Sparse approximate inverse preconditioners on high performance GPU platforms

Simulation with models based on partial differential equations often requires the solution of (sequences of) large and sparse algebraic linear systems. In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these duties. Therefore, the search for efficient preconditioners for Krylov subspace methods is a crucial theme. Recent developments, especially in computing hardware, have renewed the interest in approximate inverse preconditioners in factorized form, because their application during the solution process can be more efficient. We present here some experiences focused on the approximate inverse preconditioners proposed by Benzi and Tůma from 1996 and the sparsification and inversion proposed by van Duin in 1999. Computational costs, reorderings and implementation issues are considered both on conventional and innovative computing architectures like Graphics Programming Units (GPUs)

Multi-GPU acceleration of large-scale density-based topology optimization

This work presents a parallel implementation of density-based topology optimization using distributed GPU computing systems. The use of multiple GPU devices allows us accelerating the computing process and increasing the device memory available for GPU computing. This increment of device memory enables us to address large models that commonly do not fit into one GPU device. The most modern scientific computers incorporate these devices to design energy-efficient, low-cost, and high-computing power systems. However, we should adopt the proper techniques to take advantage of the computational resources of such high-performance many-core computing systems. It is well-known that the bottleneck of density-based topology optimization is the solving of the linear elasticity problem using Finite Element Analysis (FEA) during the topology optimization iterations. We solve the linear system of equations obtained from FEA using a distributed conjugate gradient solver preconditioned by a smooth aggregation-based algebraic multigrid (AMG) using GPU computing with multiple devices. The use of aggregation-based AMG reduces memory requirements and improves the efficiency of the interpolation operation. This fact is rewarding for GPU computing. We evaluate the performance and scalability of the distributed GPU system using structured and unstructured meshes. We also test the performance using different 3D finite elements and relaxing operators. Besides, we evaluate the use of numerical approaches to increase the topology optimization performance. Finally, we present a comparison between the many-core computing instance and one efficient multi-core implementation to highlight the advantages of using GPU computing in large-scale density-based topology optimization problems.This work has been supported by the AEI/FEDER and UE under the contract DPI2016-77538-R, and by the “Fundación Séneca – Agencia de Ciencia y Tecnología de la Región de Murcia” of Spain under the contract 20911/PI/18

Fast On-line Statistical Learning on a GPGPU

On-line Machine Learning using Stochastic Gradient Descent is an inherently sequential computation. This makes it difficult to improve performance by simply employing parallel architectures. Langford et al. made a modification to the standard stochastic gradient descent approach which opens up the possibility of parallel computation. They also proved that there is no significant loss in accuracy in their approach. They did empirically demonstrate the performance gain in speed for the case of a pipelined architecture with a few processing units. In this paper we report on applying the Langford et al. approach on a General Purpose Graphics Processing Unit (GPGPU) with a large number of processing units. We accelerate the learning speed by approximately 4.5 times compared to a standard single threaded approach with comparable accuracy. We also evaluate the GPU performance for the sequential variant of the algorithm, which has not previously been reported. Finally, we investigate how changes in the number of threads, number of blocks, and amount of delay, effects the overall performance and accuracy