Publications (27)
Decoupling multistep schemes for elliptic-parabolic problems
Robert Altmann, Abdullah Mujahid, Benjamin Unger
We study the construction and convergence of decoupling multistep schemes of higher order using the backward differentiation formulae for an elliptic-parabolic problem, which inclu…
Singular perturbation results for linear partial differential-algebraic equations of hyperbolic type
Robert Altmann, Christoph Zimmer
We consider constrained partial differential equations of hyperbolic type with a small parameter , which turn parabolic in the limit case, i.e., for .…
A decoupling and linearizing discretization for weakly coupled poroelasticity with nonlinear permeability
Robert Altmann, Roland Maier
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are o…
Port-Hamiltonian formulations of poroelastic network models
Robert Altmann, Volker Mehrmann, Benjamin Unger
We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in geosciences or medical applications. We pr…
Splitting schemes for the semi-linear wave equation with dynamic boundary conditions
Robert Altmann
This paper introduces novel bulk-surface splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For ki…
Computational Multiscale Methods for Linear Poroelasticity with High Contrast
Shubin Fu, Robert Altmann, Eric T. Chung +3
In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with…
Splitting methods for constrained diffusion-reaction systems
Robert Altmann, Alexander Ostermann
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensi…
A posteriori error estimation for parabolic problems with dynamic boundary conditions
Robert Altmann, Christoph Zimmer
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characteri…
Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials
Robert Altmann, Patrick Henning, Daniel Peterseim
This paper concerns spectral properties of linear Schrödinger operators under oscillatory high-amplitude potentials on bounded domains. Depending on the degree of disorder, we pro…
Localized computation of eigenstates of random Schrödinger operators
Robert Altmann, Daniel Peterseim
This paper concerns the numerical approximation of low-energy eigenstates of the linear random Schrödinger operator. Under oscillatory high-amplitude potentials with a sufficient…
Semi-explicit discretization schemes for weakly-coupled elliptic-parabolic problems
Robert Altmann, Roland Maier, Benjamin Unger
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled.…
Higher-order iterative decoupling for poroelasticity
Robert Altmann, Abdullah Mujahid, Benjamin Unger
For the iterative decoupling of elliptic-parabolic problems such as poroelasticity, we introduce time discretization schemes up to order based on the backward differentiation f…
Bulk-surface Lie splitting for parabolic problems with dynamic boundary conditions
Robert Altmann, Balázs Kovács, Christoph Zimmer
This paper studies bulk-surface splitting methods of first order for (semi-linear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie split…
Energy-based modeling for field-circuit coupling
Robert Altmann, Idoia Cortes Garcia, Elias Paakkunainen +2
This paper presents a generalized energy-based modeling framework extending recent formulations tailored for differential-algebraic equations. The proposed structure, inspired by t…
Energy-adaptive Riemannian optimization on the Stiefel manifold
Robert Altmann, Daniel Peterseim, Tatjana Stykel
This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross-Pitaevskii and Kohn-Sham equation arising in computational physics and chemistry. Th…
Decoupling Runge-Kutta schemes for elliptic-parabolic problems
Robert Altmann, Abdullah Mujahid, Benjamin Unger
We study the construction and convergence of semi-explicit and iterative decoupling schemes for an elliptic-parabolic problem using higher-order Runge-Kutta methods. For the semi-e…
Continuous Galerkin Schemes for Semi-Explicit Differential-Algebraic Equations
Robert Altmann, Roland Herzog
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Ou…
Time discretization schemes for hyperbolic systems on networks by -expansion
Robert Altmann, Christoph Zimmer
We consider partial differential equations on networks with a small parameter , which are hyperbolic for and parabolic for . With a combination of an -expansio…
PDE eigenvalue iterations with applications in two-dimensional photonic crystals
Robert Altmann, Marine Froidevaux
We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue prob…
A multiscale method for heterogeneous bulk-surface coupling
Robert Altmann, Barbara Verfürth
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformu…
Computational multiscale methods for linear heterogeneous poroelasticity
Robert Altmann, Eric Chung, Roland Maier +2
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly o…
Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations
Robert Altmann, Jan Heiland
The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and tempor…
Exponential integrators for semi-linear parabolic problems with linear constraints
Robert Altmann, Christoph Zimmer
This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we com…
A PDAE formulation of parabolic problems with dynamic boundary conditions
Robert Altmann
The weak formulation of parabolic problems with dynamic boundary conditions is rewritten in form of a partial differential-algebraic equation. More precisely, we consider two dynam…
Structure-Preserving Discretization and Model Reduction for Energy-Based Models
Robert Altmann, Attila Karsai, Philipp Schulze
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradien…
Localization and delocalization of ground states of Bose-Einstein condensates under disorder
Robert Altmann, Patrick Henning, Daniel Peterseim
This paper studies the localization behaviour of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the re…
The -method for the Gross-Pitaevskii eigenvalue problem
Robert Altmann, Patrick Henning, Daniel Peterseim
This paper studies the -method of [E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert spa…