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Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…
We present an adaptive scheme for isogeometric phase-field modeling, to perform suitably graded hierarchical refinement and coarsening on both single- and multi-patch geometries by considering truncated hierarchical spline constructions…
Easy to construct and optimally convergent generalisations of B-splines to unstructured meshes are essential for the application of isogeometric analysis to domains with non-trivial topologies. Nonetheless, especially for hexahedral meshes,…
This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…
Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric…
We present an isogeometric method for Kirchhoff-Love shell analysis of shell structures with geometries composed of multiple patches and which possibly possess extraordinary vertices, i.e. vertices with a valency different to four. The…
Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar…
The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
We analyze the space of bivariate functions that are piecewise polynomial of bi-degree \textless{}= (m, m') and of smoothness r along the interior edges of a planar T-mesh. We give new combinatorial lower and upper bounds for the dimension…
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform…
In this paper we develop the isogeometric B\'ezier dual mortar method. It is based on B\'ezier extraction and projection and is applicable to any spline space which can be represented in B\'ezier form (i.e., NURBS, T-splines, LR-splines,…
Although Galerkin discretizations have been intensively employed in the IgA context, an efficient implementation requires special numerical quadrature rules when constructing the system of equations. To avoid this issue, isogeometric…
In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit…
In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple…
This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love…
Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the…