Publications

Constraints for eliminating the Gibbs phenomenon in finite element approximation spaces

One of the major challenges in finite element methods is the mitigation of spurious oscillations near sharp layers and discontinuities …
Marco ten Eikelder, Stein K. F. Stoter, Yuri Bazilevs, Dominik Schillinger
DOI arXiv

Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

In this article, we study the effect of small-cut elements on the critical time-step size in an immersogeometric context. We analyze …
Stein K. F. Stoter, Sai C. Divi, E. Harald van Brummelen, Mats G. Larson, Frits de Prenter, Clemens V. Verhoosel
DOI arXiv

Stabilized immersed isogeometric analysis for the Navier–Stokes–Cahn–Hilliard equations, with applications to binary-fluid flow through porous media

Binary-fluid flows can be modeled using the Navier–Stokes–Cahn–Hilliard equations, which represent the boundary between the fluid …
Stein K. F. Stoter, Tom B. van Sluijs, Tristan H. B. Demont, E. Harald van Brummelen, Clemens V. Verhoosel
DOI arXiv

Numerical investigation of the sharp-interface limit of the Navier-Stokes-Cahn-Hilliard equations

In this article, we study the behavior of the Abels-Garcke-Grün Navier-Stokes-Cahn-Hilliard diffuse-interface model for binary-fluid …
Tristan H. B. Demont, Stein K. F. Stoter, E. Harald van Brummelen
DOI arXiv

Discontinuous Galerkin methods through the lens of variational multiscale analysis

In this article, we present a theoretical framework for integrating discontinuous Galerkin methods in the variational multiscale …
Stein K. F. Stoter, Bernardo Cockburn, Thomas J. R. Hughes, Dominik Schillinger
DOI URL

Variationally consistent mass scaling for explicit time-integration schemes of lower- and higher-order finite element methods

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics …
Stein K. F. Stoter, Thi-Hoa Nguyen, René R. Hiemstra, Dominik Schillinger
DOI arXiv

A DEIM driven reduced basis method for the diffuse Stokes/Darcy model coupled at parametric phase-field interfaces

In this article, we develop a reduced basis method for efficiently solving the coupled Stokes/Darcy equations with parametric internal …
Stein K. F. Stoter, Etienne Jessen, Viktor Niedens, Dominik Schillinger
DOI arXiv

A variational approach based on perturbed eigenvalue analysis for improving spectral properties of isogeometric multipatch discretizations

A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies and eigenmodes. For degree two and …
Thi-Hoa Nguyen, René R. Hiemstra, Stein K. F. Stoter, Dominik Schillinger
DOI arXiv

Nitsche's method as a variational multiscale formulation and a resulting boundary layer fine-scale model

We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche’s method …
Stein K. F. Stoter, Marco F. P. ten Eikelder, Frits de Prenter, Ido Akkerman, E. Harald van Brummelen, Clemens V. Verhoosel, Dominik Schillinger
DOI arXiv

Understanding and Mitigating the Dynamic Behavior of RICWS and DMS Under Wind Loading

Dynamic Messaging Signs (DMS) and Rural Intersection Conflict Warning Signs (RICWS) are roadside signs that feature much larger and …
Lauren Linderman, Michele Guala, Catherine French, Dominik Schillinger, Nicole Finley, Michael Heisel, Lam Nguyen, Stein K. F. Stoter, Josh Vievering, Qiming Zhu
URL

Reducing wind-induced vibrations of road sign structures through aerodynamic modifications: A computational pilot study for a practical example

In this article, we illustrate the potential of aerodynamic modifications of road signs to reduce wind-induced vibrations. Using a …
Qiming Zhu, Stein K. F. Stoter, Michael Heisel, Catherine E. French, Michele Guala, Lauren E. Linderman, Dominik Schillinger
DOI

The variational multiscale method for discontinuous Galerkin type finite element formulations

University of Minnesota Ph.D. dissertation. December 2019. Major: Civil Engineering. Advisor: Dominik Schillinger.
Stein K. F. Stoter
URL

Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order …
Zhilin Han, Stein K. F. Stoter, Chien-Ting Wu, Changzheng Cheng, Angelos Mantzaflaris, Sofia G. Mogilevskaya, Dominik Schillinger
DOI

The variational multiscale method for mixed finite element formulations

University of Minnesota MSc thesis. April 2018. Major: Mathematics. Advisor: Bernardo Cockburn.
Stein K. F. Stoter
URL

The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche’s method for consistently imposing Dirichlet boundary conditions on phase-field …
Lam H. Nguyen, Stein K. F. Stoter, Martin Ruess, Manuel A. Sanchez Uribe, Dominik Schillinger
DOI

Residual-based variational multiscale modeling in a discontinuous Galerkin framework

We develop the general form of the variational m ultiscale method in a discontinuous Galerkin framework. Our method is based on the …
Stein K. F. Stoter, Sergio R. Turteltaub, Steven J. Hulshoff, Dominik Schillinger
DOI arXiv

A discontinuous Galerkin residual-based variational multiscale method for modeling subgrid-scale behavior of the viscous Burgers equation

We initiate the study of the discontinuous Galerkin residual-based variational multiscale (DG-RVMS) method for incorporating …
Stein K. F. Stoter, Sergio R. Turteltaub, Steven J. Hulshoff, Dominik Schillinger
DOI

Residual-based variational multiscale modeling in a discontinuous Galerkin framework

Delft University of Technology MSc thesis. June 2017. Major: Aerospace Engineering. Advisor: Sergio Turteltaub.
Stein K. F. Stoter
URL

Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography …
Lam H. Nguyen, Stein K. F. Stoter, Thomas Baum, Jan S. Kirschke, Martin Ruess, Zohar Yosibash, Dominik Schillinger
DOI

A diffuse interface method for the Navier–Stokes/Darcy equations: Perfusion profile for a patient-specific human liver based on MRI scans

We present a diffuse interface method for coupling free and porous-medium-type flows modeled by the Navier–Stokes and Darcy equations. …
Stein K. F. Stoter, Peter Müller, Luca Cicalese, Massimiliano Tuveri, Dominik Schillinger, Thomas J. R. Hughes
DOI URL

The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements

We explore the use of the non-symmetric Nitsche method for the weak imposition of boundary and coupling conditions along interfaces …
Dominik Schillinger, Isaac Harari, Ming-Chen Hsu, David Kamensky, Stein K. F. Stoter, Yue Yu, Ying Zhao
DOI