用于离散源和连续源的自适应快速高斯变换新版本

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2024-05-09 DOI:10.1137/23m1572453

Leslie F. Greengard, Shidong Jiang, Manas Rachh, Jun Wang

{"title":"用于离散源和连续源的自适应快速高斯变换新版本","authors":"Leslie F. Greengard, Shidong Jiang, Manas Rachh, Jun Wang","doi":"10.1137/23m1572453","DOIUrl":null,"url":null,"abstract":"SIAM Review, Volume 66, Issue 2, Page 287-315, May 2024. <br/> We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a new hierarchical merging scheme. For continuous source distributions sampled on adaptive tensor product grids, we exploit the separable structure of the Gaussian kernel to accelerate the computation. For discrete sources, the scheme relies on the nonuniform fast Fourier transform (NUFFT) to construct near field plane-wave representations. The scheme has been implemented for either free-space or periodic boundary conditions. In many regimes, the speed is comparable to or better than that of the conventional FFT in work per grid point, despite being fully adaptive.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"27 1","pages":""},"PeriodicalIF":10.8000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Version of the Adaptive Fast Gauss Transform for Discrete and Continuous Sources\",\"authors\":\"Leslie F. Greengard, Shidong Jiang, Manas Rachh, Jun Wang\",\"doi\":\"10.1137/23m1572453\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Review, Volume 66, Issue 2, Page 287-315, May 2024. <br/> We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a new hierarchical merging scheme. For continuous source distributions sampled on adaptive tensor product grids, we exploit the separable structure of the Gaussian kernel to accelerate the computation. For discrete sources, the scheme relies on the nonuniform fast Fourier transform (NUFFT) to construct near field plane-wave representations. The scheme has been implemented for either free-space or periodic boundary conditions. In many regimes, the speed is comparable to or better than that of the conventional FFT in work per grid point, despite being fully adaptive.\",\"PeriodicalId\":49525,\"journal\":{\"name\":\"SIAM Review\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":10.8000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Review\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1572453\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Review","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1572453","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

SIAM Review》，第 66 卷第 2 期，第 287-315 页，2024 年 5 月。我们提出了一种适用于离散源和连续源的新版快速高斯变换（FGT）。它完全避免了经典的赫米特展开，只使用了高斯核的平面波表示和一种新的分层合并方案。对于在自适应张量乘网格上采样的连续源分布，我们利用高斯核的可分离结构来加速计算。对于离散源，该方案依靠非均匀快速傅立叶变换（NUFFT）来构建近场平面波表示。该方案已在自由空间或周期性边界条件下实施。在许多情况下，尽管是完全自适应的，但在每个网格点的工作量上，其速度与传统的 FFT 相当，甚至更好。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A New Version of the Adaptive Fast Gauss Transform for Discrete and Continuous Sources

SIAM Review, Volume 66, Issue 2, Page 287-315, May 2024.
We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a new hierarchical merging scheme. For continuous source distributions sampled on adaptive tensor product grids, we exploit the separable structure of the Gaussian kernel to accelerate the computation. For discrete sources, the scheme relies on the nonuniform fast Fourier transform (NUFFT) to construct near field plane-wave representations. The scheme has been implemented for either free-space or periodic boundary conditions. In many regimes, the speed is comparable to or better than that of the conventional FFT in work per grid point, despite being fully adaptive.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.