Immersed Finite Element Method

Brain Biomechanics

Hydrocephalus is a clinical condition characterized by abnormalities in the cerebrospinal fluid (CSF) circulation resulting in ventricular dilation.Within limits, the dilation of the ventricles can be reversed by either a shunt placement in the brain or by performing a ventriculostomy surgery, resulting in a relief from the symptoms of hydrocephalus.

Codimension One Discretisations

The deal.II finite element library ( was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly via the Finite Element Method.In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or three spacial dimensions

Generalized Immersed Finite Element Methods

The most general model for fluid structure interaction problems based on IFEM is the one developed in Heltai and Costanzo, 2012 (see below for the reference) which allows for materials with general density, general viscosity and which can be either compressible or incompressible.

Adding Thickness to FE-IBM

In the original Immersed Boundary Method, the solid is usually considered thin, or of codimension one. Thickness could be achieved by stacking together several one-dimensional fibers (like in the first movie below). A more general solution, based on Hyper-Elastic theory and standard variational principles was proposed in the reference below.

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