Pub Date : 2023-07-31DOI: 10.1007/s42967-023-00287-5
Yann-Meing Law, Daniel Appelö
The Hermite-Taylor method, introduced in 2005 by Goodrich et al. is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately, its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor correction function method (CFM), which provides exactly such a systematic approach for handling boundary conditions. Here we focus on Maxwell’s equations but note that the method is easily extended to other hyperbolic problems.
{"title":"The Hermite-Taylor Correction Function Method for Maxwell’s Equations","authors":"Yann-Meing Law, Daniel Appelö","doi":"10.1007/s42967-023-00287-5","DOIUrl":"https://doi.org/10.1007/s42967-023-00287-5","url":null,"abstract":"The Hermite-Taylor method, introduced in 2005 by Goodrich et al. is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately, its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor correction function method (CFM), which provides exactly such a systematic approach for handling boundary conditions. Here we focus on Maxwell’s equations but note that the method is easily extended to other hyperbolic problems.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135155520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-25DOI: 10.1007/s42967-023-00285-7
J. Hunter, Zheng Sun, Y. Xing
{"title":"Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation","authors":"J. Hunter, Zheng Sun, Y. Xing","doi":"10.1007/s42967-023-00285-7","DOIUrl":"https://doi.org/10.1007/s42967-023-00285-7","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83020908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-20DOI: 10.1007/s42967-023-00284-8
Bohan Chen, Kevin Miller, A. Bertozzi, Jon Schwenk
{"title":"Batch Active Learning for Multispectral and Hyperspectral Image Segmentation Using Similarity Graphs","authors":"Bohan Chen, Kevin Miller, A. Bertozzi, Jon Schwenk","doi":"10.1007/s42967-023-00284-8","DOIUrl":"https://doi.org/10.1007/s42967-023-00284-8","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"59 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77880829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-17DOI: 10.1007/s42967-023-00292-8
P. Bakhvalov, M. Surnachev
{"title":"On the Order of Accuracy of Edge-Based Schemes: a Peterson-Type Counter-Example","authors":"P. Bakhvalov, M. Surnachev","doi":"10.1007/s42967-023-00292-8","DOIUrl":"https://doi.org/10.1007/s42967-023-00292-8","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"186 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84266471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-11DOI: 10.1007/s42967-023-00279-5
F. Zheng, J. Qiu
{"title":"Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws","authors":"F. Zheng, J. Qiu","doi":"10.1007/s42967-023-00279-5","DOIUrl":"https://doi.org/10.1007/s42967-023-00279-5","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"11 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89458557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-10DOI: 10.1007/s42967-023-00281-x
Baiying Dong, Zhilin Li, Juan Ruiz-Álvarez
{"title":"A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces","authors":"Baiying Dong, Zhilin Li, Juan Ruiz-Álvarez","doi":"10.1007/s42967-023-00281-x","DOIUrl":"https://doi.org/10.1007/s42967-023-00281-x","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74996242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-20DOI: 10.1007/s42967-023-00273-x
Nicholas Richardson, Hayden Schaeffer, Giang Tran
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The randomization is both in the time window locations and the frequency sampling, which lowers the overall sampling and computational cost. The sparsification of the spectrogram leads to a sharp separation between time-frequency clusters which makes it easier to identify intrinsic modes, and thus leads to a new data-driven mode decomposition. The applications include signal representation, outlier removal, and mode decomposition. On benchmark tests, we show that our approach outperforms other state-of-the-art decomposition methods.
{"title":"SRMD: Sparse Random Mode Decomposition","authors":"Nicholas Richardson, Hayden Schaeffer, Giang Tran","doi":"10.1007/s42967-023-00273-x","DOIUrl":"https://doi.org/10.1007/s42967-023-00273-x","url":null,"abstract":"Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The randomization is both in the time window locations and the frequency sampling, which lowers the overall sampling and computational cost. The sparsification of the spectrogram leads to a sharp separation between time-frequency clusters which makes it easier to identify intrinsic modes, and thus leads to a new data-driven mode decomposition. The applications include signal representation, outlier removal, and mode decomposition. On benchmark tests, we show that our approach outperforms other state-of-the-art decomposition methods.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"275 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135091053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-19DOI: 10.1007/s42967-023-00271-z
L. Araki, Rafael Borges, N. P. D. da Silva, Chi-Wang Shu
{"title":"Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows","authors":"L. Araki, Rafael Borges, N. P. D. da Silva, Chi-Wang Shu","doi":"10.1007/s42967-023-00271-z","DOIUrl":"https://doi.org/10.1007/s42967-023-00271-z","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87391822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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