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

研究人员开发的数值算法模拟不可压缩变形膜与斯托克斯流体，其他膜和刚性壁相互作用。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边界积分公式，它只使用定义在表面上的字段，因此消除了对3D空间，这大大简化了变形边界的模拟离散化的需要。密集的线性方程组的边界积分公式的离散化和线性化所产生的使用扩展的核独立的快速多极子算法以前开发的研究人员解决。工作包括两个主要方向：可变形表面的离散化方案，基于网格和局部谱基上的构造性流形结构，以及边界积分和膜-流体相互作用的线性和非线性求解器。研究人员的目标是创建有效的计算工具，用于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细胞在血流中的行为，在流体中形成膜和基于囊泡的靶向药物递送机制的设计。开发有效的工具，这样的问题，使得有可能测试涉及复杂的边界，大量的变形细胞或囊泡的情况。

The investigators develop numerical algorithms for simulation of incompressible deformable membranes interacting with Stokesian fluids, other membranes and rigid walls. The goal of this work is to enable high-accuracy fast simulations of systems consisting of large numbers of interacting vesicles. Investigated numerical methods are based on a boundary integral formulation which only uses fields defined on the surface and therefore eliminates the need for discretization of 3D space, which considerably simplifies simulation of deformable boundaries. The dense linear systems of equations resulting from discretization and linearization of the boundary integral formulation are solved using extensions of kernel-independent fast multipole algorithms previously developed by the investigators. The work includes two main directions: discretization schemes for deformable surfaces, based on constructive manifold structures on meshes and localized spectral bases, and boundary integral and membrane-fluid interaction linear and nonlinear solvers. The investigators aim to create efficient computational tools for solving problems arising in a variety of biological and biomedical contexts. Potential applications include simulation of blood cell behavior in blood flow, formation of membranes in a fluid and design of targeted drug delivery mechanisms based on vesicles. Development of efficient tools for such problems makes it possible to test scenarios involving complex boundaries, large numbers of deforming cells or vesicles.