Manycore Algorithms for Batch Scalar and Block Tridiagonal Solvers

Laszlo, Endre; Giles, Michael B.; Appleyard, Jeremy

doi:10.1145/2830568

Cited by 18 publications

(14 citation statements)

References 22 publications

(22 reference statements)

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“…In this article we investigate the state-of-the-art in multicore/many-core algorithms for tridiagonal solvers for distributed-memory systems and re-examine the algorithmic trade-offs required at increasing machine scale to achieve good performance. The insights lead to the development of a new, highly scalable implementation extending the singlenode work of László et al [1].…”

Section: Introductionmentioning

confidence: 94%

“…They offer significant opportunities for exploiting the massive parallelism available on modern multicore CPU and many-core GPU devices. With the advent of such hardware, recent work [1] reexamined the choice between different tridiagonal solution algorithms (Thomas [2], PCR [3] and Hybrid). However, many real-world problems require such algorithms to work efficiently over multiple CPU/GPU devices due to the need for compute and memory resources beyond a single node.…”

Section: Introductionmentioning

confidence: 99%

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Scalable Many-Core Algorithms for Tridiagonal Solvers

et al. 2022

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Scalable Many-Core Algorithms for Tridiagonal Solvers

et al. 2022

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“…Since the Hines matrices are well-conditioned by definition, the computationally expensive operations like pivoting are not necessary. We can find multiple works for fast resolution on well-conditioned tridiagonal systems, such as the aforementioned work of Zhang et al [31] and the work by László et al [32]. Both works based on the use of a hybrid method to solve the tridiagonal systems, the first one is based on PCR-CR and the second one is based on PCR-Thomas.…”

Section: Related Workmentioning

confidence: 99%

Simulating the behavior of the Human Brain on GPUs

Valero-Lara

Martínez-Pérez

Sirvent

et al. 2018

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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The simulation of the behavior of the Human Brain is one of the most important challenges in computing today. The main problem consists of finding efficient ways to manipulate and compute the huge volume of data that this kind of simulations need, using the current technology. In this sense, this work is focused on one of the main steps of such simulation, which consists of computing the Voltage on neurons’ morphology. This is carried out using the Hines Algorithm and, although this algorithm is the optimum method in terms of number of operations, it is in need of non-trivial modifications to be efficiently parallelized on GPUs. We proposed several optimizations to accelerate this algorithm on GPU-based architectures, exploring the limitations of both, method and architecture, to be able to solve efficiently a high number of Hines systems (neurons). Each of the optimizations are deeply analyzed and described. Two different approaches are studied, one for mono-morphology simulations (batch of neurons with the same shape) and one for multi-morphology simulations (batch of neurons where every neuron has a different shape). In mono-morphology simulations we obtain a good performance using just a single kernel to compute all the neurons. However this turns out to be inefficient on multi-morphology simulations. Unlike the previous scenario, in multi-morphology simulations a much more complex implementation is necessary to obtain a good performance. In this case, we must execute more than one single GPU kernel. In every execution (kernel call) one specific part of the batch of the neurons is solved. These parts can be seen as multiple and independent tridiagonal systems. Although the present paper is focused on the simulation of the behavior of the Human Brain, some of these techniques, in particular those related to the solving of tridiagonal systems, can be also used for multiple oil and gas simulations. Our studies have proven that the optimizations proposed in the present work can achieve high performance on those computations with a high number of neurons, being our GPU implementations about 4× and 8× faster than the OpenMP multicore implementation (16 cores), using one and two NVIDIA K80 GPUs respectively. Also, it is important to highlight that these optimizations can continue scaling, even when dealing with a very high number of neurons.

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“…Another single-GPU implementation for the block-tridiagonal case was done in [30], whose authors tested a variety of block and matrix sizes, showing that better performance is obtained with systems with relatively large block sizes by better utilizing the available GPU threads. Recently, a comparison of the classical solvers, including the Thomas algorithm (a specialized Gaussian elimination for tridiagonal systems), was addressed in [31], implementing them on CPU, many integrated cores (MIC) architecture and GPU accelerators for the case of using a single node.…”

Section: Implementationsmentioning

confidence: 99%

MPI-CUDA parallel linear solvers for block-tridiagonal matrices in the context of SLEPc’s eigensolvers

Daviña

Román

2018

Parallel Computing

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We consider the computation of a few eigenpairs of a generalized eigenvalue problem Ax = λBx with block-tridiagonal matrices, not necessarily symmetric, in the context of Krylov methods. In this kind of computation, it is often necessary to solve a linear system of equations in each iteration of the eigensolver, for instance when B is not the identity matrix or when computing interior eigenvalues with the shift-and-invert spectral transformation. In this work, we aim to compare different direct linear solvers that can exploit the block-tridiagonal structure. Block cyclic reduction and the Spike algorithm are considered. A parallel implementation based on MPI is developed in the context of the SLEPc library. The use of GPU devices to accelerate local computations shows to be competitive for large block sizes.

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Manycore Algorithms for Batch Scalar and Block Tridiagonal Solvers

Cited by 18 publications

References 22 publications

Scalable Many-Core Algorithms for Tridiagonal Solvers

Scalable Many-Core Algorithms for Tridiagonal Solvers

Simulating the behavior of the Human Brain on GPUs

MPI-CUDA parallel linear solvers for block-tridiagonal matrices in the context of SLEPc’s eigensolvers

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