Related papers: XIGA: An eXtended IsoGeometric Analysis approach f…
In the context of isogeometric analysis, globally $C^1$ isogeometric spaces over unstructured quadrilateral meshes allow the direct solution of fourth order partial differential equations on complex geometries via their Galerkin…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
Deep learning has achieved great success in a wide spectrum of multimedia applications such as image classification, natural language processing and multimodal data analysis. Recent years have seen the development of many deep learning…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
We derive a new stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions for elliptic problems of second order in cut isogeometric analysis (CutIGA). We consider $C^1$ splines and stabilize the standard Nitsche…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
We present an approximately $C^1$-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 high order smoothness within a single patch. To represent more…
We propose a numerical scheme based on the principles of Isogeometric Analysis (IgA) for a geometrical pattern formation induced evolution of manifolds. The development is modelled by the use of the Gray-Scott equations for pattern…
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…
In this work we address the complexity problem of the isogeometric Boundary Element Method by proposing a collocation scheme for practical problems in linear elasticity and the application of hierarchical matrices. For mixed boundary value…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
Engineering design via CAD software relies on Non-Uniform Rational B-Splines (NURBS) as a means for representing and communicating geometry. Therefore, in general, a NURBS description of a given design can be considered the exact…
A seamless integration of neural networks with Isogeometric Analysis (IGA) was first introduced in [1] under the name of Hierarchical Deep-learning Neural Network (HiDeNN) and has systematically evolved into Isogeometric Convolution HiDeNN…
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…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
Nonlinear diffusion-reaction systems model a multitude of physical phenomena. A common situation is biological development modeling where such systems have been widely used to study spatiotemporal phenomena in cell biology. Systems of…
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,…