LECTURES ON THE IMMERSED BOUNDARY METHOD
by Charles S. Peskin
Courant Institute of Mathematical Sciences, New York University

Copyright, Charles S. Peskin, 2007, 2011, 2019, 2021, 2023, and 2024

I. The Immersed Boundary Method in a Simple Special Case

2D Matlab implementation

INTERACTIVE 2D implementation by Guanhua Sun
(browser must support webGPU for simulation to run)

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

Notes on finite element description of a general hyperelastic 3D material
The above notes are an expository introduction
to the content of the following paper by Devendran & Peskin:
An immersed boundary energy-based method for incompressible viscoelasticity
J Comput. Phys. 231: 4613–4642, 2012

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 (2023) 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

Notes on the differential geometry of surface stretching,
with a scheme at the end for evaluating the stretching energy of a triangulated surface.
(This scheme is employed in the 3D matlab implementation cited above.)

Matlab programs for a nice triangulation of a sphere to any level of refinement

III. The Stochastic Immersed Boundary Method

Notes on the time-dependent Stokes equations with random forcing on a periodic domain

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

VII. On the Numerical Stability of Target Point Forces in the Immersed Boundary Method

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