Related papers: Adaptive optimization of isogeometric multi-patch …
Isogeometric analysis (IGA) is a numerical method that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a NURBS…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…
We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise…
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…
Isogeometric analysis (IGA) enables exact representations of computational geometries and higher-order approximation of PDEs. In non-smooth domains, however, singularities near corners limit the effectiveness of IGA, since standard methods…
We study the dimension and construct a basis for $C^1$-smooth isogeometric function spaces over two-patch domains. In this context, an isogeometric function is a function defined on a B-spline domain, whose graph surface also has a B-spline…
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…
We consider dual-primal isogeometric tearing and interconnection (IETI-DP) solvers for multi-patch geometries in Isogeometric Analysis. Recently, the authors have published a convergence analysis for those solvers that is explicit in both…
Isogeometric Analysis is a spline-based discretization method to partial differential equations which shows the approximation power of a high-order method. The number of degrees of freedom, however, is as small as the number of degrees of…
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…
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
We present a framework for solving the triharmonic equation over bilinearly parameterized planar multi-patch domains by means of isogeometric analysis. Our approach is based on the construction of a globally $C^2$-smooth isogeometric spline…
We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach is based on the use of the globally $C^4$-smooth isogeometric spline space…
Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions,…
Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. We deal with a particular class of $C^0$ planar multi-patch spline parametrizations called analysis-suitable $G^1$…
Isogeometric Analysis (IgA) is a versatile method for the discretization of partial differential equations on complex domains, which arise in various applications of science and engineering. Some complex geometries can be better described…
In this paper we investigate adaptive discretization of the iteratively regularized Gauss- Newton method IRGNM. All-at-once formulations considering the PDE and the measurement equation simultaneously allow to avoid (approximate) solution…
Future e-mobility calls for efficient electrical machines. For different areas of operation, these machines have to satisfy certain desired properties that often depend on their design. Here we investigate the use of multipatch Isogeometric…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…