Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. In this work, we ...

• Matrix-free algorithms for FE matrix-multivector products with thousands of vectors on multi-node CPU and GPU architectures.
• Hardware-tuned batched evaluation strategies for improved data locality.
• Architecture-specific ...

We propose a methodology to address the programmability issues derived from the emergence of new-generation shared-memory NUMA architectures. For this purpose, we employ dense matrix factorizations and matrix inversion (DMFI) as a use ...

• Exposure of the performance penalty introduced by NUMA-oblivious implementations.

• We introduce PIPECG-OATI-c to solve complex Hermitian and symmetric linear systems.

Preconditioned Conjugate Gradient (PCG) is a popular method for solving large and sparse linear systems of equations. The performance of PCG at scale is affected due to the costly global synchronization steps that arise in dot-products ...

This paper contains the results of research on the general matrix multiplication routine performance on modern heterogeneous computing systems. In addition to the single-threaded and multi-threaded performance of the routine for ...

• The performance of GEMM routines on heterogeneous computing systems has been studied.

In this work we have implemented a novel Linear Algebra Library on top of the task-based runtime OmpSs-2. We have used some of the most advanced OmpSs-2 features; weak dependencies and regions, together with the final clause for the ...

• Development of a highly optimized auto-tuned library for BLAS-3 and LAPACK operations.

We investigate the iterative solution of a symmetric positive definite linear system involving the shifted Laplacian as the system matrix on General Purpose Graphics Processing Units (GPGPUs). We consider in particular the Chebyshev ...

• Solution of batched tridiagonal linear systems on GPUs.
• Problems originating ...

The sparse matrix–vector multiply (SpMV) operation is a key computational kernel in many simulations and linear solvers. The large communication requirements associated with a reference implementation of a parallel SpMV result in poor ...

This work optimizes tensor-times-dense matrix multiply (Ttm) for general sparse and semi-sparse tensors on CPU and NVIDIA GPU platforms. Ttm is a computational kernel in tensor methods-based data analytics and data mining applications, ...

• Designed an in-place SpTTM algorithm to avoid tensor-matrix data transformation.

Asynchronous iterative methods for solving linear systems are gaining renewed interest due to the high cost of synchronization points in massively parallel codes. Historically, theory on asynchronous iterative methods has focused on ...

• We study the asynchronous Jacobi (AJ) method for solving sparse linear systems.

When using incomplete factorization preconditioners with an iterative method to solve large sparse linear systems, each application of the preconditioner involves solving two sparse triangular systems. These triangular systems are ...

• Jacobi solvers for sparse incomplete factor preconditioning are extensively tested.

This paper presents a new procedure to compute many or all of the eigenvalues and eigenvectors of symmetric Toeplitz matrices. The key to this algorithm is the use of the ''Shift-and-Invert'' technique applied with iterative methods, which allows the ...

The Singular Value Decomposition (SVD) is a vital problem that finds a place in numerous application domains in science and engineering. As an example, SVDs are used in processing voluminous datasets. Many sequential and parallel algorithms have been ...

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block tridiagonal divide-and-conquer algorithm for computing ...

The main results of this paper are based on the idea that most load balancing algorithms can be described in the framework of optimization theory. It enables to involve classical results linked with convergence, its speed and other elements. We ...

The solution of linear and nonlinear convection-diffusion problems via parallel subdomain methods is considered. MPI implementation of parallel Schwarz alternating methods on distributed memory multiprocessors is discussed. Parallel synchronous and ...

Several message passing-based parallel solvers have been developed for general (non-symmetric) sparse LU factorization with partial pivoting. Existing solvers were mostly deployed and evaluated on parallel computing platforms with high message passing ...

This paper investigates the computation of matrix product on both partially pipelined and fully pipelined modular linear arrays. These investigations are guided by a constructive and unified approach for both target architectures. First, permissible ...

We present a class of parallel preconditioning strategies utilizing multilevel block incomplete LU (ILU) factorization techniques to solve large sparse linear systems. The preconditioners are constructed by exploiting the concept of block independent ...

In this paper, we propose a generic method of automatic parallelization for sparse matrix computation. This method is based on both a refinement of the data-dependence test proposed by Bernstein and an inspector-executor scheme which is specialized to ...

This paper examines the explicit communication characteristics of several sophisticated scientific applications, which, by themselves, constitute a representative suite of publicly available benchmarks for large cluster architectures. By focusing on the ...