5 papers
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…
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…
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…
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 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…