相关论文: Adaptive isogeometric analysis with hierarchical b…
We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…
Polynomial splines are ubiquitous in the fields of computer aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly versatile since local mesh adaptivity enables efficient…
We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially consider 1D spline spaces of arbitrary degree spanned over…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions…
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…
We present an isogeometric framework based on collocation to construct a $C^2$-smooth approximation of the solution of the Poisson's equation over planar bilinearly parameterized multi-patch domains. The construction of the used globally…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
We present a new analytical and numerical framework for solution of Partial Differential Equations (PDEs) that is based on an exact transformation that moves the boundary constraints into the dynamics of the corresponding governing…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
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…
Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are…
In this article we suggest two discretization methods based on isogeometric analysis (IGA) for planar linear elasticity. On the one hand, we apply the well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a…
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 domain (possibly with holes) having a polygonal boundary. We…
The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from…
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…
This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when…
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…
We study the spectral approximation properties of isogeometric analysis with local continuity reduction of the basis. Such continuity reduction results in a reduction in the interconnection between the degrees of freedom of the mesh, which…