Stability and conditioning of immersed finite element methods: analysis and remedies

F de Prenter, CV Verhoosel, EH van Brummelen… - … Methods in Engineering, 2023‏ - Springer
This review paper discusses the developments in immersed or unfitted finite element
methods over the past decade. The main focus is the analysis and the treatment of the …

An immersogeometric variational framework for fluid–structure interaction: Application to bioprosthetic heart valves

D Kamensky, MC Hsu, D Schillinger, JA Evans… - Computer methods in …, 2015‏ - Elsevier
In this paper, we develop a geometrically flexible technique for computational fluid–structure
interaction (FSI). The motivating application is the simulation of tri-leaflet bioprosthetic heart …

The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems

A Main, G Scovazzi - Journal of Computational Physics, 2018‏ - Elsevier
We propose a new finite element method for embedded domain computations, which falls in
the category of surrogate/approximate boundary algorithms. The key feature of the proposed …

The aggregated unfitted finite element method for elliptic problems

S Badia, F Verdugo, AF Martín - Computer Methods in Applied Mechanics …, 2018‏ - Elsevier
Unfitted finite element techniques are valuable tools in different applications where the
generation of body-fitted meshes is difficult. However, these techniques are prone to severe …

Condition number analysis and preconditioning of the finite cell method

F de Prenter, CV Verhoosel, GJ van Zwieten… - Computer Methods in …, 2017‏ - Elsevier
Abstract The (Isogeometric) Finite Cell Method–in which a domain is immersed in a
structured background mesh–suffers from conditioning problems when cells with small …

The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries

F Xu, D Schillinger, D Kamensky, V Varduhn, C Wang… - Computers & …, 2016‏ - Elsevier
We present a tetrahedral finite cell method for the simulation of incompressible flow around
geometrically complex objects. The method immerses such objects into non-boundary-fitted …

The shifted boundary method for embedded domain computations. Part II: Linear advection–diffusion and incompressible Navier–Stokes equations

A Main, G Scovazzi - Journal of Computational Physics, 2018‏ - Elsevier
We propose a new embedded finite element method for the linear advection–diffusion
equation and the laminar and turbulent incompressible Navier–Stokes equations. The …

[HTML][HTML] Shape optimisation with multiresolution subdivision surfaces and immersed finite elements

K Bandara, T Rüberg, F Cirak - Computer Methods in Applied Mechanics …, 2016‏ - Elsevier
We develop a new optimisation technique that combines multiresolution subdivision
surfaces for boundary description with immersed finite elements for the discretisation of the …

A subdivision-stabilized B-spline mixed material point method

AA Madadi, B Dortdivanlioglu - Computer Methods in Applied Mechanics …, 2024‏ - Elsevier
Subjected to external loadings, polymeric materials, eg, biological tissues, hydrogels, and
elastomers, may undergo extreme, nearly incompressible,(self-) contact deformations. For …

The shifted interface method: a flexible approach to embedded interface computations

K Li, NM Atallah, GA Main… - International Journal for …, 2020‏ - Wiley Online Library
We propose a new embedded finite element method to simulate partial differential equations
over domains with internal interfaces. Our approach belongs to the family of …