About: Cache-Aware Matrix Polynomials

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Attributes	Values
type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	Cache-Aware Matrix Polynomials
Creator	Huber, Dominik Schreiber, Martin Schulz, Martin Yang, Dai
source	PMC
abstract	Efficient solvers for partial differential equations are among the most important areas of algorithmic research in high-performance computing. In this paper we present a new optimization for solving linear autonomous partial differential equations. Our approach is based on polynomial approximations for exponential time integration, which involves the computation of matrix polynomial terms ([Image: see text]) in every time step. This operation is very memory intensive and requires targeted optimizations. In our approach, we exploit the cache-hierarchy of modern computer architectures using a temporal cache blocking approach over the matrix polynomial terms. We develop two single-core implementations realizing cache blocking over several sparse matrix-vector multiplications of the polynomial approximation and compare it to a reference method that performs the computation in the traditional iterative way. We evaluate our approach on three different hardware platforms and for a wide range of different matrices and demonstrate that our approach achieves time savings of up to 50% for a large number of matrices. This is especially the case on platforms with large caches, significantly increasing the performance to solve linear autonomous differential equations.
has issue date	2020-05-26(xsd:dateTime)
bibo:doi	10.1007/978-3-030-50371-0_10
has license	no-cc
sha1sum (hex)	a03ae33bda7d338be38fe26e7bc210264b3c5f60
schema:url	https://doi.org/10.1007/978-3-030-50371-0_10
resource representing a document's title	Cache-Aware Matrix Polynomials
has PubMed Central identifier	PMC7302405
schema:publication	Computational Science - ICCS 2020
resource representing a document's body	covid:a03ae33bda7d338be38fe26e7bc210264b3c5f60#body_text
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