THE IMMERSED BOUNDARY METHOD
by Charles S. Peskin

Handwritten lecture notes of a course taught at the Courant Institute of Mathematical Sciences, New York University

Copyright, Charles S. Peskin, 2007 & 2011 & 2019 & 2021

I. The Immersed Boundary Method in a Simple Special Case

2D matlab implementation

3D matlab implemtation by Guanhua Sun
with vectorized delta-function routines by Tristan Goodwill

IBAMR by Boyce Griffith


II. Energy Functions for the Representation of Immersed Elastic Boundaries and Materials

A penalty immersed boundary method for a rigid body in fluid. Phys. Fluids 28: 033603, 2016
Homework related to the rigid pIB method
Statement an algorithm that implements the pIB method for this homework problem, by Ramiro Rebolledo

Notes for the application of the pIB method to a neutrally buoyant rigid body

Notes on the theory of Kirchhoff rods -- constrained and unconstrained

Dynamics of a closed rod with bend and twist in fluid. SIAM J Sci. Comput. 31(1): 273–302, 2008

Notes on the differential geometry of surface curvature

Notes on a vertex-oriented scheme for evaluating and differentiating the bending energy and area-preserving energy of a triangulated surface
Matlab programs for a nice triangulation of a sphere to any level of refinement


III. The Stochastic Immersed Boundary Method

Slides from guest lecture by Paul Atzberger

Simulation of osmotic swelling by the stochastic immersed boundary method SIAM J Sci Comput 37(4):B660–B688, 2015
Stochastic reductions for inertial fluid-structure interactions subject to thermal fluctuations SIAM J Appl Math 75(4):1884–1914, 2015
Fluctuating hydrodynamics methods for dynamic coarse-grained implicit-solvent simulations in LAMMPS
SIAM J Sci Comput 38(5):S62–S77, 2016


IV. Improved Volume Conservation

An immersed boundary method with divergence-free velocity interpolation and force spreading. J Comput. Phys. 347: 183-206, 2017
Gaussian-like immersed boundary kernels with three continuous derivatives and improved translation invariance arXiv:1505.07529v4


V. Mathematical Derivation of the Immersed Boundary Method


VI. Jump Conditions Across an Immersed Boundary Derived from the Mathematical Formulation of the IB Method