Related papers: Robust Trimmed Multipatch IGA with Singular Maps
We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neighborhood of a point at the boundary. Our…
In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and singular sources. This class of problems covers general point sources, line sources and the combination…
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…
Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with…
One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…
In this paper, we conduct a systematic numerical analysis of the spectral properties of the collocation and mass matrices in the isogeometric least-squares collocation method (IGA-L), for the approximation of the Poisson problem with…
Trimming is a common operation in CAD, and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming the geometric description of the patch remains…
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…
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…
Unfitted mesh formulations for interface problems generally adopt two distinct methodologies: (i) penalty-based approaches and (ii) explicit enrichment space techniques. While Stable Generalized Finite Element Method (SGFEM) has been…
This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA…
We use the refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems $({Ku=\lambda Mu})$. The rIGA framework conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) discretizations while…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
We propose an efficient and robust iterative solution to the multi-object matching problem. We first clarify serious limitations of current methods as well as the inappropriateness of the standard iteratively reweighted least squares…
Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of equations at given data parameters. By appending auxiliary…
This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the…
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…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…