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

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

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

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


III. Improved Volume Conservation

An immersed boundary method with divergence-free velocity interpolation and force spreading. J Comput. Phys. 347: 183-206, 2017


IV. Mathematical Derivation of the Immersed Boundary Method


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