TCBG Seminar

Fast algorithms for three-dimensional vesicle flow simulations

Professor George Biros
Schools of Computational Science and Engineering and The Wallace H. Coulter Department of Biomedical Engineering
Georgia Institute of Technology and Emory University
Atlanta, GA

Monday, November 1, 2010
3:00 pm (CT)
2269 Beckman Institute


Vesicles are area-preserving membranes that resist bending. They can be manufactured in a wet lab and are used to study the mechanics of lipid bilayers. In addition, vesicles are proxies for red-blood cells, intracellular organelles and viral particles. We are interested in developing simulation tools for dilute and concentrated suspensions of deformable vesicles. By ``fast algorithm'', we refer to a method that (1) is unconditionally stable, (2) the work per time-step scales linearly with the number of vesicles and (3) the depth per time-step scales logarithmically with the number of vesicles. Methods: To achieve an efficient scheme, we use an integro-differential formulation in which we couple a boundary integral formulation for the Stokes equations with a Helfrich free energy term for the vesicle's membrane elasticity. We use a spectral Galerkin approximation do discretize in space. We time-march using a second-order accurate semi-implicit scheme. In implementing this scheme, we deploy an arsenal of celebrated methods in mathematics and computer science: Fourier and and Legendre transforms, adaptive fast multipole methods, antializing, remeshing, Galerkin projections, multi-step time methods, fast spherical harmonics rotations, spectral quadratures for smooth and weakly singular integrals, preconditioned Krylov linear solvers and dense linear algebra operations. All of these components are end-to-end parallelized on distributed/shared/vectorized memory architectures.

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