Preliminary Implementation of PETSc Using GPUs

Minden, Victor; Barry, Smith; Knepley, Matthew G.

doi:10.1007/978-3-642-16405-7_7

Cited by 37 publications

(33 citation statements)

References 16 publications

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“…Later, support was extended for sparse matrix operations via CUSPARSE. The GPU model considered in PETSc uses MPI for communication between different processes, each of them having access to a single GPU [7]. The implementation includes mechanisms to guarantee coherence of the mirrored data-structures in the host and the device.…”

Section: Slepc Solvers On Gpumentioning

confidence: 99%

GPU Implementation of Krylov Solvers for Block-Tridiagonal Eigenvalue Problems

Daviña

Román

2016

Parallel Processing and Applied Mathematics

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Abstract. In an eigenvalue problem defined by one or two matrices with block-tridiagonal structure, if only a few eigenpairs are required it is interesting to consider iterative methods based on Krylov subspaces, even if matrix blocks are dense. In this context, using the GPU for the associated dense linear algebra may provide high performance. We analyze this in an implementation done in the context of SLEPc, the Scalable Library for Eigenvalue Problem Computations. In the case of a generalized eigenproblem or when interior eigenvalues are computed with shift-andinvert, the main computational kernel is the solution of linear systems with a block-tridiagonal matrix. We explore possible implementations of this operation on the GPU, including a block cyclic reduction algorithm.

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Section: Slepc Solvers On Gpumentioning

confidence: 99%

GPU Implementation of Krylov Solvers for Block-Tridiagonal Eigenvalue Problems

Daviña

Román

2016

Parallel Processing and Applied Mathematics

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“…This is an open-source C++ library that provides a high level template implementation of sparse linear solvers. CUSP is used by PETSc [5] within its GPU component [17]. We use an example implementation of GMRES from CUSP that uses a single GPU.…”

Section: Impact On Sparse Iterative Solvermentioning

confidence: 99%

High Performance Multi-GPU SpMV for Multi-component PDE-Based Applications

Abdelfattah

Ltaief

Keyes

2015

Lecture Notes in Computer Science

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Abstract. Leveraging optimization techniques (e.g., register blocking and double buffering) introduced in the context of KBLAS, a Level 2 BLAS high performance library on GPUs, the authors implement dense matrix-vector multiplications within a sparse-block structure. While these optimizations are important for high performance dense kernel executions, they are even more critical when dealing with sparse linear algebra operations. The most time-consuming phase of many multicomponent applications, such as models of reacting flows or petroleum reservoirs, is the solution at each implicit time step of large, sparse spatially structured or unstructured linear systems. The standard method is a preconditioned Krylov solver. The Sparse Matrix-Vector multiplication (SpMV) is, in turn, one of the most time-consuming operations in such solvers. Because there is no data reuse of the elements of the matrix within a single SpMV, kernel performance is limited by the speed at which data can be transferred from memory to registers, making the bus bandwidth the major bottleneck. On the other hand, in case of a multi-species model, the resulting Jacobian has a dense block structure. For contemporary petroleum reservoir simulations, the block size typically ranges from three to a few dozen among different models, and still larger blocks are relevant within adaptively model-refined regions of the domain, though generally the size of the blocks, related to the number of conserved species, is constant over large regions within a given model. This structure can be exploited beyond the convenience of a block compressed row data format, because it offers opportunities to hide the data motion with useful computations. The new SpMV kernel outperforms existing state-of-the-art implementations on single and multi-GPUs using matrices with dense block structure representative of porous media applications with both structured and unstructured multi-component grids.

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“…The third library we used was the preliminary implementation of PETSc for the CUDA architecture presented in Minden et al (2010). With the help of the Thrust and Cusp libraries, a large part of the PETSc Vector and some parts of the Matrix class have been implemented.…”

Section: Librariesmentioning

confidence: 99%

“…With the help of the Thrust and Cusp libraries, a large part of the PETSc Vector and some parts of the Matrix class have been implemented. The fundamental problems of interaction of PETSc with the GPU have been resolved, but only the routines that were necessary for the example treated in Minden et al (2010) have been implemented. Basically this "PETSc GPU" extends the built-in structures by a value that indicates in which memory the most recent data are stored.…”

Section: Librariesmentioning

confidence: 99%

Porting marine ecosystem model spin-up using transport matrices to GPUs

2013

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Abstract.We have ported an implementation of the spin-up for marine ecosystem models based on transport matrices to graphics processing units (GPUs). The original implementation was designed for distributed-memory architectures and uses the Portable, Extensible Toolkit for Scientific Computation (PETSc) library that is based on the Message Passing Interface (MPI) standard. The spin-up computes a steady seasonal cycle of ecosystem tracers with climatological ocean circulation data as forcing. Since the transport is linear with respect to the tracers, the resulting operator is represented by matrices. Each iteration of the spin-up involves two matrixvector multiplications and the evaluation of the used biogeochemical model. The original code was written in C and Fortran. On the GPU, we use the Compute Unified Device Architecture (CUDA) standard, a customized version of PETSc and a commercial CUDA Fortran compiler. We describe the extensions to PETSc and the modifications of the original C and Fortran codes that had to be done. Here we make use of freely available libraries for the GPU. We analyze the computational effort of the main parts of the spin-up for two exemplar ecosystem models and compare the overall computational time to those necessary on different CPUs. The results show that a consumer GPU can compete with a significant number of cluster CPUs without further code optimization.

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Preliminary Implementation of PETSc Using GPUs

Cited by 37 publications

References 16 publications

GPU Implementation of Krylov Solvers for Block-Tridiagonal Eigenvalue Problems

GPU Implementation of Krylov Solvers for Block-Tridiagonal Eigenvalue Problems

High Performance Multi-GPU SpMV for Multi-component PDE-Based Applications

Porting marine ecosystem model spin-up using transport matrices to GPUs

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