The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models

D Schillinger, M Ruess - Archives of Computational Methods in …, 2015 - Springer
The finite cell method is an embedded domain method, which combines the fictitious domain
approach with higher-order finite elements, adaptive integration, and weak enforcement of …

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 …

An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD …

D Schillinger, L Dede, MA Scott, JA Evans… - Computer Methods in …, 2012 - Elsevier
We explore hierarchical refinement of NURBS as a basis for adaptive isogeometric and
immersed boundary analysis. We use the principle of B-spline subdivision to derive a local …

Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations

D Schillinger, JA Evans, A Reali, MA Scott… - Computer Methods in …, 2013 - Elsevier
We compare isogeometric collocation with isogeometric Galerkin and standard C 0 finite
element methods with respect to the cost of forming the matrix and residual vector, the cost …

Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion

W Betz, I Papaioannou, D Straub - Computer Methods in Applied …, 2014 - Elsevier
The computational efficiency of random field representations with the Karhunen–Loève (KL)
expansion relies on the solution of a Fredholm integral eigenvalue problem. This …

Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries

M Ruess, D Schillinger, AI Oezcan, E Rank - Computer Methods in Applied …, 2014 - Elsevier
Nitsche's method can be used as a coupling tool for non-matching discretizations by weakly
enforcing interface constraints. We explore the use of weak coupling based on Nitsche's …

Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates

S Yin, JS Hale, T Yu, TQ Bui, SPA Bordas - Composite Structures, 2014 - Elsevier
An effective, simple, robust and locking-free plate formulation is proposed to analyze the
static bending, buckling, and free vibration of homogeneous and functionally graded plates …

Geometric modeling, isogeometric analysis and the finite cell method

E Rank, M Ruess, S Kollmannsberger… - Computer Methods in …, 2012 - Elsevier
The advent of isogeometric analysis (IGA) using the same basis functions for design and
analysis constitutes a milestone in the unification of geometric modeling and numerical …

Weakly enforced essential boundary conditions for NURBS‐embedded and trimmed NURBS geometries on the basis of the finite cell method

M Ruess, D Schillinger, Y Bazilevs… - … journal for numerical …, 2013 - Wiley Online Library
Enforcing essential boundary conditions plays a central role in immersed boundary
methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and …