This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and NURBS (non-uniform rational B-splines) discretizations that are employed in Isogeometric Analysis [23]. We make use of quadratic discretizations that are C-continuous across element boundaries in standard finite elements, and C-continuous in the case of NURBS. T...

Tissue expansion is a popular technique in plastic and reconstructive surgery that grows skin in vivo for correction of large defects such as burns and giant congenital nevi. Despite its widespread use, planning and executing an expansion protocol is challenging due to the difficulty in measuring the deformation imposed at each inflation step and over the length of the procedure. Quantifying th...

Isogeometric analysis (IGA) is a numerical simulation method which is directly based on the NURBS-based representation of CAD models. It exploits the tensor-product structure of 2- or 3-dimensional NURBS objects to parameterize the physical domain. Hence the physical domain is parameterized with respect to a rectangle or to a cube. Consequently, singularly parameterized NURBS surfaces and NURBS...

Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requ...

Alireza H. Taheri, Krishnan Suresh* Department of Mechanical Engineering, UW-Madison, Madison, Wisconsin 53706, USA. * Corresponding author, email: [email protected] Abstract A new isogeometric density based approach for the topology optimization of multi-material structures is presented. In this method, the density fields of multiple material phases are represented using the isogeometric NURBS-...

This paper deals with the isogeometric analysis using B-splines of space rods subject to Kirchhoff-Love hypotheses. A multi-patch isogeometric approach for the numerical analysis of the three-dimensional Kirchhoff-Love rod theory is developed. We use Bezier and B-splines interpolations and we show that they are able to attain very good accuracy for rod structures, particularly for developing a ...

We initiate the study of efficient quadrature rules for NURBS-based isogeometric analysis. A rule of thumb emerges, the “half-point rule”, indicating that optimal rules involve a number of points roughly equal to half the number of degrees-of-freedom, or equivalently half the number of basis functions of the space under consideration. The half-point rule is independent of the polynomial order o...

Isogeometric methods were introduced by Hughes et al. in 2005. Since its introduction these methods have been used in many practical problems in science and engineering. However, so far, only few papers appeared in the field of iterative solvers for these methods. This thesis contributes to the development of fast iterative solvers for the matrices arising in isogeometric discretization of elli...

In computational hemodynamics we typically need to solve incompressible fluids in domains given by curved pipes or network of pipes. To reduce the computational costs, or conversely to improve models based on a pure 1D (axial) modeling, an approach called “Hierarchical Model reduction” (HiMod) was recently proposed. It consists of a diverse numerical approximation of the axial and of the transv...

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on...