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

研究人员开发了数值算法，用于模拟不可压缩变形膜与斯托克斯流体、其他膜和刚性壁的相互作用。 这项工作的目标是使高精度的快速模拟系统组成的大量相互作用的囊泡。 研究的数值方法是基于ona边界积分公式，它只使用定义在thesurface上的字段，因此消除了对3D空间离散化的需要，这大大简化了变形边界的模拟。稠密线性方程组的边界积分formulationfromdiscretization和线性化的解决使用扩展的核独立的快速multipolealgorithms以前开发的调查。工作包括两个主要方向：基于网格和局部谱基上的构造性流形结构的可变形表面的离散化方案，以及边界积分和膜-流体相互作用的线性和非线性求解器。研究人员的目标是为解决各种生物和生物医学背景下出现的问题创建有效的计算工具。潜在的应用包括模拟血细胞在血流中的行为，在流体中形成膜和设计基于囊泡的靶向药物递送机制。 开发针对此类问题的有效工具，使得测试涉及复杂边界、大量变形细胞或囊泡的场景成为可能。

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.