47 citations · 166 across the 18 of their papers we have counts for
19 papers
Adaptively-refinable polar-spline discrete differential forms: hierarchical construction, exactness, and applications
Diogo C. Cabanas, Deepesh Toshniwal, Rafael Vazquez
A common approach to representing disk-like and sphere-like geometries in isogeometric analysis is to use collapsed-edge singularities in the underlying parameterization. The resul…
Structure-preserving Variational Multiscale Stabilization of the Incompressible Navier-Stokes Equations
Kevin Dijkstra, Deepesh Toshniwal
This paper introduces a Variational Multiscale Stabilization (VMS) formulation of the incompressible Navier--Stokes equations that utilizes the Finite Element Exterior Calculus (FE…
Macro-element Refinement schemes for THB-Splines: Applications to Bézier Projection and Structure-Preserving Discretizations
Kevin Dijkstra, Carlotta Giannelli, Deepesh Toshniwal
This paper introduces a novel adaptive refinement strategy for Isogeometric Analysis (IGA) using Truncated Hierarchical B-splines (THB-splines). The proposed strategy enhances loca…
Construction of exact refinements for the two-dimensional hierarchical B-spline de Rham complex
Diogo C. Cabanas, Kendrick M. Shepherd, Deepesh Toshniwal +1
The de Rham complex arises naturally when studying problems in electromagnetism and fluid mechanics. Stable numerical methods to solve these problems can be obtained by using a dis…
Decoupled structure-preserving discretization of incompressible MHD equations with general boundary conditions
Yi Zhang, Artur Palha, Andrea Brugnoli +2
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is pro…
A characterization of linear independence of THB-splines in and application to Bézier projection
Kevin Dijkstra, Deepesh Toshniwal
In this paper we propose a local projector for truncated hierarchical B-splines (THB-splines). The local THB-spline projector is an adaptation of the Bézier projector proposed by T…
A comparison of smooth basis constructions for isogeometric analysis
H. M. Verhelst, P. Weinmüller, A. Mantzaflaris +2
In order to perform isogeometric analysis with increased smoothness on complex domains, trimming, variational coupling or unstructured spline methods can be used. The latter two cl…
Locally-verifiable sufficient conditions for exactness of the hierarchical B-spline discrete de Rham complex in
Kendrick Shepherd, Deepesh Toshniwal
Given a domain , the de Rham complex of differential forms arises naturally in the study of problems in electromagnetism and fluid mechanics defined on ,…
Almost- splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems
Thomas Takacs, Deepesh Toshniwal
Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objecti…
An optimally convergent smooth blended B-spline construction for semi-structured quadrilateral and hexahedral meshes
Kim Jie Koh, Deepesh Toshniwal, Fehmi Cirak
Easy to construct and optimally convergent generalisations of B-splines to unstructured meshes are essential for the application of isogeometric analysis to domains with non-trivia…
Algebraic Methods for Supersmooth Spline Spaces
Deepesh Toshniwal, Nelly Villamizar
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of appli…
A general class of smooth rational splines: Application to construction of exact ellipses and ellipsoids
Hendrik Speleers, Deepesh Toshniwal
In this paper, we describe a general class of smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids - some of the most important…
The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics
Hugo Casquero, Carles Bona-Casas, Deepesh Toshniwal +3
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids.…
A Tchebycheffian extension of multi-degree B-splines: Algorithmic computation and properties
Rene R. Hiemstra, Thomas J. R. Hughes, Carla Manni +2
In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The exte…
Counting the dimension of splines of mixed smoothness: A general recipe, and its application to meshes of arbitrary topologies
Deepesh Toshniwal, Michael DiPasquale
In this paper we study the dimension of bivariate polynomial splines of mixed smoothness on polygonal meshes. Here, "mixed smoothness" refers to the choice of different orders of s…
Dimension of polynomial splines of mixed smoothness on T-meshes
Deepesh Toshniwal, Nelly Villamizar
In this paper we study the dimension of splines of mixed smoothness on axis-aligned T-meshes. This is the setting when different orders of smoothness are required across the edges…
Polynomial spline spaces of non-uniform bi-degree on T-meshes: Combinatorial bounds on the dimension
Deepesh Toshniwal, Bernard Mourrain, Thomas Hughes
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…
An isogeometric finite element formulation for phase transitions on deforming surfaces
Christopher Zimmermann, Deepesh Toshniwal, Chad M. Landis +3
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem i…
A Geometric Approach Towards Momentum Conservation
D. Toshniwal, R. H. M. Huijsmans, M. I. Gerritsma
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating momentum as a covector-valued volume-form. The novelty of this approach is that we tre…