Related papers: Multipatch Approximation of the de Rham Sequence a…
In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose…
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline based interpolation method for spectral codes is presented. The theory links the order of the…
Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…
The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently…
In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as…
We construct over a given bilinear multi-patch domain a novel $C^s$-smooth mixed degree and regularity isogeometric spline space, which possesses the degree $p=2s+1$ and regularity $r=s$ in a small neighborhood around the edges and…
The local bounded commuting projection operators of nonstandard finite element de Rham complexes in two and three dimensions are constructed systematically. The assumptions of the main result are mild and can be verified. For three…
We study the dimension and construct a basis for $C^1$-smooth isogeometric function spaces over two-patch domains. In this context, an isogeometric function is a function defined on a B-spline domain, whose graph surface also has a B-spline…
A discretisation of differential geometry using the Whitney forms of algebraic topology is consistently extended via the introduction of a pairing on the space of chains. This pairing of chains enables us to give a definition of the…
We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the authors have developed an analysis for the first biharmonic…
The focus on locally refined spline spaces has grown rapidly in recent years due to the need in Isogeoemtric analysis (IgA) of spline spaces with local adaptivity: a property not offered by the strict regular structure of tensor product…
This paper introduces a novel adaptive refinement strategy for Isogeometric Analysis (IGA) using Truncated Hierarchical B-splines (THB-splines). The proposed strategy enhances locally-refined meshes for specific applications, simplifying…
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline functions, that are a partition of unity, instead to the…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…
We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous…
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
In this short note we describe a simple adaptation of biharmonic surfaces to interpolate boundary cross-derivatives given in ribbon form, and compare with the recently proposed Generalized B-spline patches.
This paper considers the minimization of a continuously differentiable function over a cardinality constraint. We focus on smooth and relatively smooth functions. These smoothness criteria result in new descent lemmas. Based on the new…