Isogeometric analysis has been proposed as a methodology for bridging the gap between computer aided design (CAD) and finite element analysis (FEA). Although both the traditional and isogeometric pipelines rely upon the same conceptualization to solid model steps, they drastically differ in how they bring the solid model both to and through the analysis process. The isogeometric analysis proces...

In this paper we consider a variant of the dual-primal isogeometric tearing and interconnecting (IETI-DP) method for solving large-sacle linear systems of algebraic equations arising from discontinuous Galerkin (dG) isogeometric analysis of diffusion problems on multipatch domains with non-matching meshes. The dG formulation is used to couple the local problems across patch interfaces. The purp...

The dual-primal isogeometric tearing and interconnecting (IETI-DP) method is the adaption of the dual-primal finite element tearing and interconnecting (FETI-DP) method to isogeometric analysis of scalar elliptic boundary value problems like, e.g., diffusion problems with heterogeneous diffusion coefficients. The purpose of this paper is to extent the already existing results on condition numbe...

We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. We observe that the performance of standard V-cycle iteration is highly dependent on the spatial dimension as well as the spline degree of the discretization space. Conjugate gradient iteration preconditioned with one V-c...

The paper presents a Bézier triangle based isogeometric shape optimization method. Bézier triangles are used to represent both the geometry and physical fields. For a given physical domain defined by B-spline boundary, a coarse Bézier triangular parameterization is automatically generated. This coarse mesh is used to maintain parameterization quality and move mesh by solving a pseudo linear ela...

Analysis of the laminated composite plates under transverse loading is considered using the new method of Isogeometric Analysis (IGA). Non-Uniform Rational B-Splines(NURBS)are used as shape functions for modeling the geometry of the structure and also are used as shape functions in the analysis process. To show robustness of the new technique, some examples are represented and are compared with...

Isogeometric Analysis (IGA) has recently emerged as a cost-effective alternative to classic isoparametric Finite Element Analysis. In this work a novel computational framework is proposed in order to get IGA-suitable geometries to simulate different vascular minimally-invasive procedures. The preliminary results show the capability of the framework to import in a straightforward way patient-spe...

Gk (geometrically continuous surface) constructions were developed to create surfaces that are smooth also at irregular points where, in a quad-mesh, three or more than four elements come together. Isogeometric elements were developed to unify the representation of geometry and of engineering analysis. We show how matched Gk constructions for geometry and analysis automatically yield Ck isogeom...