Tridiagonal matrix algorithm

Abstract: The solving of tridiagonal systems is one of the most computationally expensive parts in many applications, so that multiple studies have explored the use of NVIDIA GPUs to accelerate such computation. However, these studies have mainly focused on using parallel algorithms to compute such systems, which can efficiently exploit the shared memory and are able to saturate the GPUs capacity with a low number of systems, presenting a poor scalability when dealing with a relatively high number of systems. We propose a new implementation (cuThomasBatch) based on the Thomas algorithm. To achieve a good scalability using this approach is necessary to carry out a transformation in the way that the inputs are stored in memory to exploit coalescence (contiguous threads access to contiguous memory locations). The results given in this study proves that the implementation carried out in this work is able to beat the reference code when dealing with a relatively large number of Tridiagonal systems (2,000–256,000), being closed to \(3{\times }\) (in double precision) and \(4{\times }\) (in single precision) faster using one Kepler NVIDIA GPU.

Abstract: A mathematical model is developed for solar drying of green peas (Botanical name: Pisum Sativum). The problem is solved assuming the shape of the green peas is spherical. The governing transient mass transfer equation is discretized into finite difference scheme. The time marching is performed by implicit scheme. The governing equations and boundary conditions are non-dimensionalized to get generic results. The product in the chamber is in contact with air which is heated by solar energy, so the boundary conditions of third kind (convective boundary conditions) are considered. By space and time discretization a set of algebraic equations are generated and these algebraic equations are solved by tridiagonal matrix algorithm. A computer code is developed in MATLAB in order to compute the transient moisture content distribution inside the product. Center point, boundary and mean moisture of green peas are estimated at different temperatures and drying time. Present numerical result is compared with experimental result from literature and it was found that there is a good agreement of results. The drying time is predicted for how quickly the mean moisture of green peas is reached to 50, 40, 30, 20 and 10% of its initial moisture corresponding to different temperatures.

Abstract: A vorticity-velocity formulation of the Navier-Stokes equations is employed for the solution of natural-convection-dominated melting problems. Body-fitted coordinates are used for mapping the irregular shape of the timewise-changing solid-liquid interface. The quasi-stationary approximation is adopted for tracking the phase front, and a direct solution procedure is used for solving simultaneously the dependent flow variables along a grid line using a block tridiagonal matrix algorithm. The method is evaluated based on solving a test problem involving the melting of gallium. Results show excellent agreement with other numerical results. The method is an attractive alternative for cases in which the vorticity-streamfunction formulation has severe limitations.