Related papers: Adaptive Refinement for Unstructured T-Splines wit…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
Converting quad meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distributions of recent G-spline constructions with the refinability of subdivision surfaces. Specifically, we present a C2…
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…
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…
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…
We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been…
This paper proposes an Adaptive Isogeometric Topology Optimization framework for shell structures based on PHT-splines (PHT-AITO). In this framework, the design domain, displacement, and density are represented by PHT-splines. Leveraging…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow…
We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended…
Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain,…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
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…
We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…
We present a method to jointly refine the geometry and semantic segmentation of 3D surface meshes. Our method alternates between updating the shape and the semantic labels. In the geometry refinement step, the mesh is deformed with…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…
In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. The additional flexibility provided by the hierarchy of…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…