Exact Singularity Subtraction from Boundary Integral Equations in Modeling Vesicles and Red Blood Cells
Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 4 : pp. 413–434
Abstract
The study of vesicles, capsules and red blood cells (RBCs) under flow is a field of active research, belonging to the general problematic of fluid/structure interactions. Here, we are interested in modeling vesicles, capsules and RBCs using a boundary integral formulation, and focus on exact singularity subtractions of the kernel of the integral equations in 3D. In order to increase the precision of singular and near-singular integration, we propose here a refinement procedure in the vicinity of the pole of the Green-Oseen kernel. The refinement is performed homogeneously everywhere on the source surface in order to reuse the additional quadrature nodes when calculating boundary integrals in multiple target points. We also introduce a multi-level look-up algorithm in order to select the additional quadrature nodes in vicinity of the pole of the Green-Oseen kernel. The expected convergence rate of the proposed algorithm is of order $\mathcal{O}(1/N^2)$ while the computational complexity is of order $\mathcal{O}$($N^2$ln$N$), where $N$ is the number of degrees of freedom used for surface discretization. Several numerical tests are presented to demonstrate the convergence and the efficiency of the method.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.1308si
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 4 : pp. 413–434
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stokes flow fluid structure interaction boundary integral method red blood cells singularity subtraction.
-
Effects of membrane viscoelasticity on the red blood cell dynamics in a microcapillary
Gürbüz, Ali | Pak, On Shun | Taylor, Michael | Sivaselvan, Mettupalayam V. | Sachs, FrederickBiophysical Journal, Vol. 122 (2023), Iss. 11 P.2230
https://doi.org/10.1016/j.bpj.2023.01.010 [Citations: 5] -
Isogeometric FEM-BEM simulations of drop, capsule and vesicle dynamics in Stokes flow
Boedec, Gwenn | Leonetti, Marc | Jaeger, MarcJournal of Computational Physics, Vol. 342 (2017), Iss. P.117
https://doi.org/10.1016/j.jcp.2017.04.024 [Citations: 23] -
A natural framework for isogeometric fluid–structure interaction based on BEM–shell coupling
Heltai, Luca | Kiendl, Josef | DeSimone, Antonio | Reali, AlessandroComputer Methods in Applied Mechanics and Engineering, Vol. 316 (2017), Iss. P.522
https://doi.org/10.1016/j.cma.2016.08.008 [Citations: 29]