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...tation Kernel fusion is based on the multi-stage formulation of algorithms for the RA operators. Multi-stage algorithms are common to sorting [31], pattern matching [39], algebraic multi-grid solvers =-=[5]-=-, or compression [17]. This formulation is popular for GPU algorithms in particular since it enables one to separate the structured components of the algorithm from the irregular or unstructured compo...

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... using the nonlinear conjugate gradient method and the required gradient computations were performed using algorithmic differentiation [31,32] with GPU-acceleratedssparse vector and matrix operations =-=[33]-=-. The unknown scale factor between source power and pixelsintensities was calibrated using a phantom withsknown homogeneous scattering (8 cm-1) and negligible absorption (0.1 cm-1). Minimization of th...

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...xtensive research has been devoted to improving the performance of parallel coarsening algorithms, leading to notable improvements on CPU architectures [9, 28, 27, 21, 11, 8, 22, 28], on a single GPU =-=[3, 26, 19]-=-, and on multiple GPUs [12], the setup phase is still considered a bottleneck in parallel AMG methods. We mention the work in [3], where a smoothed aggregation setup is developed in CUDA for GPUs. Key...

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...eral Krylov solvers and ILU preconditioner were implemented on GPU. Haase et al. developed a parallel AMG solvers using a GPU cluster [12]. Researchers from NVIDIA also developed an AMG solver on GPU =-=[9, 13]-=-. The setup and solving phases were both run on GPU, which made their AMG very fast. Chen et al. from University of Calgary designed a new matrix format HEC (Hybrid of Ell and CSR), fast SpMV kernel [...

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... is also used in scientific computing. For instance, it is often a performance bottleneck for Algebraic Multigrid (AMG), where it is used in the setup phase for restricting and interpolating matrices =-=[7]-=-. Schur complement methods in hybrid linear solvers [49] also require fast SpGEMM. In electronic structure calculations, linear-scaling methods exploit Kohn’s “nearsightedness” principle of electrons ...

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...cation has a lower execution time for Section 1, as shown in Fig. 6. This is due to the fact that the GPU architecture is more suitable for fine-grained data parallelism, as opposed to multicore CPUs =-=[12]-=-. Fig. 6 shows that, however, coarse-grained parallelism offers a lower execution time for Section 3. This is essentially due to the structure of the last section, which consists of an outer loop nest...

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...lacian [5]. This approach is orthogonal to our implemented optimizations and their technique could be incorporated in future work. Studies have explored the performance of algebraic multigrid on GPUs =-=[1]-=-, [2], while Sturmer et al. examined geometric multigrid [25]. Perhaps the most closely related work is that performed in Treibig’s, which implements a 2D GSRB on SIMD architectures by separating and ...

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...amount of algorithmic innovation. 2. Related Work We explore the Geometric Multigrid on GPU’s. Bell et al. have explored the performance of algebraic (sparse rather than structured) multigrid on GPUs =-=[9]-=-. Sellapa et al. explore constant coefficient elliptical partial differential equations on structured grids [11]. Perhaps the most closely related work is that performed in Treibig’s, which implements...

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... parallel implementations of algebraic multigrid target finescale parallelism as required on clusters of GPUs, where the problem must be split into many independent threads to obtain good performance =-=[26]-=-, [27], [28]. Finally, we briefly contrast AMG and GMG approaches. The advantages of AMG are that it can be used as a blackbox algorithm and does not require geometry or mesh information (except for t...

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...le Paralution [33], VexCL [44], or ViennaCL [45]. A substantial amount of research has been conducted on various preconditioning techniques for iterative solvers on GPUs including algebraic multigrid =-=[6, 13, 34, 46]-=-, incomplete factorizations [23, 30], or sparse approximate inverses [10, 25, 40]. Nevertheless, hardware-efficient and scalable black-box preconditioners for GPUs are not available, but instead the u...