In this article, we explore the acceleration of tensor product operations in finite element methods, leveraging the computational power of the NVIDIA A100 GPU Tensor Cores. We provide an accessible overview of the necessary mathematical background and ...

Compact schemes are often preferred in performing scientific computing for their superior spectral resolution. Error-free parallelization of a compact scheme is a challenging task due to the requirement of additional closures at the inter-processor ...

Sparse matrix-vector multiplication (SpMV) operations are commonly used in various scientific and engineering applications. The performance of the SpMV operation often depends on exploiting regularity patterns in the matrix. Various representations and ...

A new accuracy-preserving parallel algorithm employing compact schemes is presented for direct numerical simulation of the Navier-Stokes equations. Here the connotation of accuracy preservation is having the same level of accuracy obtained by the ...

Traditional solution approaches for problems in quantum mechanics scale as O(M³), where M is the number of electrons. Various methods have been proposed to address this issue and obtain a linear scaling O(M). One promising formulation is the direct ...

Efficient processing of Irregular Matrices on Single Instruction, Multiple Data (SIMD)-type architectures is a persistent challenge. Resolving it requires innovations in the development of data formats, computational techniques, and implementations that ...

We describe the application of a communication-reduction technique for the PageRank algorithm that dynamically adapts the precision of the data access to the numerical requirements of the algorithm as the iteration converges. Our variable-precision ...

This article presents matrix-free finite-element techniques for efficiently solving partial differential equations on modern many-core processors, such as graphics cards. We develop a GPU parallelization of a matrix-free geometric multigrid iterative ...

We investigate outer-product--parallel, inner-product--parallel, and row-by-row-product--parallel formulations of sparse matrix-matrix multiplication (SpGEMM) on distributed memory architectures. For each of these three formulations, we propose a ...

This article derives trade-offs between three basic costs of a parallel algorithm: synchronization, data movement, and computational cost. These trade-offs are lower bounds on the execution time of the algorithm that are independent of the number of ...

We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes both the ...

We present a new online algorithm for profit-oriented scheduling on multiple speed-scalable processors and provide a tight analysis of the algorithm’s competitiveness. Our results generalize and improve upon work by Chan et al. [2010], which considers a ...

We present an algorithm for inversion of symmetric positive definite matrices that combines the practical requirement of an optimal number of arithmetic operations and the theoretical goal of a polylogarithmic critical path length. The algorithm reduces ...

Next-generation HPC computing platforms are likely to be characterized by significant, unpredictable nonuniformities in execution time among compute nodes and cores. The resulting load imbalances from this nonuniformity are expected to arise from a ...

The running time of an algorithm depends on both arithmetic and communication (i.e., data movement) costs, and the relative costs of communication are growing over time. In this work, we present sequential and distributed-memory parallel algorithms for ...