Publications (39)
Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems
Christian Engwer, Mario Ohlberger, Lukas Renelt
We investigate parametrized variational problems where for each parameter the solution may originate from a different parameter-dependent function space. Our main motivation is the…
Vectorized Parallel in Time methods for low-order discretizations with application to Porous Media problems
Christian Engwer, Alexander Schell, Nils-Arne Dreier
High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to l…
The DUNE Framework: Basic Concepts and Recent Developments
Peter Bastian, Markus Blatt, Andreas Dedner +9
This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that hap…
The Distributed and Unified Numerics Environment (DUNE), Version 2.10
Markus Blatt, Samuel Burbulla, Ansgar Burchardt +9
Version 2.10 of the Distributed and Unified Numerics Environment DUNE introduces a range of enhancements across its core and extension modules, with a continued emphasis on modern…
ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications
Andreas Buhr, Christian Engwer, Mario Ohlberger +1
Engineers manually optimizing a structure using Finite Element based simulation software often employ an iterative approach where in each iteration they change the structure slight…
A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations
Andreas Buhr, Christian Engwer, Mario Ohlberger +1
The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirem…
A Mixed Finite Element Method to Solve the EEG Forward Problem
Johannes Vorwerk, Christian Engwer, Sampsa Pursiainen +1
Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and im…
DoD stabilization for higher-order advection in two dimensions
Florian Streitbürger, Gunnar Birke, Christian Engwer +1
When solving time-dependent hyperbolic conservation laws on cut cell meshes one has to overcome the small cell problem: standard explicit time stepping is not stable on small cut c…
Geometric Integration Over Irregular Domains with topologic Guarantees
Christian Engwer, Andreas NüÃing
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equation…
The Local Subtraction Approach For EEG and MEG Forward Modeling
Malte B. Höltershinken, Pia Lange, Tim Erdbrügger +7
EDIT: A revised version of this article has been published in the SIAM Journal on Scientific Computing, see https://epubs.siam.org/doi/full/10.1137/23M1582874. In the revised versi…
Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems
Christian Engwer, Mario Ohlberger, Lukas Renelt
This contribution introduces a model order reduction approach for an advection-reaction problem with a parametrized reaction function. The underlying discretization uses an ultrawe…
DoD Stabilization of linear hyperbolic PDEs on general cut-cell meshes
Gunnar Birke, Christian Engwer, Sandra May +1
Standard numerical methods for hyperbolic PDEs require for stability a CFL-condition which implies that the time step size depends on the size of the elements of the mesh. On cut-c…
A high-level C++ approach to manage local errors, asynchrony and faults in an MPI application
Christian Engwer, Mirco Altenbernd, Nils-Arne Dreier +1
C++ advocates exceptions as the preferred way to handle unexpected behaviour of an implementation in the code. This does not integrate well with the error handling of MPI, which mo…
DUNEuro -- A software toolbox for forward modeling in bioelectromagnetism
Sophie Schrader, Andreas Westhoff, Maria Carla Piastra +6
Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper prese…
An optimally stable approximation of reactive transport using discrete test and infinite trial spaces
Lukas Renelt, Christian Engwer, Mario Ohlberger
In this contribution we propose an optimally stable ultraweak Petrov-Galerkin variational formulation and subsequent discretization for stationary reactive transport problems. The…
A Hardware-aware and Stable Orthogonalization Framework
Nils-Arne Dreier, Christian Engwer
The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram…
An Energy-Preserving Domain of Dependence Stabilization for the Linear Wave Equation on Cut-Cell Meshes
Gunnar Birke, Christian Engwer, Sandra May +2
We present an energy-preserving (either energy-conservative or energy-dissipative) domain of dependence stabilization method for the linear wave equation on cut-cell meshes. Our sc…
The interface for functions in the dune-functions module
Christian Engwer, Carsten Gräser, Steffen Müthing +1
The dune-functions dune module introduces a new programmer interface for discrete and non-discrete functions. Unlike the previous interfaces considered in the existing dune modules…
CutFEM forward modeling for EEG source analysis
Tim Erdbrügger, Andreas Westhoff, Malte Hoeltershinken +9
Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is…
Construction of local reduced spaces for Friedrichs' systems via randomized training
Christian Engwer, Mario Ohlberger, Lukas Renelt
This contribution extends the localized training approach, traditionally employed for multiscale problems and parameterized partial differential equations (PDEs) featuring locally…
Realistic head modeling of electromagnetic brain activity: An integrated Brainstorm pipeline from MRI data to the FEM solution
Takfarinas Medani, Juan Garcia-Prieto, Francois Tadel +6
Human brain activity generates scalp potentials (electroencephalography EEG), intracranial potentials (iEEG), and external magnetic fields (magnetoencephalography MEG), all capable…
Domain of Dependence stabilization for the acoustic wave equation on 2D cut-cell meshes
Gunnar Birke, Christian Engwer, Sandra May +1
Cut-cell meshes are an attractive alternative to avoid common mesh generation problems. For hyperbolic problems they pose additional challenges, as elements can become arbitrarily…
Exa-Dune -- Flexible PDE Solvers, Numerical Methods and Applications
Peter Bastian, Mirco Altenbernd, Nils-Arne Dreier +13
In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future…
Function space bases in the dune-functions module
Christian Engwer, Carsten Gräser, Steffen Müthing +1
The dune-functions Dune module provides interfaces for functions and function space bases. It forms one abstraction level above grids, shape functions, and linear algebra, and prov…
On the consistency of the Domain of Dependence cut cell stabilization
Gunnar Birke, Christian Engwer, Jan Giesselmann +1
So called cartesian cut cell meshes provide efficient ways to generate meshes but do require tailored numerical methods to not suffer from stabilization issues, especially in the h…
Monotonicity considerations for stabilized DG cut cell schemes for the unsteady advection equation
Florian Streitbürger, Christian Engwer, Sandra May +1
For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect…
A discontinuous Galerkin Method for the EEG Forward Problem using the Subtraction Approach
Christian Engwer, Johannes Vorwerk, Jakob Ludewig +1
In order to perform electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrod…
The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem
Andreas NüÃing, Carsten H. Wolters, Heinrich Brinck +1
Objective: The purpose of this study is to introduce and evaluate the unfitted discontinuous Galerkin finite element method (UDG-FEM) for solving the electroencephalography (EEG) f…
Concepts for Composing Finite Element Function Space Bases
Christian Engwer, Carsten Gräser, Steffen Müthing +2
Finite Element discretizations of coupled multi-physics partial differential equation models require the handling of composed function spaces. In this paper we discuss software con…
Estimating the extent of glioblastoma invasion
Christian Engwer, Michael Wenske
Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential eq…
Error analysis of a first-order DoD cut cell method for 2D unsteady advection
Gunnar Birke, Christian Engwer, Jan Giesselmann +1
In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization…
An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces
Christian Engwer, Thomas Ranner, Sebastian Westerheide
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and…
Efficient implementation of the Localized Orthogonal Decomposition method
Christian Engwer, Patrick Henning, Axel MÃ¥lqvist +1
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulat…
The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable
Louis Petri, Gunnar Birke, Christian Engwer +1
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by red…
Domain-of-dependence-stabilized cut-cell discretizations of linear kinetic models with summation-by-parts properties
Louis Petri, Sigrun Ortleb, Gunnar Birke +2
We employ the summation-by-parts (SBP) framework to extend the recent domain-of-dependence (DoD) stabilization for cut cells to linear kinetic models in diffusion scaling. Numerica…
Strategies for the vectorized Block Conjugate Gradients method
Nils-Arne Dreier, Christian Engwer
Block Krylov methods have recently gained a lot of attraction. Due to their increased arithmetic intensity they offer a promising way to improve performance on modern hardware. Rec…
Dynamic and weighted stabilizations of the -scheme applied to a phase-field model for fracture propagation
Christian Engwer, Iuliu Sorin Pop, Thomas Wick
We consider a phase-field fracture propagation model, which consists of two (nonlinear) coupled partial differential equations. The first equation describes the displacement evolut…
A stabilized DG cut cell method for discretizing the linear transport equation
Christian Engwer, Sandra May, Andreas NüÃing +1
We present new stabilization terms for solving the linear transport equation on a cut cell mesh using the discontinuous Galerkin (DG) method in two dimensions with piecewise linear…
ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics
Andreas Buhr, Christian Engwer, Mario Ohlberger +1
The simulation method ArbiLoMod has the goal to provide users of Finite Element based simulation software with quick re-simulation after localized changes to the model under consid…