Low-Storage Integral Deferred Correction Methods for Scientific Computing

Crockatt, Michael; Christlieb, Andrew

doi:10.1137/18m117368x

Cited by 3 publications

(3 citation statements)

References 30 publications

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“…1 that is still fully computed with values from correction step k, although for ι < l, the values w n,[k+1],ι are readily available. If we consider a Gauss-Seidel type approach, similar to the one found in [19], we change this so that in I l , we replace w n,[k],ι by w n,[k+1],ι for ι < l. Here, we show that that this not only leads to a more accurate scheme, but it is also lower storage.…”

Section: Improved Algorithm and Scaling Resultsmentioning

confidence: 87%

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Parallel-in-time high-order multiderivative IMEX solvers

Schütz¹,

Seal²,

Zeifang³

2021

Preprint

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In this work, we present a novel class of parallelizable high-order time integration schemes for the approximate solution of additive ODEs. The methods achieve high order through a combination of a suitable quadrature formula involving multiple derivatives of the ODE's right-hand side and a predictor-corrector ansatz. The latter approach is designed in such a way that parallelism in time is made possible. We present thorough analysis as well as numerical results that showcase scaling opportunities of methods from this class of solvers.

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Section: Improved Algorithm and Scaling Resultsmentioning

confidence: 87%

“…We call this modification "Gauß-Seidel style" as "better" information is used as soon as it is available [38]. Note that similar ideas have been pursued for an integral deferred correction method in [19].…”

Section: Influence Of the Modificationsmentioning

confidence: 99%

Parallel-in-time high-order multiderivative IMEX solvers

Schütz¹,

Seal²,

Zeifang³

2021

Preprint

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“…erefore, many graduates ignore innovation and entrepreneurship. With the development of science and technology, digital technology is changing people's lives, so innovation and entrepreneurship education should also keep pace with the times, using technology and information to study innovation and entrepreneurship [24].…”

Section: Discussionmentioning

confidence: 99%

The Application of Web‐Based Scientific Computing System in Innovation and Entrepreneurship

Cheng

2022

Discrete Dynamics in Nature and Society

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In the past ten years, the number of newly added labor forces in China has continued to grow. At the same time, with the increase in the number of university candidates, the number of university employments is also increasing. Due to employment pressure from society and alumni, the government promotes innovation and entrepreneurship and promotes innovative slogans through entrepreneurship. Universities have become the people who are concerned about this slogan. As an important tool for solving large-scale computer problems, scientific computing is increasingly used in various fields of science and engineering. With the development of high-performance computing technology, various parallel computers have appeared and are widely used. This article uses a scientific computing system to conduct research on innovation and entrepreneurship. The entire scientific computing system is a typical three-tier architecture, and the small service program is responsible for analyzing the scientific computing request in the request and generating related calculation expressions. Get the comprehensive evaluation level of innovation and entrepreneurship risk: excellent score is 3.45, good score is 2.56, general score is 1.68, and difference is 0.68.

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