Related papers: Isogeometric mortar methods
A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary…
We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…
We develop a mixed formulation for incompressible hyper-elastodynamics based on a continuum modeling framework recently developed and smooth generalizations of the Taylor-Hood element based on non-uniform rational B-splines (NURBS). This…
This paper investigates nonlinear bending and buckling behaviours of composite plates characterized by a thickness variation. Layer interfaces are described as functions of inplane coordinates. Top and bottom surfaces of the plate are…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…
This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
The damage spreading method (DS) provided a useful tool to obtain analytical results of the thermodynamics and stability of the 2D Ising model --amongst many others--, but it suffered both from ambiguities in its results and from large…
We present an isogeometric framework based on collocation to construct a $C^2$-smooth approximation of the solution of the Poisson's equation over planar bilinearly parameterized multi-patch domains. The construction of the used globally…
In this paper, we focus on the exploration of solution uniqueness, sharpness, and robust recovery in sparse regularization with a gauge $J$. Based on the criteria for the uniqueness of Lagrange multipliers in the dual problem, we give a…
We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling…
Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non Uniform Rational B-splines) to generate cohesive elements…
We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the…
Isogeometric analysis (IGA) enables exact representations of computational geometries and higher-order approximation of PDEs. In non-smooth domains, however, singularities near corners limit the effectiveness of IGA, since standard methods…
It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf-sup approximation stability even if a stable high fidelity method was used to generate…