62 citations · 213 across the 26 of their papers we have counts for
27 papers
Constructing limit surfaces from unstructured splines via averaging and refinement
Syeda Hijab Zahra, Thomas Takacs
In this paper we present a construction for unstructured splines over quadrilateral meshes by iterative averaging and refinement. We represent the spline as a multi-patch B-spline,…
Robust approximation error estimates for analysis-suitable isogeometric multi-patch discretizations
Fatima Hasanova, Stefan Takacs, Thomas Takacs
We prove -robust approximation error estimates for -conforming isogeometric discretizations over planar multi-patch domains. Possible applications are fourth order boundary…
Adaptive optimization of isogeometric multi-patch discretizations using artificial neural networks
Dany Rios, Felix Scholz, Thomas Takacs
In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. The…
IGA Using Offset-based Overlapping Domain Parameterizations
Somayeh Kargaran, Bert Jüttler, Thomas Takacs
Isogeometric analysis (IGA) is a numerical method that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represent…
Construction of Smooth Isogeometric Function Spaces on Singularly Parameterized Domains
Thomas Takacs
We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a…
A comparison of smooth basis constructions for isogeometric analysis
H. M. Verhelst, P. Weinmüller, A. Mantzaflaris +2
In order to perform isogeometric analysis with increased smoothness on complex domains, trimming, variational coupling or unstructured spline methods can be used. The latter two cl…
Imposing nonlocal boundary conditions in Galerkin-type methods based on non-interpolatory functions
Svajūnas Sajavičius, Thomas Takacs
The imposition of inhomogeneous Dirichlet (essential) boundary conditions is a fundamental challenge in the application of Galerkin-type methods based on non-interpolatory function…
Approximation properties over self-similar meshes of curved finite elements and applications to subdivision based isogeometric analysis
Thomas Takacs
In this study we consider domains that are composed of an infinite sequence of self-similar rings and corresponding finite element spaces over those domains. The rings are paramete…
Isogeometric mortar method
Andrea Benvenuti, Gabriele Loli, Giancarlo Sangalli +1
We present an isogeometric mortar method for the discretization of the biharmonic equation posed on multi-patch domains. We assume only -conformity at interfaces and employs a…
-smooth isogeometric spline functions of general degree over planar mixed meshes: The case of two quadratic mesh elements
Jan Grošelj, Mario Kapl, Marjeta Knez +2
Splines over triangulations and splines over quadrangulations (tensor product splines) are two common ways to extend bivariate polynomials to splines. However, combination of both…
Locally refined quad meshing for linear elasticity problems based on convolutional neural networks
Chiu Ling Chan, Felix Scholz, Thomas Takacs
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar d…
An approximate multi-patch space for isogeometric analysis with a comparison to Nitsche's method
Pascal Weinmüller, Thomas Takacs
We present an approximately -smooth multi-patch spline construction which can be used in isogeometric analysis (IGA). A key property of IGA is that it is simple to achieve hig…
Almost- splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems
Thomas Takacs, Deepesh Toshniwal
Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objecti…
Adaptive Refinement for Unstructured T-Splines with Linear Complexity
Roland Maier, Philipp Morgenstern, Thomas Takacs
We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertica…
Construction of approximate bases for isogeometric analysis on two-patch domains
Pascal Weinmüller, Thomas Takacs
In this paper, we develop and study approximately smooth basis constructions for isogeometric analysis over two-patch domains. One key element of isogeometric analysis is that it a…
A family of quadrilateral finite elements
Mario Kapl, Giancarlo Sangalli, Thomas Takacs
We present a novel family of quadrilateral finite elements, which define global spaces over a general quadrilateral mesh with vertices of arbitrary valency. The element…
A super-smooth spline space over planar mixed triangle and quadrilateral meshes
Jan Grošelj, Mario Kapl, Marjeta Knez +2
In this paper we introduce a spline space over mixed meshes composed of triangles and quadrilaterals, suitable for FEM-based or isogeometric analysis. In this context, a mesh…
Manifold-based B-splines on unstructured meshes
Qiaoling Zhang, Thomas Takacs, Fehmi Cirak
We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to repr…
Isogeometric analysis with functions on unstructured quadrilateral meshes
Mario Kapl, Giancarlo Sangalli, Thomas Takacs
In the context of isogeometric analysis, globally isogeometric spaces over unstructured quadrilateral meshes allow the direct solution of fourth order partial differential eq…
The Argyris isogeometric space on unstructured multi-patch planar domains
Mario Kapl, Giancarlo Sangalli, Thomas Takacs
Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. We deal with a particular class of planar multi-patch…
Construction of analysis-suitable planar multi-patch parameterizations
Mario Kapl, Giancarlo Sangalli, Thomas Takacs
Isogeometric analysis allows to define shape functions of global continuity (or of higher continuity) over multi-patch geometries. The construction of such -smooth i…
Dimension and basis construction for analysis-suitable two-patch parameterizations
Mario Kapl, Giancarlo Sangalli, Thomas Takacs
We study the dimension and construct a basis for -smooth isogeometric function spaces over two-patch domains. In this context, an isogeometric function is a function defined o…
Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces
Guozhi Dong, Bert Juettler, Otmar Scherzer +1
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysi…
Analysis-suitable multi-patch parametrizations for isogeometric spaces
Annabelle Collin, Giancarlo Sangalli, Thomas Takacs
One key feature of isogeometric analysis is that it allows smooth shape functions. Indeed, when isogeometric spaces are constructed from -degree splines (and extensions, such as…