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Stokesian流体、其他膜和刚性壁相互作用的数值算法。这项工作的目标是能够对由大量相互作用的小泡组成的系统进行高精度的快速模拟。所研究的数值方法基于边界积分公式，该公式只使用定义在表面上的场，因此不需要对三维空间进行离散，这大大简化了变形边界的模拟。由边界积分公式的离散化和线性化得到的稠密线性方程组，使用研究者先前发展的核无关的快速多极算法的扩展来求解。这项工作包括两个主要方向：基于网格和局域谱基上的构造流形结构的变形曲面离散格式，以及边界积分和膜-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的问题。潜在的应用包括模拟血细胞在血液流动中的行为，在液体中形成膜，以及设计基于囊泡的靶向药物输送机制。针对这类问题的有效工具的开发使测试涉及复杂边界、大量变形的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.