首页|Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods

Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods

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Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.

Mixed precisionRunge-Kutta methodsAdditive methodsAccuracy

Ben Burnett、Sigal Gottlieb、Zachary J.Grant

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Center for Scientific Computing and Data Science Research,UMass Dartmouth,North Dartmouth,Massachusetts,USA

CSME,Michigan State University,East Lansing,Michigan,USA

ONR UMass Dartmouth Marine and UnderSea Technology(MUST)ONR UMass Dartmouth Marine and UnderSea Technology(MUST)美国能源部项目美国能源部项目美国空军科学研究办公室项目美国空军科学研究办公室项目Michigan State University美国空军科学研究办公室项目美国空军科学研究办公室项目美国能源部项目

N00014-20-1-2849S31320000049160DE-SC0023164RC114586-UMDFA9550-18-1-0383FA9550-23-1-0037FA9550-19-1-0281FA9550-18-1-0383DE-SC0023164

2024

10.1007/s42967-023-00315-4

应用数学与计算数学学报
上海大学

应用数学与计算数学学报

影响因子：0.165
ISSN：1006-6330
年,卷(期)：2024.6(1)
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