{"title":"Interface Splitting Algorithm: A Parallel Solution to Diagonally Dominant Tridiagonal Systems","authors":"Arpiruk Hokpunna","doi":"10.3390/computation11090187","DOIUrl":null,"url":null,"abstract":"We present an interface-splitting algorithm (ITS) for solving diagonally dominant tridiagonal systems in parallel. The construction of the ITS algorithm profits from bidirectional links in modern networks, and it only needs one synchronization step to solve the system. The algorithm trades some necessary accuracy for better parallel performance. The accuracy and the performance of the ITS algorithm are evaluated on four different parallel machines of up to 2048 processors. The proposed algorithm scales very well, and it is significantly faster than the algorithm used in ScaLAPACK. The applicability of the algorithm is demonstrated in the three-dimensional simulations of turbulent channel flow at Reynolds number 41,430.","PeriodicalId":52148,"journal":{"name":"Computation","volume":"84 1","pages":"0"},"PeriodicalIF":1.9000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/computation11090187","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We present an interface-splitting algorithm (ITS) for solving diagonally dominant tridiagonal systems in parallel. The construction of the ITS algorithm profits from bidirectional links in modern networks, and it only needs one synchronization step to solve the system. The algorithm trades some necessary accuracy for better parallel performance. The accuracy and the performance of the ITS algorithm are evaluated on four different parallel machines of up to 2048 processors. The proposed algorithm scales very well, and it is significantly faster than the algorithm used in ScaLAPACK. The applicability of the algorithm is demonstrated in the three-dimensional simulations of turbulent channel flow at Reynolds number 41,430.
期刊介绍：
Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.
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