# Gunilla Kreiss

Professor at Department of Information Technology; Division of Scientific Computing

- Telephone:
- +46 18 471 29 68
- Mobile phone:
- +46 70 167 90 16
- E-mail:
- Gunilla.Kreiss@it.uu.se
- Visiting address:
- Hus 10, Lägerhyddsvägen 1
- Postal address:
- Box 337

751 05 UPPSALA

- Academic merits:
- Docent

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## Short presentation

I am professor of Numerical Analysis at the division for scientific computing at Uppsala University.

## Research

I am interested in numerical methods for partial differential equations.

Hyperbolic systems has been a special interest for a long time. Currantly I am working on methods for second order wave equations, and models for the flow in a network of channels based on the shallow water equation. Over the last 10 years much work has concerned perfectly matched absorbing layers for wave propagation problems.

Navier-Stokes equations is another long standing interest. Currently my work is directed towards numerical simulation of multiphase flow, but I have recently become involved in work concerning boundary closures for LES.

A more recent interest is multiscale methods for magnetization dynamics. Numerical techniques based on several different descriptions of the physics, each valid at different scales, are used to simulate phenomena at large scales, while including effects of small-scale variations.

Over the last 10 years much work has concerned perfectly matched absorbing layers for wave propagation problems. In addition to the scalar wave eqaution and the system of elastic wave equation, I have also considered the Schrödinger equation, which also supports waves. In the group working on numerical methods for Quantum Dynamics, I have focused on high order approximations and accurate numerical boundary closures.

## Publications

### Selection of publications

- Temporal upscaling in micromagnetism via heterogeneous multiscale methods (2019)
- A stabilized Nitsche cut element method for the wave equation (2016)

### Recent publications

- Improved accuracy of plane-wave electromagnetic modelling by application of the total and scattered field decomposition and perfectly matched layers (2023)
- A Finite Difference-Discontinuous Galerkin Method for the Wave Equation in Second Order Form (2023)
- On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation (vol 350, pg 898, 2019) (2022)
- High Order Discontinuous Cut Finite Element Methods for Linear Hyperbolic Conservation Laws with an Interface (2022)
- An Energy-Based Summation-by-Parts Finite Difference Method For the Wave Equation in Second Order Form (2022)

### All publications

#### Articles

- Improved accuracy of plane-wave electromagnetic modelling by application of the total and scattered field decomposition and perfectly matched layers (2023)
- A Finite Difference-Discontinuous Galerkin Method for the Wave Equation in Second Order Form (2023)
- On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation (vol 350, pg 898, 2019) (2022)
- High Order Discontinuous Cut Finite Element Methods for Linear Hyperbolic Conservation Laws with an Interface (2022)
- An Energy-Based Summation-by-Parts Finite Difference Method For the Wave Equation in Second Order Form (2022)
- Stability analysis of high order methods for the wave equation (2022)
- High Order Cut Discontinuous Galerkin Methods For Hyperbolic Conservation Laws In One Space Dimension (2021)
- Modelling long-range interactions in multiscale simulations of ferromagnetic materials (2020)
- A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form (2020)
- Existence result for the coupling of shallow water and Borda–Carnot equations with Riemann data (2020)
- Multiscale approach for magnetization dynamics (2020)
- High-order cut discontinuous Galerkin methods with local time stepping for acoustics (2020)
- High-order cut finite elements for the elastic wave equation (2020)
- Temporal upscaling in micromagnetism via heterogeneous multiscale methods (2019)
- On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation (2019)
- A hydrodynamic model of movement of a contact line over a curved wall (2019)
- Higher order cut finite elements for the wave equation (2019)
- An equation-free approach for second order multiscale hyperbolic problems in non-divergence form (2018)
- Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature (2018)
- Effective slip over partially filled microcavities and its possible failure (2018)
- Preface (2018)
- High-order numerical methods for 2D parabolic problems in single and composite domains (2018)
- Coupling atomistic and continuum modelling of magnetism (2018)
- Convergence of finite difference methods for the wave equation in two space dimensions (2018)
- An explicit Hermite–Taylor method for the Schrödinger equation (2017)
- A computational multiscale model for contact line dynamics (2017)
- A phase-field microscale enhancement for macro models of capillary-driven contact point dynamics (2017)
- Convergence of summation-by-parts finite difference methods for the wave equation (2017)
- Analysis of stretched grids as buffer zones in simulations of wave propagation (2016)
- Scale transitions in magnetisation dynamics (2016)
- A stabilized Nitsche cut element method for the wave equation (2016)
- High order finite difference methods for the wave equation with non-conforming grid interfaces (2016)
- Boundary conditions and stability of a perfectly matched layer for the elastic wave equation in first order form (2015)
- Towards accurate modeling of moving contact lines (2015)
- Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations (2015)
- Elastic wave propagation in complex geometries (2015)
- Interface waves in almost incompressible elastic materials (2015)
- Boundary waves and stability of the perfectly matched layer for the two space dimensional elastic wave equation in second order form (2014)
- Efficient and stable perfectly matched layer for CEM (2014)
- Numerical interaction of boundary waves with perfectly matched layers in two space dimensional elastic waveguides (2014)
- Stable and high-order accurate boundary treatments for the elastic wave equation on second-order form (2014)
- A Riemann problem at a junction of open canals (2013)
- A delayed feedback control for network of open canals (2013)
- Discrete stability of perfectly matched layers for anisotropic wave equations in first and second order formulation (2013)
- High order stable finite difference methods for the Schrödinger equation (2013)
- A uniformly well-conditioned, unfitted Nitsche method for interface problems (2013)
- On the accuracy and stability of the perfectly matched layer in transient waveguides (2012)
- A well-posed and discretely stable perfectly matched layer for elastic wave equations in second order formulation (2012)
- A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity (2012)
- Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation (2012)
- Spurious currents in finite element based level set methods for two-phase flow (2012)
- A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition (2011)
- An optimized perfectly matched layer for the Schrödinger equation (2011)
- A perfectly matched layer applied to a reactive scattering problem (2010)
- Direct numerical simulations of localized disturbances in pipe Poiseuille flow (2010)
- A conservative level set method for contact line dynamics (2009)
- Stress chain solutions in two-dimensional isostatic granular systems (2008)
- Analysis of stresses in two-dimensional isostatic granular systems (2008)
- Stability of viscous shocks on finite intervals (2008)
- Application of a perfectly matched layer to the nonlinear wave equation (2007)
- Modeling of contact line dynamics for two-phase flow (2007)
- A conservative level set method for two phase flow II (2007)
- Perfectly matched layers for hyperbolic systems (2006)
- A conservative level set method for two phase flow (2005)
- Elimination of first order errors in shock calculations (2001)
- Stability of systems of viscous conservation laws (1998)
- Using preconditioned iterative methods in electromagnetic geophysical modelling including perfectly-matched layers

#### Books

#### Chapters

- Finite difference methods (2015)
- An algebraic approach for controlling cascade of reaches in irrigation canals (2012)

#### Conferences

- Boundary waves and stability of perfectly matched layers II (2013)
- Boundary waves and stability of perfectly matched layers I (2013)
- Surface waves in almost incompressible elastic materials (2013)
- Analysis of boundary conditions in numerical simulations of geological CO
_{2}storage (2011) - Stable perfectly matched layers for the Schrödinger equations (2010)
- Analysis of stretched grids as buffer zones in aero-acoustic simulations (2009)
- A hybrid level-set Cahn–Hilliard model for two-phase flow (2008)
- Asynchronous time integration of flux-conservative transport (2008)
- An interface capturing method for two-phase flow with moving contact lines (2008)

#### Reports

- Effective slip over partially filled microcavities and its possible failure (2017)
- Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations (2013)
- Numerical interaction of boundary waves with perfectly matched layers in elastic waveguides (2012)
- Boundary waves and stability of the perfectly matched layer (2012)
- Stable and conservative time propagators for second order hyperbolic systems (2011)
- A hybrid level-set-phase-field method for two-phase flow with contact lines (2011)
- Multiscale modeling of capillary-driven contact line dynamics (2011)
- High order stable finite difference methods for the Schrödinger equation (2011)
- Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation (2011)
- A Well-posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation (2010)
- An optimized perfectly matched layer for the Schrödinger equation (2009)
- Spurious currents in a finite-element based level set method for two phase flow (2009)