60 citations · 167 across the 19 of their papers we have counts for
20 papers
Wigner-Eckart Factorization of the Polyatomic Boltzmann Collision Operator
Torsten Keßler, Bas W. T. Gieling, René R. Hiemstra +1
We extend the Wigner-Eckart factorization of the spectral Boltzmann collision operator to polyatomic gases with continuous internal energy. Because internal energies are invariant…
Isogeometric Analysis for Explicit Wave Propagation in Poroelastic Media
Maarten M. Hodzelmans, René R. Hiemstra, Joris J. C. Remmers +1
For higher-order discretizations of explicit dynamics problems, Isogeometric Analysis (IGA) has several favorable properties as compared to classical Finite Element Analysis (FEA).…
Wigner-Eckart Factorization of the Spectral Boltzmann Collision Operator
René R. Hiemstra, Torsten Keßler, Michael R. A. Abdelmalik
We reduce the eight-dimensional weak form of the bilinear Boltzmann collision operator to a five-dimensional kinematic core by rigidly rotating the laboratory frame to align with t…
A locking-free isogeometric thin shell formulation based on higher order accurate diagonalized strain projection via approximate dual splines
Thi-Hoa Nguyen, René R. Hiemstra, Dominik Schillinger
We present a novel isogeometric discretization approach for the Kirchhoff-Love shell formulation based on the Hellinger-Reissner variational principle. For mitigating membrane lock…
The matrix-free macro-element hybridized Discontinuous Galerkin method for steady and unsteady compressible flows
Vahid Badrkhani, Marco F. P. ten Eikelder, Rene R. Hiemstra +1
The macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we…
Matrix-free polynomial preconditioning of saddle point systems using the hyper-power method
Michał Łukasz Mika, Marco ten Eikelder, Dominik Schillinger +1
This study explores the integration of the hyper-power sequence, a method commonly employed for approximating the Moore-Penrose inverse, to enhance the effectiveness of an existing…
Higher order accurate mass lumping for explicit isogeometric methods based on approximate dual basis functions
Rene Hiemstra, Thi-Hoa Nguyen, Sascha Eisentrager +2
This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and rowsum mass lumping. We demonstrate that the approach ma…
Nonlinear dynamic analysis of shear- and torsion-free rods using isogeometric discretization and outlier removal
Thi-Hoa Nguyen, Bruno A. Roccia, René R. Hiemstra +2
In this paper, we present a discrete formulation of nonlinear shear- and torsion-free rods introduced by Gebhardt and Romero in [20] that uses isogeometric discretization and robus…
Fast immersed boundary method based on weighted quadrature
Benjamin Marussig, René Hiemstra, Dominik Schillinger
Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts t…
Fourier analysis of membrane locking and unlocking
Rene R. Hiemstra, Federico Fuentes, Dominik Schillinger
Membrane locking in finite element approximations of thin beams and shells has remained an unresolved topic despite four decades of research. In this article, we utilize Fourier an…
Towards higher-order accurate mass lumping in explicit isogeometric analysis for structural dynamics
Thi-Hoa Nguyen, René R. Hiemstra, Sascha Eisenträger +1
We present a mass lumping approach based on an isogeometric Petrov-Galerkin method that preserves higher-order spatial accuracy in explicit dynamics calculations irrespective of th…
A matrix-free macro-element variant of the hybridized discontinuous Galerkin method
Vahid Badrkhani, Rene R. Hiemstra, Michal Mika +1
We investigate a macro-element variant of the hybridized discontinuous Galerkin (HDG) method, using patches of standard simplicial elements that can have non-matching interfaces. C…
Variationally consistent mass scaling for explicit time-integration schemes of lower- and higher-order finite element methods
Stein K. F. Stoter, Thi-Hoa Nguyen, René R. Hiemstra +1
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach…
A variational approach based on perturbed eigenvalue analysis for improving spectral properties of isogeometric multipatch discretizations
Thi-Hoa Nguyen, René R. Hiemstra, Stein K. F. Stoter +1
A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies and eigenmodes. For degree two and higher, however, optical branches of spurious…
Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler-Bernoulli beam
Thi-Hoa Nguyen, René R. Hiemstra, Dominik Schillinger
In this paper, we take a fresh look at using spectral analysis for assessing locking phenomena in finite element formulations. We propose to "measure" locking by comparing the diff…
A comparison of matrix-free isogeometric Galerkin and collocation methods for Karhunen--Loève expansion
Michal Lukasz Mika, René Rinke Hiemstra, Thomas Joseph Robert Hughes +1
Numerical computation of the Karhunen--Loève expansion is computationally challenging in terms of both memory requirements and computing time. We compare two state-of-the-art metho…
The Quad Layout Immersion: A Mathematically Equivalent Representation of a Surface Quadrilateral Layout
Kendrick M. Shepherd, René R. Hiemstra, Thomas J. R. Hughes
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such…
A matrix-free isogeometric Galerkin method for Karhunen-Loève approximation of random fields using tensor product splines, tensor contraction and interpolation based quadrature
Michal Lukasz Mika, Thomas Joseph Robert Hughes, Dominik Schillinger +2
The Karhunen-Loève series expansion (KLE) decomposes a stochastic process into an infinite series of pairwise uncorrelated random variables and pairwise -orthogonal functions.…
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…
Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
Artur Palha, Pedro Pinto Rebelo, René Hiemstra +2
This paper introduces the basic concepts for physics-compatible discretization techniques. The paper gives a clear distinction between vectors and forms. Based on the difference be…