Related papers: Trivariate Spline Representations for Computer Aid…
Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
The spline space $C_k^r(\Delta)$ attached to a subdivided domain $\Delta$ of $\R^{d} $ is the vector space of functions of class $C^{r}$ which are polynomials of degree $\le k$ on each piece of this subdivision. Classical splines on planar…
Electroencephalographic signals are represented as multidimensional datasets. We introduce an enhancement to the augmented covariance method (ACM), exploiting more thoroughly its mathematical properties, in order to improve motor imagery…
Reachable Minimally supported (RM) B-splines have been recently introduced as a novel B-spline--like basis. They feature local linear independence and admit a fast de Boor--like evaluation algorithm. These properties make them particularly…
In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community…
BSplines are one of the most promising curves in computer graphics. They are blessed with some superior geometric properties which make them an ideal candidate for several applications in computer aided design industry. In this article,…
During the last decade, additive manufacturing has become increasingly popular for rapid prototyping, but has remained relatively marginal beyond the scope of prototyping when it comes to applications with tight tolerance specifications,…
The isogeometric formulation of Boundary Element Method (BEM) is investigated within the adaptivity framework. Suitable weighted quadrature rules to evaluate integrals appearing in the Galerkin BEM formulation of 2D Laplace model problems…
Amorphous solids form an enormous and underutilized class of materials. In order to drive the discovery of new useful amorphous materials further we need to achieve a closer convergence between computational and experimental methods. In…
Splines over triangulations and splines over quadrangulations (tensor product splines) are two common ways to extend bivariate polynomials to splines. However, combination of both approaches leads to splines defined over mixed triangle and…
We present a flexible illustrative line style model for the visualization of streamline data. Our model partitions view-oriented line strips into parallel bands whose basic visual properties can be controlled independently. We thus extend…
Polynomial splines are ubiquitous in the fields of computer aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly versatile since local mesh adaptivity enables efficient…
This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from Micro-CT images featuring intricate microstructures. The proposed method is guided by…
It is often desirable to build a statistical emulator of a complex computer simulator in order to perform analysis which would otherwise be computationally infeasible. We propose methodology to model multivariate output from a computer…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
Thin-walled structures capable of large, reversible deformation are key to multistable structures, origami, kirigami, and soft robotics. However, conventional fabrication techniques, including 3D printing, casting, and laser cutting, suffer…
The use of machine learning is becoming increasingly common in computational materials science. To build effective models of the chemistry of materials, useful machine-based representations of atoms and their compounds are required. We…