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

研究人员开发了模拟不可压缩可变形膜与斯托克流体、其他膜和刚性壁相互作用的数值算法。这项工作的目标是实现由大量相互作用的囊泡组成的系统的高精度快速模拟。所研究的数值方法基于边界积分公式，仅使用表面上定义的场，因此无需对三维空间进行离散化，从而大大简化了可变形边界的模拟。由边界积分公式的离散化和线性化所产生的密集线性方程组，使用先前由研究者开发的核无关快速多极算法的扩展来求解。研究工作包括两个主要方向：基于网格和局域谱基的建设性流形结构的可变形曲面的离散化方案，边界积分和膜-流体相互作用的线性和非线性求解。研究人员的目标是创建有效的计算工具来解决各种生物和生物医学背景下出现的问题。潜在的应用包括模拟血液流动中的血细胞行为，流体中膜的形成以及基于囊泡的靶向药物递送机制的设计。针对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.