{"title":"基于STVDRK积分和SENO插值的球面对角方程自适应光线追踪方法","authors":"Wai Ming Chau, Shingyu Leung","doi":"10.1016/j.jcp.2025.114100","DOIUrl":null,"url":null,"abstract":"<div><div>We develop an efficient adaptive framework for obtaining high-order multivalued solutions to wavefront propagation problems on a unit sphere, as described by the surface eikonal equations. A key development in our approach is the reformulation of the conventional ray-tracing system, which typically tracks solutions in <span><math><mrow><msup><mi>S</mi><mn>2</mn></msup><mo>×</mo><msup><mi>R</mi><mn>3</mn></msup></mrow></math></span>, into a system of differential equations where the phase space is <span><math><mrow><msup><mi>S</mi><mn>2</mn></msup><mo>×</mo><msup><mi>S</mi><mn>2</mn></msup></mrow></math></span>. Central to our methodology are the SLERP Total Variation Diminishing Runge-Kutta (STVDRK) methods and Spherical Essentially Non-Oscillatory (SENO) interpolation techniques. These numerical innovations provide a robust adaptive strategy for modeling the evolution of the wavefront without relying on any projection steps. By effectively maintaining accuracy and stability while evolving solutions on the unit sphere, our framework significantly enhances the representation of evolving curves and improves the overall robustness of the numerical solutions. This adaptive approach significantly surpasses traditional methods, providing a way for more accurate modeling of wavefront propagation in complex geometries.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114100"},"PeriodicalIF":3.8000,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An adaptive ray-tracing method for eikonal equations on spheres using STVDRK integrators and SENO interpolations\",\"authors\":\"Wai Ming Chau, Shingyu Leung\",\"doi\":\"10.1016/j.jcp.2025.114100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We develop an efficient adaptive framework for obtaining high-order multivalued solutions to wavefront propagation problems on a unit sphere, as described by the surface eikonal equations. A key development in our approach is the reformulation of the conventional ray-tracing system, which typically tracks solutions in <span><math><mrow><msup><mi>S</mi><mn>2</mn></msup><mo>×</mo><msup><mi>R</mi><mn>3</mn></msup></mrow></math></span>, into a system of differential equations where the phase space is <span><math><mrow><msup><mi>S</mi><mn>2</mn></msup><mo>×</mo><msup><mi>S</mi><mn>2</mn></msup></mrow></math></span>. Central to our methodology are the SLERP Total Variation Diminishing Runge-Kutta (STVDRK) methods and Spherical Essentially Non-Oscillatory (SENO) interpolation techniques. These numerical innovations provide a robust adaptive strategy for modeling the evolution of the wavefront without relying on any projection steps. By effectively maintaining accuracy and stability while evolving solutions on the unit sphere, our framework significantly enhances the representation of evolving curves and improves the overall robustness of the numerical solutions. This adaptive approach significantly surpasses traditional methods, providing a way for more accurate modeling of wavefront propagation in complex geometries.</div></div>\",\"PeriodicalId\":352,\"journal\":{\"name\":\"Journal of Computational Physics\",\"volume\":\"537 \",\"pages\":\"Article 114100\"},\"PeriodicalIF\":3.8000,\"publicationDate\":\"2025-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021999125003833\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021999125003833","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
An adaptive ray-tracing method for eikonal equations on spheres using STVDRK integrators and SENO interpolations
We develop an efficient adaptive framework for obtaining high-order multivalued solutions to wavefront propagation problems on a unit sphere, as described by the surface eikonal equations. A key development in our approach is the reformulation of the conventional ray-tracing system, which typically tracks solutions in , into a system of differential equations where the phase space is . Central to our methodology are the SLERP Total Variation Diminishing Runge-Kutta (STVDRK) methods and Spherical Essentially Non-Oscillatory (SENO) interpolation techniques. These numerical innovations provide a robust adaptive strategy for modeling the evolution of the wavefront without relying on any projection steps. By effectively maintaining accuracy and stability while evolving solutions on the unit sphere, our framework significantly enhances the representation of evolving curves and improves the overall robustness of the numerical solutions. This adaptive approach significantly surpasses traditional methods, providing a way for more accurate modeling of wavefront propagation in complex geometries.
期刊介绍:
Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries.
The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.