Related papers: Constructing IGA-suitable planar parameterization …
This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with B\'ezier tetrahedra. The…
This work undertakes to combine the interests of IsoGeometric Analysis (IGA) and standard Finite Element Methods (FEM) for the global/local simulation of structures. The idea is to adopt a hybrid global-IGA/local-FEM modeling, thereby…
Recently proposed as a stable means of evaluating geometric compactness, the isoperimetric profile of a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain.…
Border basis schemes are open subschemes of Hilbert schemes parametrizing 0-dimensional subschemes of $\mathbb{P}^n$ of given length. They yield open coverings and are easy to describe and to compute with. Our topic is to find re-embeddings…
A novel approach to the simulation with the boundary element method using trimmed NURBS patches is presented. The advantage of this approach is its efficiency and easy implementation. The analysis with trimmed NURBS is achieved by double…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. Boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional…
We present an isogeometric mortar method for the discretization of the biharmonic equation posed on multi-patch domains. We assume only $C^0$-conformity at interfaces and employs a mortar approach to weakly enforce $C^1$-continuity across…
We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…
We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…
This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…
We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of…
Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves.…
We consider a cut isogeometric method, where the boundary of the domain is allowed to cut through the background mesh in an arbitrary fashion for a second order elliptic model problem. In order to stabilize the method on the cut boundary we…
We propose a local type of B-bar formulation, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) hierarchical B-splines. We show that the…
The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…