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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 refinement procedure , which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher(More)
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 valve function over the complete cardiac cycle. Due to the complex motion of the heart valve leaflets, the fluid domain undergoes large deformations, including(More)
The Finite Cell Method (FCM), which combines the fictitious domain concept with high-order p-FEM, permits the effective solution of problems with very complex geometry, since it circumvents the computationally expensive mesh generation and guarantees exponential convergence rates for smooth problems. The present contribution deals with the coupling of the(More)
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 of direct and iterative solvers, the accuracy versus degrees of freedom and the accuracy versus computing time. On this basis, we show that isogeometric collocation has the(More)
The advent of isogeometric analysis (IGA) using the same basis functions for design and analysis constitutes a milestone in the unification of geometric model-ing and numerical simulation. However, an important class of geometric models based on the CSG (Constructive Solid Geometry) concept such as trimmed NURBS surfaces do not fully support the(More)
hp-refinement schemes have proven to be an excellent approach to locally adapt the accuracy of a Finite Element discretization. However, the implementation of hp-adaptivity remains challenging as hanging nodes, edges, and faces have to be constrained to ensure compatibility of the shape functions. For this reason, most hp-code frameworks restrict themselves(More)
This paper addresses some practical aspects of making Isogeometric Analysis (IGA) more accessible to design engineers and analysts. An interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of IGA to improve their product design and performance. We develop several Rhino 3D plug-ins(More)
We continue the study initiated in [29] in search of optimal quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis. These rules are optimal in the sense that there exists no other quadrature rule that can exactly integrate the elements of the given spline space with fewer quadrature points. We extend the algorithm(More)
The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and(More)