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 ...
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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. The gtsvStridedBatch routine in the cuSPARSE NVIDIA package is one of these examples, which is used as reference in this article. We propose a new implementation (cuthomasBatch) based on the thomas algorithm. Unlike other algorithms, the thomas algorithm is sequential, and so a coarse-grained approach is implemented where one CUDA thread solves a complete tridiagonal system instead of one CUDA block as in gtsvStridedBatch. To achieve a good scalability using this approach, it 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). Different variants regarding the transformation of the data are explored in detail. We also explore some variants for the case of variable batch, when the size of the systems of the batch has different size (cuthomasVBatch). The results given in this study prove that the implementations carried out in this work are able to beat the reference code, being up to 5x (in double precision) and 6x (in single precision) faster using the latest NVIDIA GPU architecture, the Pascal P100.
In the present paper, the modified cubic B-spline differential quadrature method (MCB-DQM) has been implemented for the numerical computation of two-dimensional biological population model (BPM). The method is based o...
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In the present paper, the modified cubic B-spline differential quadrature method (MCB-DQM) has been implemented for the numerical computation of two-dimensional biological population model (BPM). The method is based on differential quadrature in which the weighting coefficients are computed by using MCB as a set of basis functions. We present three test problems to confirm the efficiency and accuracy of the method for BPM, which shows that the MCB-DQM solutions are in good agreement with the results obtained by the recent schemes: improved element-free Galerkin method by Zhang et al. and element-free kp-Ritz method by Cheng et al. The order of convergence of MCB-DQM for the solutions of BPM is shown to be quadratic.
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