Related papers: Isogeometric collocation on planar multi-patch dom…
This paper studies elasto-plastic large deformation behavior of thin shell structures using the isogeometric computational approach with the main focus on the efficiency in modelling the multi-patches and arbitrary material formulations. In…
Although Galerkin discretizations have been intensively employed in the IgA context, an efficient implementation requires special numerical quadrature rules when constructing the system of equations. To avoid this issue, isogeometric…
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…
We present a novel stabilized isogeometric formulation for the Stokes problem, where the geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) patches, i.e., one patch on top of another in an arbitrary but…
In this work we adapt classical residual-based stabilization techniques to the spline collocation setting. Inspired by the Streamline-Upwind-Petrov-Galerkin and Pressure-Stabilizing-Petrov-Galerkin methods, our stabilized collocation…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators.…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary…
This paper presents a brand new methodology to deal with isotopic fine structure calculations. By using the Poisson approximation in an entirely novel way, we introduce mathematical elegance into the discussion on the trade-off between…
This work is motivated by the difficulty in assembling the Galerkin matrix when solving Partial Differential Equations (PDEs) with Isogeometric Analysis (IGA) using B-splines of moderate-to-high polynomial degree. To mitigate this problem,…
Suppose that $A \in \mathbb{R}^{N \times N}$ is symmetric positive semidefinite with rank $K \le N$. Our goal is to decompose $A$ into $K$ rank-one matrices $\sum_{k=1}^K g_k g_k^T$ where the modes $\{g_{k}\}_{k=1}^K$ are required to be as…
Splines over triangulations and splines over quadrangulations (tensor product splines) are two common ways to extend bivariate polynomials to splines. However, combination of both approaches leads to splines defined over mixed triangle and…
Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…
We study approximation error bounds of isogeometric function spaces on a specific type of singularly parameterized domains. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a…
We study space--time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p, both in space and time. We propose a space--time variational formulation that is obtained by adding a…
Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis}…
In this paper we develop an isogeometric B\'ezier dual mortar method for the biharmonic problem on multi-patch domains. The well-posedness of the discrete biharmonic problem requires a discretization with $C^1$ continuous basis functions.…
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gau{\ss}-Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with…