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This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the…
The advent of multi-material additive manufacturing and automated composite manufacturing has enabled the design of structures featuring complex curvilinear anisotropy. To take advantage of the new design space, efficient computational…
We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the…
We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degree…
A Nitche's method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented. In a non-conforming for- mulation,…
In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…
This work utilizes the Immersed Boundary Conformal Method (IBCM) to analyze Kirchhoff-Love and Reissner-Mindlin shell structures within an immersed domain framework. Immersed boundary methods involve embedding complex geometries within a…
In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…
We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time…
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…
We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. In contrast, Nesterov's accelerated…
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…
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but {\em not} differentiable. The need to define physical quantities on this…
The space of $C^1$ cubic Clough-Tocher splines is a classical finite element approximation space over triangulations for solving partial differential equations. However, for such a space there is no B-spline basis available, which is a…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…
Shell structures with a high stiffness-to-weight ratio are desirable in various engineering applications. In such scenarios, topology optimization serves as a popular and effective tool for shell structures design. Among the topology…
The art of analysis involves the subtle combination of approximation, inequalities, and geometric intuition as well as being able to work at different scales. With this subtlety in mind, we present this paper in a manner designed for wide…
We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this…