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Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…
The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined…
We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…
A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it…
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…
We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…
In this paper we address the problem of constructing $G^2$ planar Pythagorean--hodograph (PH) spline curves, that interpolate points, tangent directions and curvatures, and have prescribed arc-length. The interpolation scheme is completely…
Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
In this paper, equilibrium and stability equations of functionally graded material (FGM) plate under thermal environment are formulated based on isogeometric analysis (IGA) in combination with higher-order shear deformation theory (HSDT).…
This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the…
A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed from element-scale quadrature…
In this paper, we develop approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard…
Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation…
The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical…
The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…