We extend the softFEM idea to isogeometric analysis (IGA) reduce stiffness (consequently, condition numbers) of IGA discretized problem. refer resulting approximation technique as softIGA. obtain discretization by first removing spectral outliers system’s stiffness. then add high-order derivative-jump penalization terms (with negative penalty parameters) standard bilinear forms. The parameter s...

The space of C-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains is considered. The investigation of the dimension of the spaces of biquintic and bisixtic C-smooth geometrically continuous isogeometric functions on such domains is presented. In addition, C-smooth isogeometric functions are constructed to be used for performing L-approximation a...

Isogeometric analysis allows to define shape functions of global C continuity (or of higher continuity) over multi-patch geometries. The construction of such C-smooth isogeometric functions is a non-trivial task and requires particular multi-patch parameterizations, so-called analysis-suitable G (in short, AS-G) parameterizations, to ensure that the resulting C isogeometric spaces possess optim...

The fast solution of linear systems arising from an isogeometric discretization of a partial differential equation is of great importance for the practical use of Isogeometric Analysis. For classical finite element discretizations, multigrid methods are well known to be fast solvers showing optimal convergence behavior. However, if a geometric multigrid solver is naively applied to a linear sys...

In the present paper, an approach is proposed for structural topology optimization based on combination of Radial Basis Function (RBF) Level Set Method (LSM) with Isogeometric Analysis (IGA). The corresponding combined algorithm is detailed. First, in this approach, the discrete problem is formulated in Isogeometric Analysis framework. The objective function based on compliance of particular lo...

In this paper, we present a boundary integral based approach to isogeometric analysis and shape optimization. For analysis, it uses the same basis, Non-Uniform Rational B-Spline (NURBS) basis, for both representing object boundary and for approximating physical fields in analysis via a Boundary-Integral-Equation Method (BIEM). We propose the use of boundary points corresponding to Greville absc...

NURBS-based isogeometric analysis (IGA) has currently been applied as a new numerical method in a considerable range of engineering problems. Due to non-interpolatory characteristic of NURBS basis functions, the properties of Kronecker Delta are not satisfied in IGA, and as a consequence, the imposition of essential boundary condition needs special treatment. The main contribution of this study...

Isogeometric Analysis uses NURBS representations of the domain for performing numerical simulations. The first part of this paper presents a variational framework for generating NURBS parameterizations of swept volumes. The class of these volumes covers a number of interesting free-form shapes, such as blades of turbines and propellers, ship hulls or wings of airplanes. The second part of the p...

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...

We derive Newton-type solution algorithms for a Bernoulli-type freeboundary problem at the continuous level. The Newton schemes are obtained by applying Hadamard shape derivatives to a suitable weak formulation of the freeboundary problem. At each Newton iteration, an updated free boundary position is obtained by solving a boundary-value problem at the current approximate domain. Since the boun...