Collaborative Research: Fast High-Order Methods for Vesicle-Fluid and Membrane-Fluid Interaction and Adhesion

合作研究：囊泡-流体和膜-流体相互作用和粘附的快速高阶方法

• 批准号: 0612624
• 负责人: Denis Zorin
• 金额: $ 15.5万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0612624&HistoricalAwards=false
• 关键词: Collaborative; Research; Fast; Order; Methods

The investigators develop numerical algorithms for simulation ofincompressible deformable membranes interacting with Stokesian fluids,other membranes and rigid walls. The goal of this work is to enablehigh-accuracy fast simulations of systems consisting of large numbersof interacting vesicles. Investigated numerical methods are based ona boundary integral formulation which only uses fields defined on thesurface and therefore eliminates the need for discretization of 3Dspace, which considerably simplifies simulation of deformableboundaries. The dense linear systems of equations resulting fromdiscretization and linearization of the boundary integral formulationare solved using extensions of kernel-independent fast multipolealgorithms previously developed by the investigators. The workincludes two main directions: discretization schemes for deformablesurfaces, based on constructive manifold structures on meshes andlocalized spectral bases, and boundary integral and membrane-fluidinteraction linear and nonlinear solvers.The investigators aim to create efficient computational tools forsolving problems arising in a variety of biological and biomedicalcontexts. Potential applications include simulation of blood cellbehavior in blood flow, formation of membranes in a fluid and designof targeted drug delivery mechanisms based on vesicles. Developmentof efficient tools for such problems makes it possible to testscenarios involving complex boundaries, large numbers of deformingcells or vesicles.

研究人员开发了用于模拟与斯托克斯流体，其他膜和刚性壁相互作用的不可压缩膜的数值算法。 这项工作的目的是启用由大量相互作用囊泡组成的系统的快速模拟。 研究的数值方法基于Ona边界积分公式，该公式仅使用在截面上定义的字段，因此消除了3DDSPACE离散化的需求，这大大简化了对可变形的模拟的模拟。方程的密集线性系统，导致边界积分配方层的发射和线性化，使用了研究者先前开发的内核非依赖性快速多载值的扩展。这些工作包括两个主要方向：基于网格和局部化光谱基础的建设性歧管结构，以及边界积分和膜 - 荧光互动线性和非线性求解器的离散化方案。潜在的应用包括模拟血流中血细胞行为的模拟，基于囊泡的液体中形成液体和靶向药物输送机制的膜。 用于此类问题的有效工具的开发使得测试涉及复杂边界，大量变形感或囊泡的范围。