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Stability and conditioning of immersed finite element methods: analysis and remedies
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 …
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
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 …
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
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 category of surrogate/approximate boundary algorithms. The key feature of the proposed …
The aggregated unfitted finite element method for elliptic problems
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 …
generation of body-fitted meshes is difficult. However, these techniques are prone to severe …
Condition number analysis and preconditioning of the finite cell method
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 …
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
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 …
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
We propose a new embedded finite element method for the linear advection–diffusion
equation and the laminar and turbulent incompressible Navier–Stokes equations. The …
equation and the laminar and turbulent incompressible Navier–Stokes equations. The …
[HTML][HTML] Shape optimisation with multiresolution subdivision surfaces and immersed finite elements
We develop a new optimisation technique that combines multiresolution subdivision
surfaces for boundary description with immersed finite elements for the discretisation of the …
surfaces for boundary description with immersed finite elements for the discretisation of the …
A subdivision-stabilized B-spline mixed material point method
Subjected to external loadings, polymeric materials, eg, biological tissues, hydrogels, and
elastomers, may undergo extreme, nearly incompressible,(self-) contact deformations. For …
elastomers, may undergo extreme, nearly incompressible,(self-) contact deformations. For …
The shifted interface method: a flexible approach to embedded interface computations
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 …
over domains with internal interfaces. Our approach belongs to the family of …