an explicit Godunov-type scheme. The diffusion stage is addressed using the Chebyshev explicit iterative scheme. The resulting scheme ensures the fulfillment of the fundamental conservation laws at the difference level, and its algorithmic structure is well suited for parallelization. [ABSTRACT FROM AUTHOR]