Moritz Kreutzer

A Unified Sparse Matrix Data Format for Efficient General Sparse Matrix-Vector Multiplication on Modern Processors with Wide SIMD Units

Sparse matrix-vector multiplication (spMVM) is the most time-consuming kernel in many numerical algorithms and has been studied extensively on all modern processor and accelerator architectures. However, the optimal sparse matrix data storage format is highly hardware-specific, which could become an obstacle when using heterogeneous systems. Also, it is as yet unclear how the wide single instruction multiple data (SIMD) units in current multi- and many-core processors should be used most efficiently if there is no structure in the sparsity pattern of the matrix. We suggest SELL-

Increasing the Performance of the Jacobi--Davidson Method by Blocking

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GHOST: Building Blocks for High Performance Sparse Linear Algebra on Heterogeneous Systems

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High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

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Performance Engineering of the Kernel Polynomal Method on Large-Scale CPU-GPU Systems

, a variant of Sliced ELLPACK, as a SIMD-friendly data format which combines long-standing ideas from general-purpose graphics processing units and vector computer programming. We discuss the advantages of SELL-

A SURVEY OF CHECKPOINT/RESTART TECHNIQUES ON DISTRIBUTED MEMORY SYSTEMS

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Optimization and performance evaluation of the IDR iterative Krylov solver on GPUs

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Building a Fault Tolerant Application Using the GASPI Communication Layer

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ESSEX - Equipping Sparse Solvers for Exascale

compared to established formats like Compressed Row Storage and ELLPACK and show its suitability on a variety of hardware platforms (Intel Sandy Bridge, Intel Xeon Phi, and Nvidia Tesla K20) for a wi...

Preconditioned Krylov Solvers on GPUs

Block variants of the Jacobi--Davidson method for computing a few eigenpairs of a large sparse matrix are known to improve the robustness of the standard algorithm when it comes to computing multiple or clustered eigenvalues. In practice, however, they are typically avoided because the total number of matrix-vector operations increases. In this paper we present the implementation of a block Jacobi--Davidson solver. By detailed performance engineering and numerical experiments we demonstrate that the increase in operations is typically more than compensated by performance gains through better cache usage on modern CPUs, resulting in a method that is both more efficient and robust than its single vector counterpart. The steps to be taken to achieve a block speedup involve both kernel optimizations for sparse matrix and block vector operations, and algorithmic choices to allow using blocked operations in most parts of the computation. We discuss the aspect of avoiding synchronization in the algorithm and sho...