Finite Element Method

Coupling between BEM and SHELL models

 The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications.

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.

Arbitrary Manifold Descriptions in Finite Element Codes

One of the main advantages of using the deal.II library ( when discretising partial differential equations, is the support for adaptively refined grids on high performance infrastructures. Adaptively refining a Finite Element Mesh requires adding new vertices to a triangulation.

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.

Finite Element Immersed Boundary Method

A major difficulty associated with the numerical approximation of fluid structure interaction problems is given by the fact that the natural frameworks for dealing with fluids and solids are different: it is customary and convenient to describe fluids in an Eulerian framework, where the unknowns are expressed at fixed points in space, while for solids the natural frame

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