A5083989030- Advanced Numerical Methods in Computational Mathematics
- Advanced Mathematical Modeling in Engineering
- Computational Fluid Dynamics and Aerodynamics
- Advanced MRI Techniques and Applications
- Lattice Boltzmann Simulation Studies
- Electromagnetic Simulation and Numerical Methods
- Parallel Computing and Optimization Techniques
- Mathematical Biology Tumor Growth
- Model Reduction and Neural Networks
- Numerical methods in engineering
- Distributed and Parallel Computing Systems
- Neural dynamics and brain function
- Numerical methods for differential equations
- Functional Brain Connectivity Studies
- Matrix Theory and Algorithms
- Electrical and Bioimpedance Tomography
- Sparse and Compressive Sensing Techniques
- Fluid Dynamics and Turbulent Flows
- Advanced Software Engineering Methodologies
- Computer Graphics and Visualization Techniques
- Navier-Stokes equation solutions
- Distributed systems and fault tolerance
- Advanced Data Storage Technologies
- Soil and Unsaturated Flow
- Software Testing and Debugging Techniques
University of Münster
2016-2025
FH Münster
2018-2023
Applied Mathematics (United States)
2016-2023
University of Stuttgart
2008-2020
TU Dortmund University
2020
Fraunhofer Institute for Industrial Mathematics
2020
Clausthal University of Technology
2020
Heidelberg University
2005-2020
Blackberry (United States)
2016
This paper presents the basic concepts and module structure of Distributed Unified Numerics Environment reflects on recent developments general changes that happened since release first Dune version in 2007 main papers describing state Bastian etal. (2008a, 2008b). discussion is accompanied with a description various advanced features, such as coupling domains cut cells, grid modifications adaptation moving domains, high order discretizations node level performance, non-smooth multigrid...
We present a simple and fast phase aberration compensation method in digital holographic microscopy (DHM) for quantitative imaging of living cells. By analyzing the frequency spectrum an off-axis hologram, aberrations can be compensated automatically without fitting or pre-knowledge setup and/or object. Simple effective computation makes suitable online monitoring with highly variable DHM systems. Results from automated NIH-3T3 mouse fibroblasts demonstrate effectiveness feasibility method.
Abstract Signal‐to‐noise ratio (SNR) maps are a good way to visualize electroencephalography (EEG) and magnetoencephalography (MEG) sensitivity. SNR extend the knowledge about modulation of EEG MEG signals by source locations orientations can therefore help better understand interpret measured as well reconstruction results thereof. Our work has two main objectives. First, we investigated accuracy reliability finite element method (FEM)‐based sensitivity for three different head models,...
Abstract In this paper we present a new approach to simulations on complex‐shaped domains. The method is based discontinuous Galerkin (DG) method, using trial and test functions defined structured grid. Essential boundary conditions are imposed weakly via the DG formulation. This offers discretization where number of unknowns independent complexity domain. We will show numerical computations for an elliptic scalar model problem in ℝ 2 3 . Convergence rates different polynomial degrees...
The Dune project has released version 2.4 on September 25, 2015. This paper describes the most significant improvements, interface and other changes for core modules Dune- Common, Dune-Geometry, Dune-Grid, Dune-ISTL, Dune-LocalFunctions.
Accurate and efficient source analysis in electro- magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free open-source C++ software toolbox for the computation of forward solutions bioelectromagnetism. Building upon DUNE framework, it provides implementations modern fitted unfitted finite element methods to efficiently solve problems magnetoencephalography. The user can choose between variety different...
Human brain activity generates scalp potentials (electroencephalography - EEG), intracranial (iEEG), and external magnetic fields (magnetoencephalography MEG). These electrophysiology (e-phys) signals can often be measured simultaneously for research clinical applications. The forward problem involves modeling these at their sensors a given equivalent current dipole configuration within the brain. While earlier researchers modeled head as simple set of isotropic spheres, today's resonance...
Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main cells that can develop into neoplasms. They highly invasive lead to irregular tumor margins not precisely identifiable by medical imaging, thus rendering precise enough resection very difficult. The understanding glioma spread patterns hence essential for both radiological therapy as well surgical treatment. In this paper we propose multiscale model growth including interactions with...
In order to perform electroencephalography (EEG) source reconstruction, i.e., localize the sources underlying a measured EEG, electric potential distribution at electrodes generated by dipolar current in brain has be simulated, which is so-called EEG forward problem. To solve it accurately, necessary apply numerical methods that are able take individual geometry and conductivity of subject's head into account. this context, finite element (FE) method (FEM) shown high accuracy with...
In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement for source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become of dominant approaches solving problem over last decades. Recently, a discontinuous FEM (DG-FEM) EEG approach been proposed as an alternative to CG-FEM (Engwer et al., 2017). It was shown that DG-FEM preserves property conservation charge it can, in certain situations such so-called skull leakages, be...
SUMMARY A discontinuous Galerkin method for the solution of immiscible and incompressible two‐phase flow problem based on nonsymmetric interior penalty is presented. Therefore, Navier–Stokes equation solved a domain decomposed into two subdomains with different values viscosity density as well singular surface tension force. On basis piecewise linear approximation interface, meshes both phases are cut out structured mesh. The finite elements defined resulting Cartesian cut‐cell mesh may...
In silico experiments bear the potential for further understanding of biological transport processes by allowing a systematic modification any spatial property and providing immediate simulation results. Cell polarization reorganization membrane proteins are fundamental cell division, chemotaxis morphogenesis. We chose yeast Saccharomyces cerevisiae as an exemplary model system which entails shuttling small Rho GTPases such Cdc42 Rho, between active membrane-bound form inactive cytosolic...
Journal Article Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons previous settings Get access Christian Engwer, Engwer Institute Computational Applied Mathematics, University of Münster, Orleans-Ring 10, D-48149 Germany Search other works by this author on: Oxford Academic Google Scholar Alexander Hunt, Hunt Technische Universität Kaiserslautern, Fachbereich Mathematik, D-67653 *Corresponding author: hunt@mathematik.uni-kl.de...
We propose a multiscale model for tumor cell migration in tissue network. The system of equations involves structured population the density, which besides time and position depends on further variable characterizing cellular state with respect to amount receptors bound soluble insoluble ligands. Moreover, this equation features pH-taxis adhesion, along an integral term describing proliferation conditioned by receptor binding. interaction cells their surroundings calls two more evolution...
Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable realistic modeling of complex geometries important conductive features such as anisotropic conductivities. To date, most presented approaches rely on same underlying formulation, continuous Galerkin (CG)-FEM. In this article, a novel approach solve based mixed finite method (Mixed-FEM) is introduced. obtain Mixed-FEM electric current introduced an additional...
We present new stabilization terms for solving the linear transport equation on a cut cell mesh using discontinuous Galerkin (DG) method in two dimensions with piecewise polynomials. The goal is to allow explicit time stepping schemes despite presence of cells. Using lines approach, we start standard upwind DG discretization background and add penalty that stabilize solution small cells conservative way. Then one can use stepping, even cells, step length appropriate mesh. In dimension, show...
The purpose of this study is to introduce and evaluate the unfitted discontinuous Galerkin finite element method (UDG-FEM) for solving electroencephalography (EEG) forward problem.This new approach source analysis does not use a geometry conforming volume triangulation, but instead uses structured mesh that resolve geometry. described using level set functions incorporated implicitly in its mathematical formulation. As no triangulation necessary, complexity simulation pipeline need manual...
We deduce a model for glioma invasion that accounts the dynamics of brain tissue being actively degraded by tumor cells via excessive acidity production, but also according to local orientation fibers. Our approach has multiscale character: we start with microscopic description single cell including biochemical and/or biophysical effects microenvironment, translated on one hand into stress and corresponding forces other receptor binding dynamics. These lead mesoscopic level kinetic equations...