The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models
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 …
approach with higher-order finite elements, adaptive integration, and weak enforcement of …
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 …
An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD …
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 …
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
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 …
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
The computational efficiency of random field representations with the Karhunen–Loève (KL)
expansion relies on the solution of a Fredholm integral eigenvalue problem. This …
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
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 …
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
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 …
static bending, buckling, and free vibration of homogeneous and functionally graded plates …
Geometric modeling, isogeometric analysis and the finite cell method
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 …
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
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 …
methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and …