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The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by…
In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer…
Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
Taking the l^1-completion and the topological dual of the singular chain complex gives rise to l^1-homology and bounded cohomology respectively. In contrast to l^1-homology, major structural properties of bounded cohomology are well…
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but {\em not} differentiable. The need to define physical quantities on this…
The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the…
This article describes the geometry of isomorphisms between complements of geometrically irreducible closed curves in the affine plane $\mathbb{A}^2$, over an arbitrary field, which do not extend to an automorphism of $\mathbb{A}^2$. We…
The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness…
We study scaling function geometry. We show the existence of the scaling function of a geometrically finite one-dimensional mapping. This scaling function is discontinuous. We prove that the scaling function and the asymmetries at the…
We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for $G^1$ smoothness are given, which, up to a certain degenerate case, are also…
In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…
The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the…
In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization of domain geometry, then…
One of the theoretically intriguing problems in computer-aided geometric modeling comes from the stitching of the tensor product Bezier patches. When they share an extraordinary vertex, it is not possible to obtain continuity C1 or G1 along…
This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when…
In this work, we study the approximation properties of multi-patch dG-IgA methods, that apply the multipatch Isogeometric Analysis (IgA) discretization concept and the discontinuous Galerkin (dG) technique on the interfaces between the…