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In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are…

Numerical Analysis · Mathematics 2019-03-27 Massimo Carraturo , Carlotta Giannelli , Alessandro Reali , Rafael Vázquez

The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined…

Numerical Analysis · Mathematics 2020-04-22 Luca Coradello , Pablo Antolin , Rafael Vázquez , Annalisa Buffa

We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement…

Numerical Analysis · Mathematics 2017-04-05 Paul Hennig , Markus Kästner , Philipp Morgenstern , Daniel Peterseim

Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines)…

Numerical Analysis · Mathematics 2025-03-20 H. M. Verhelst , A. Mantzaflaris , M. Möller , J. H. Den Besten

The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…

Numerical Analysis · Mathematics 2015-04-21 Annalisa Buffa , Carlotta Giannelli

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…

Numerical Analysis · Mathematics 2017-11-20 Gregor Gantner , Daniel Haberlik , Dirk Praetorius

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…

Numerical Analysis · Mathematics 2026-01-14 Kevin Dijkstra , Carlotta Giannelli , Deepesh Toshniwal

This chapter reviews the work conducted by our team on scan-based immersed isogeometric analysis for flow problems. To leverage the advantageous properties of isogeometric analysis on complex scan-based domains, various innovations have…

Numerical Analysis · Mathematics 2022-09-01 Clemens V. Verhoosel , E. Harald van Brummelen , Sai C. Divi , Frits de Prenter

This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…

Numerical Analysis · Mathematics 2022-12-05 Mathias Schmidt , Lise Noel , Keenan Doble , John A. Evans , Kurt Maute

In this paper we describe an adaptive refinement strategy for LR B-splines. The presented strategy ensures, at each iteration, local linear independence of the obtained set of LR B-splines. This property is then exploited in two…

Numerical Analysis · Mathematics 2020-07-15 Francesco Patrizi , Carla Manni , Francesca Pelosi , Hendrik Speleers

This paper presents a PDE-based planar parameterization framework with support for Truncated Hierarchical B-Splines (THB-splines). For this, we adopt the a posteriori refinement strategy of Dual Weighted Residual and present several…

Numerical Analysis · Mathematics 2021-11-23 Jochen Hinz , Michael Abdelmalik , Matthias Möller

Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer aided design, which generates meshes that are unfitted with the described…

Numerical Analysis · Mathematics 2022-08-10 Annalisa Buffa , Ondine Chanon , Rafael Vázquez

To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by…

Numerical Analysis · Mathematics 2022-02-23 S. C. Divi , C. V. Verhoosel , F. Auricchio , A. Reali , E. H. van Brummelen

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd…

Numerical Analysis · Mathematics 2020-09-07 Gregor Gantner , Dirk Praetorius

This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…

Numerical Analysis · Mathematics 2019-09-25 L. Noel , M. Schmidt , C. Messe , J. A. Evans , K. Maute

We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed weighted-residual error estimator is reliable and converges at…

Numerical Analysis · Mathematics 2022-08-24 Gregor Gantner , Dirk Praetorius

The concept of trimming, embedding, or immersing geometries into a computational background mesh has gained considerable attention in recent years, particularly in isogeometric analysis (IGA). In this approach, the physical domain is…

Numerical Analysis · Mathematics 2026-05-01 Christoph Hollweck , Andrea Gorgi , Nicolo Antonelli , Marcus Wagner , Roland Wüchner

The Stokes-Brinkman equations model flow in heterogeneous porous media by combining the Stokes and Darcy models of flow into a single system of equations. With suitable parameters, the equations can model either flow without detailed…

Numerical Analysis · Mathematics 2019-08-28 Kevin Williamson , Pavel Burda , Bedřich Sousedík

The paper is concerned with locally stabilized space-time IgA approximations to initial boundary value problems of the parabolic type. Originally, similar schemes (but weighted with a global mesh parameter) was presented and studied by U.…

Numerical Analysis · Mathematics 2018-07-17 Ulrich Langer , Svetlana Matculevich , Sergey Repin

This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…

Numerical Analysis · Mathematics 2025-11-07 Alessandra Aimi , Giulia Di Credico , Heiko Gimperlein , Chiara Guardasoni
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