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.
