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Numerical analysis and computation for partial differential equations on surfaces

曲面偏微分方程的数值分析与计算

基本信息

批准号：
EP/G010404/1
负责人：
Charlie Elliott
金额：
$ 36.57万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2008
资助国家：
英国
起止时间：
2008 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FG010404%2F1
关键词：
Numerical analysis computation partial differential

项目摘要

This proposal is concerned with the numerical analysis and computation of partial differential equations on surfaces. There is a vast amount of research concerned with partial differential equations posed on domains in three space dimensions, say, but relatively very little on differential equations on hypersurfaces which may be the boundaries of bulk three dimensional domains. Such surface partial differential equations are of increasing importance in modelling complex surface processes in biology and materials. Traditionally equations on spheres arise in climate and weather modelling. Numerical methods in this setting can exploit the spherical geometry. However in the applications we have in mind, (eg cell biology, alloy surface dissolution, surfactants on fluid interfaces) the morpohology of the surface is arbitrary and may be complex. The challenges to be addressed in this project include:-mathematical analysis of degenerate equations related to discretization, hard numerical analysis, development of algorithms and application to complicated systems. The project is ambitious in scope because of the novelty and technicality of the mathematical problems and the scale of the applications. A PDRA will work closely with the PI on the adventurous complex problems and will receive advanced training in computational applied mathematics in an emerging and burgeoning area. Also involved will be two visiting researchers who are ongoing collaborators of the PI. The project will result in theorems concerning new methods, the development of algorithms and simulations of complex physical processes. Dissemination will be publication in high quality research articles and talks at conferences.

这个建议是关于曲面上偏微分方程的数值分析和计算。有大量的研究涉及偏微分方程的域上的三维空间，说，但相对很少的微分方程的超曲面，可能是边界的散装三维域。这种表面偏微分方程在模拟生物学和材料中的复杂表面过程中越来越重要。传统上，球面方程出现在气候和天气建模中。在这种情况下，数值方法可以利用球面几何。然而，在我们考虑的应用中（例如细胞生物学，合金表面溶解，流体界面上的表面活性剂），表面的形态是任意的，并且可能是复杂的。在这个项目中要解决的挑战包括：-退化方程的数学分析与离散化，硬数值分析，算法的开发和应用到复杂的系统。该项目是雄心勃勃的范围，因为新奇和技术性的数学问题和规模的应用。PDRA将与PI在冒险的复杂问题上密切合作，并将在新兴和蓬勃发展的领域接受计算应用数学的高级培训。还将涉及两名访问研究人员，他们是PI的持续合作者。该项目将导致有关新方法的定理，算法的开发和复杂物理过程的模拟。传播将发表在高质量的研究文章和会议上的谈话。