Projects
Below you find a list of projects of all members of the chair of Applied Mathematics 1. Further information on projects is given on the pages of the individual researchers.
Extension and evaluation of Transomics data sets with artificially generated data using AI and the incorporation of biology
(Third Party Funds Group – Sub project)Overall project: Erweiterung und Auswertung von Transomics-Datensätzen mit künstlich erzeugten Daten mittels KI unter Einbezug der Biologie
Term: 01-04-2024 - 30-11-2026
Funding source: Bayerisches Staatsministerium für Wirtschaft, Landesentwicklung und Energie (StMWi) (seit 2018)P25: Multiscale modeling with evolving microstructure: An approach to emergence in the rhizosphere via effective soil functions
(Third Party Funds Single)Term: 01-11-2022 - 31-10-2025
Funding source: DFG / Schwerpunktprogramm (SPP)To couple three interwoven areas of rhizosphere research “Processes, Methods and Applications”, we utilize and improve mechanistic, mathematical models in forms of combined cellular automata and PDE/ODE systems on the microscale, offering the opportunity to bridge scales by homogenization techniques. The
systematic study of the interaction of transformation processes in the rhizosphere focussing on mucilage and root hairs, and its couplings to soil structure, geochemistry, microbiology, and to upscaled soil
functions will contribute to the focal question of the PP, how resilience emerges from self-organised spatiotemporal pattern formation in the rhizosphere.In more detail:
H1: The development of the selforganization in the rhizosphere in connection with the spatiotemporal
patterns of nutrients, water and biomass can be studied with the realized extension of the existing model and simulation tool now in relation to the data of phase 1.H2: The connection between soil structure formation, habitat conditions - also influenced by the
production and degradation of mucilage - and the microbial communities.H3: The size of the rhizosphere is determined by the radial extent of pattern formation controlled by root
activity/morphology. We want to study in particular the interaction of soil structure (in particular porosity), root exudates and transport properties relevant for the plant. Thus we address the focal topics
aggregate formation / soil structure with pore scale modeling and water flux / mucilage.We refer in particular to the following research questions of phase 2:
III. How do carbon flow and structure interact (with P19, P22)?
V. What is the relevance of mucilage for the soilplant system regarding drought resilience, but also mechanistic understanding for mucilage at the microscale - evidence for relevance at system scale, plant-soil system is still lacking (with P4,P5,P23,P24)
VI. What is the mechanistic function of root hairs - quantify the maintenance of hydraulic continuity, the effect on nutrients uptake, and extension of depletion zones (with P7,P4)In close cooperation with the experimental partners we evaluate the interplay of the mechanisms in concrete PP rhizosphere settings, and will also refer to the spatiotemporal patterns identified by P21 from high resolution correlative imaging. The necessary basis for 3D simulations will be the parallelized, efficient algorithms, and machine learning techniques to systematically explore the upscaling of soil functions. The simulation tool delivers its value through the capability to illustrate, compare, and reveal influencing factors and mechanisms by abstracting relevant processes. It is not intended to ’redraw’ data curves of the experiments but to gain new insights through the ability to analyze separately, but also to study the interplay of several processes in an integrative simulation. Thus it intends to bridge a knowledge gap that laboratory experiments can currently not fill alone.
DG Methoden und Parameterschätzer für Mikrostrukturmodelle in porösen Medien
(Third Party Funds Single)Term: 01-01-2022 - 31-12-2023
Funding source: Deutscher Akademischer Austauschdienst (DAAD)DAAD Projektbezogener Personenaustausch mit Finnland DG Methoden und Parameterschätzer für Mikrostrukturmodelle in porösen Medien
(Third Party Funds Single)Term: 01-01-2022 - 31-12-2023
Funding source: Deutscher Akademischer Austauschdienst (DAAD)Parallel mesh loading and partitioning for large-scale simulation
(Third Party Funds Single)Term: since 01-01-2021
Funding source: Bayerisches Staatsministerium für Wissenschaft und Kunst (StMWK) (seit 2018)
URL: https://www.konwihr.de/Mechanistic, Integrative Multiscale Modelling of the Turnover of Soil Microaggregates
(Third Party Funds Group – Sub project)Overall project: MAD Soil - Microaggregates: Formation and turnover of the structural building blocks of soils
Term: 01-04-2020 - 31-08-2024
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)The grand goal of this group is the development, analytical, and numerical investigation of a mechanistic model describing processes of formation, stability, and turnover of soil micro-aggregates. In contrast to existing conceptual aggregation models and compartment models for carbon turnover and aggregation, we focus on specific, experimentally identified transformation processes of soil micro-aggregates. Since we are interested in giving an improved mechanistic, qualitative and even quantitative description of aggregation, we transfer the gained insights to a mechanistic model in terms of ordinary differential equations (ODEs), partial differential equations (PDEs), and perhaps algebraic equations (AEs). To that end, we aim to take into account information/identified processes on different spatial scales as well as spatial heterogeneity and variability. All our modeling is done in a rigorous, deterministic way and our modeling concepts are based on continuum mechanics. We start our investigations at the pore scale and apply multiscale techniques to obtain a comprehensive mathematical model at the macroscale (bottom up). In particular, the interplay of geochemistry and microbiology is considered, and also their link to soil functions. The coupled ODE/PDE systems and complex micro-macro problems cannot be treated numerically with standard software packages. The number of species, the nonlinearity of the processes and the heterogeneity of the medium results in a high computational effort that requires accurate and efficient discretization methods and solution algorithms. Moreover sophisticated numerical multiscale methods have to be applied. In our simulations, we do not aim to recreate reality in every detail. Instead, we aim to illustrate, compare, and reveal influencing factors and mechanisms by abstracting relevant processes.Maschinelles Lernen bei korrelativer MR und Hochdurchsatz-NanoCT
(Third Party Funds Single)Term: 01-04-2020 - 31-03-2023
Funding source: Bundesministerium für Bildung und Forschung (BMBF)Mechanistische, integrative Mehrskalenmodellierung der Umwandlung von Bodenmikroaggregaten
(Third Party Funds Single)Term: 01-11-2019 - 31-10-2022
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)Multiscale modeling with evolving microstructure: An approach to emergence in the rhizosphere via effective soil functions
(Third Party Funds Group – Sub project)Overall project: DFG Priority Programme 2089 “Rhizosphere Spatiotemporal Organisation – a Key to Rhizosphere Functions”
Term: 01-02-2019 - 31-01-2022
Funding source: DFG / Schwerpunktprogramm (SPP)
URL: https://www.ufz.de/spp-rhizosphere/index.php?en=46495The self-organization of the aggregates in the rhizosphere by various
attracting forces influenced by geochemistry, and microbiology shall
be studied by a novel, comprehensive model. This model should
account for processes on the microscale (single roots, pore scale),
and then be upscaled to the root system scale (macroscale) by
mathematical homogenization. This goal exceeds the functional range
of existing models for aggregation and needs the introduction of an
explicit phase of mucilage, and attachment properties of root hairs in
the rhizosheath. The project aims at the development of a mechanistic modeling approach that allows for dynamic structural reorganization of the rhizosphere at the single root scale and couples this evolving microscale model to the root system scale including the inference of soil functions. This means that we do not assume a static rhizosphere but develop a tool that is capable to dynamically track this zone on the basis of the underlying spatiotemporal aggregegate formation and geochemical patterns. The collaboration with experimental groups – analyzing CT images in various moisture and growth conditions - the Central Experiment will allow to derive the properties of the mucilage phase, the pore structure and thus the
influence of root hairs on aggregation mechanisms.PPP Frankreich 2019 Phase I
(Third Party Funds Single)Term: 01-01-2019 - 31-12-2020
Funding source: Deutscher Akademischer Austauschdienst (DAAD)Nonlocal Methods for Arbitrary Data Sources
(Third Party Funds Group – Sub project)Overall project: Nonlocal Methods for Arbitrary Data Sources
Term: 01-10-2018 - 28-02-2022
Funding source: EU - 8. Rahmenprogramm - Horizon 2020Integriertes und an Raum-Zeit-Messungsskalen angepasstes Global Random Walk - Modell für reaktiven Transport im Grundwasser
(Third Party Funds Single)Term: 01-10-2018 - 30-09-2021
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)Implementation of vector operations for SBCL
(Third Party Funds Single)Term: 10-07-2018 - 31-03-2019
Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)Ziel des Projekts ist es, AVX2 Vektoroperationen für die Common LispImplementierung SBCL verfügbar zu machen. SBCL ist derpopulärste und am weitesten Entwickelte freie Compiler für CommonLisp. Die Verbesserungen aus diesem Projekt machen es möglichCommon Lisp Programme zu schreiben, deren Ausführungsgeschwindigkeitmit C++ und Fortran Programmen auf Augenhöhe liegt. Dadurchergeben sich interessante Möglichkeiten der Metaprogrammierung imwissenschaftlichen Rechnen.Innovationsfonds 2017: Urkunden und Buchgutscheine für gute Leistungen in Anfängervorlesungen
(FAU Funds)Term: 01-07-2017 - 30-09-2020Um den Vorlesungs- und Prüfungsbetrieb persönlicher zu gestalten, wird bei sehr guten Leistungen in meinen Anfängervorlesungen "Mathematik für Ingenieure" ein wenig symbolisches Lob in der Form von Urkunden und auch ein wenig finanzielles Lob in der Form von Buchgutscheinen ausgeteilt."Verbundprojekt MED4D: Dynamische Medizinische Bildgebung: Modellierung und Analyse medizinischer Daten für verbesserte Diagnose, Überwachung und Arzneimittelentwicklung"
(Non-FAU Project)Term: 01-12-2016 - 30-11-2019
Funding source: Bundesministerium für Bildung und Forschung (BMBF)Mechanistic modelling of the formation and consolidation of soil microaggregates
(Third Party Funds Group – Sub project)Overall project: DFG RU 2179 “MAD Soil - Microaggregates: Formation and turnover of the structural building blocks of soils”
Term: 01-01-2016 - 31-12-2019
Funding source: Deutsche Forschungsgemeinschaft (DFG)German-Norwegian collaborative research support scheme
(Third Party Funds Single)Term: 01-01-2016 - 31-12-2017
Funding source: Deutscher Akademischer Austauschdienst (DAAD)Homogenisierung reaktiven Transports in variablen Mikrostrukturen
Scientific Computing for Improved Detection and Therapy of Sepsis
(Non-FAU Project)Verteiltes Höchstleistungsrechnen in Common Lisp
(Third Party Funds Single)Term: 01-10-2015 - 31-03-2016
Funding source: Bayerisches Staatsministerium für Wissenschaft, Forschung und Kunst (StMWFK) (bis 09/2013)The Message Passing Interface\cite{mpi-standard} (MPI) is the de facto
standard for distributed programming on all modern compute clusters and
supercomputers. It features a large number of communication patterns with
virtually no overhead. Our work on bringing MPI functionality to Common
Lisp resulted in vast improvements to the message passing library CL-MPI
and the development of severaly new approaches to distributed computing.
DAAD Exchange Service: PPP Finnland 2017: Bayesian Inverse Problems in Banach Space
(Non-FAU Project)Term: 25-01-2015 - 31-12-2017
Funding source: Deutscher Akademischer Austauschdienst (DAAD)Variational Methods for Dynamic Inverse Problems in the Life Sciences
(Non-FAU Project)Term: 01-03-2014 - 28-02-2019
Funding source: Europäische Union (EU)Implementation and optimization of stencil operations on staggered hierarchical meshes
(Third Party Funds Single)Term: 01-06-2013 - 01-10-2014
Funding source: Bayerisches Staatsministerium für Wissenschaft, Forschung und Kunst (StMWFK) (bis 09/2013)
URL: http://www.konwihr.uni-erlangen.de/projekte/multicore-software-initiative/stencils-on-staggered-hierarchical-meshes.shtmlWe optimized and parallelized a framework which compiles stencil operations defined by abstract operators into code, which performs the corresponding stencil update. Therefore, we are now able to formulate solvers for a large number of application problems (flow simulation, image analysis, ...) in an abstract way, and then solve efficiently on structured meshes.
MPFA and MHFE methods for flow and transport in porous media
(Third Party Funds Single)Term: 01-01-2012 - 31-12-2013
Funding source: Deutscher Akademischer Austauschdienst (DAAD)Nonlinear (multiphase) flow and reactive multicomponent transport problems in highly heterogeneous porous media and their numerical simulation are of great interest for evaluating site remediation, energy exploitation or CO2 sequestration scenarios. The resulting advection-diffusion-reaction-systems are coupled nonlinear parabolic partial differential equations, and we have parabolic or elliptic nonlinear flow equations, possibly degenerate. The development of convergent and efficient numerical schemes is very challenging and the mixed (hybrid) finite element method M(H)FEM and the multipoint flux approximation MPFA are powerful locally mass conservative choices. They offer also the advantage of continuous flux approximations over the element faces. Analogies between the two techniques should help to prove order of convergence estimates and monotonicity for the multicomponent transport problems, but also for multiphase flow. Furthermore numerical diffusion of the schemes should be quantified to assess the accuracy of the methods. Simulation examples should include realistic scenarios on heterogeneous, log normally distributed random parameter fields.
Development of filtration systems for air cleaning from nanoparticles, organic admixtures and bacteria with the help of numerical simulations
(Third Party Funds Single)Term: 01-10-2009 - 30-09-2011
Funding source: Bundesministerium für Bildung und Forschung (BMBF)The project was a cooperation of a group of applied mathematicians with the Russian company Aeroservice for the development and optimization of new photocatalytic filter systems for air cleaning of nanoparticles and organic substances with the help of mathematical simulation tools. For the simulation of aerosol transport in the filter made of polypropylene fibers, which is used in hospitals or airports, e.g., mathematical models and efficient solution algorithms had to be developed. These allow on the one hand to take stochastic components into account, as the heterogeneous conductivity distribution in the filter. On the other hand these methods were coupled with highly accurate computation schemes as mixed finite element methods, which guarantee local mass conservation for the transport processes. The design parameters of real experiments can be optimized with the help of such simulation tools and their sensitivity with respect to filter efficiency analysed. Among the used methods are particle filtration in porous media, based on the Darcy equation, and coupled Eulerian and Lagrangeian simulation of transport processes, including Monte Carlo approaches with given filter geometries.
Efficient Numerical Methods for Large Partial Differential Complementarity Systems arising in Multispecies Reactive Transport with Minerals in Porous Media
(Third Party Funds Single)Term: 01-01-2007 - 31-12-2011
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)The project focuses on the accurate and efficient numerical treatment of time-dependent reactive transport problems with many species (in porous media) in 2 or 3 space dimensions with local complementarity conditions as essential ingredient. The problem takes the form of a differential algebraic set of equations and complementarity constraints, consisting of time dependent (possibly convection-dominated) semilinear partial differential equations (PDEs), nonlinear ordinary differential equations, nonlinear algebraic equalities, and inequalities. Taking a typical species number of 10 to 20 and of nodal degrees of freedom of 104 to 106, also for an appropriate (e.g., local mass conservative) discretization, the solution of the emerging finite dimensional complementarity system is a formidable task, whose efficient algorithmic treatment is the main topic of the project. Algorithms of semismooth Newton type are the principal choice. Aims are the investigation and improvement of the algorithms w.r.t. efficiency and robustness, and comparing them to other (e.g., interiorpoint-) methods. The algorithms to be developed are supposed to heavily take advantage of knowledge about the substructuring of the problem. The emerging methods and software, also for parallel computers, is supposed to handle several large real world problems, not yet treatable satisfactorily.The Influence of Colloids on Water Flow and Solute Transport in Soils: Side Effect or Key Process?
(Third Party Funds Single)Term: 01-11-2006 - 31-12-2009
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)Soil colloids may influence the interaction between solutes and the immobile solid phase. A coupling to the fluid transport is possible by processes of sedimentation, flocculation, precipitation, filtration and deposition. The objective of this research project is the qualitative and quantitative examination of the crucial aspects of colloidal-influenced solute- and fluid transport by means of systematic, prognostic simulation. In detail,
- the attachment and detachment of colloids under consideration air-water interface of the soil,
- the transformation of the pore space and the thus induced coupling to the fluid transport in soil, and
- the transformation of the surface properties of the solid phase and the thus induced coupling to the solute transport
have to be analyzed. The main hypothesis of this project states that the couplings incorporated in the model conception affect the praxis-relevant situations not only qualitatively, but also quantitatively in a significant way. The deterministic description of the physicochemical mechanisms on basis of the conservation laws for mass, impulse and energy results in systems of time-dependent non-linear partial differential equations. In order to make the model operative with respect to the problem formulation, one has to approximate it via numerical methods and to implement those in a software tool. For each level of complexity which has to be achieved, a comparison with existing experimental data has to be accomplished. In particular, these datasets have is to be used to obtain a realistic parametrization of the model via inverse modelling.
Identifizierung nichtlinearer Koeffizientenfunktionen des reaktiven Transports durch poröse Medien unter Verwendung rekursiver und formfreier Ansätze
(Third Party Funds Group – Sub project)Overall project: Identifikation, Optimierung und Steuerung für technische Anwendungen
Term: 01-06-2006 - 30-04-2010
Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)In dem Internationalen Doktorandenkolleg wird vor dem Hintergrund konkreter Anwendungsprobleme der Bogen von der mathematischen Modellierung über die mathematische Analyse und die Entwicklung numerischer Methoden bis hin zum Wissenschaftlichen Rechnen und der Implementierung von Software auf Hoch- und Höchstleistungsrechnern gespannt. Dies geschieht auf den Gebieten der Identifikation, Optimierung und Steuerung komplexer technischer, medizinischer, naturwissenschaftlicher und wirtschaftswissenschaftlicher Systeme.
Eine stärkere Einbindung von Ingenieurprojekten in der zweiten Phase des Kollegs wird die Integration der erarbeiteten Konzepte und Algorithmen in konkrete Anwendungsbereiche ermöglichen. Darüber hinaus lassen spezifische Betreuungs- und Lehrkonzepte die fachübergreifende Zusammenarbeit fruchtbar werden.
Identifikation, Optimierung und Steuerung haben eine große Bedeutung für die technologische Entwicklung. Die Fokussierung auf dieses Gebiet ist deshalb das besondere Merkmal dieses mathematisch orientierten Netzwerkes. Im nordbayerischen Raum bieten sich wegen der dort gegebenen Konzentration international anerkannter Wissenschaftler in diesem Forschungsumfeld die besten Voraussetzungen. Das Ziel des Doktorandenkollegs ist es, den Schritt von der modellbasierten Simulation zum modellgestützten optimalen Design und Steuerung zu vollziehen. Dieser Schritt wird erst durch die Verzahnung der rasanten Entwicklung mathematischer Methoden der Optimierung und der Numerik und mit Hilfe von Hochleistungsrechnern möglich.Modelling of the reactive transport of contaminants in the (un-)saturated zone for the prognosis of natural attenuation
(Third Party Funds Group – Sub project)Overall project: Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Böden und Grundwässer (BMBF Förderschwerpunkt KORA)
Term: 01-04-2004 - 31-12-2008
Funding source: BMBF / VerbundprojektThe evaluation of the potential of contaminated sites concerning natural attenuation needs comprehensive process descriptions and accurate, reliable numerical algorithms. Numerical errors may lead to qualitatively completely wrong conclusions concerning the potential of the site for degradation. It has been developed a comprehensive and flexible simulation tool, that is outstanding concerning the variety of processes, the quality and efficiency of the calculations ensured by modern numerical methods as well as the usability. The existing software platform RICHY has been extended, which is already intensely and successfully used by universities, institutes and consultants for the simulation of reactive transport and parameter identification. Among previous modules for coupled sufactant transport, preferential, unsaturated flow or carrier facilitated transport the project could realize new model components that surpass most of all existing software packages. The extensions contain complete descriptions of microbially catalysed degradation with arbitrary reaction partners and inhibition, general multicomponent reactions including the effects of ionic strength, as well as mineral dissolution and precipitation. The efficient and highly accurate, newly developed mathematical solution algorithms for the resulting coupled systems of partial differential equations could show their quality in complex international benchmark studies. Locally mass conserving, mixed hybrid finite element discretisations of the flow problem have been combined with globally implicit, reactive multicomponent models. Novel reduction methods for the latter rely on the linear transformation of the equation systems and variables and lead to the consideration of conservation quantities which can be handled efficiently, as a part of the transport – reaction – equations decouples. Another approach that has been pursued simultaneously relies on a modified Newton method and results in efficiency enhancements by the neglection of coupling terms in the Jacobian matrix. This algorithm can be applied fully adaptively, in 1D as well as in 2D. Both approaches could be combined with adaptive techniques for the automatic, efficient choice of time steps and spatial grid sizes, which makes the calculation of these complex problems feasible on PCs.
Development of a simulation tool for the prognosis of the spreading and the degradation of contaminants in the saturated and vadose zone
(Third Party Funds Group – Sub project)Overall project: Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens
Term: 01-06-2001 - 31-05-2003
Funding source: Bayerisches Staatsministerium für Umwelt und Gesundheit (StMUG) (bis 09/2013)
URL: https://www.altlasten-bayern.de/projekte/verbundvorhaben-na/The project included the mathematical modelling of natural attenuation processes in the subsurface and the extension of a software tool for complex reactive multicomponent processes in the framework of mixed hybrid and conforming finite elements. New parameter identification methods allow the parametrization of unknown functions or a formfree optimization, and help to overcome the dilemma of missing data in complex models. Work included instationary 3D simulations and scenarios of contaminated sites explored by project partners. The findings of the joint research project resulted in guidelines for authorities and consulting engineers dealing with natural attenuation at contaminated sites.
Quantification of Contaminant Sources and Transport Prognosis in Aquifers
(Third Party Funds Group – Sub project)Overall project: BMBF Förderschwerpunkt Sickerwasserprognose
Term: 01-01-2001 - 31-12-2004
Funding source: Bundesministerium für Bildung und Forschung (BMBF)Mathematical simulation tools allow the quantitative integration of competing transport and transformation processes which are relevant for a seepage water risk prognosis. Therefore model simulations have to contain a comprehensive process description, while they can serve for parameter identification by inverse modelling of suitable column or batch experiments, and allow to quantify the dependence of a key variable on parameters through a simultaneous sensitivity analysis. The software platform RICHY1D has been extended and is already intensively and successfully used in universities, institutes and by consultants for the 1D simulation of complex reactive transport and for parameter identification. It stands out by the application of efficient and highly accurate mathematical solution strategies for the resulting systems of partial differential equations (e.g. locally mass conserving mixed hybrid finite element discretisations, modified Newton’s method). Besides the formerly existing modules for coupled surfactant-water transport, multiphase flow, saturated-unsaturated flow or carrier facilitated transport, the extensions contain in particular source terms (boundary conditions, distributed sources, arbitrarily time dependent, nonlinear and multiple (de-)sorption kinetics, mobilisation from a residual NAPL phase), preferential flow with solute transport, and heat transport in soils with coupling to reaction parameters of the contaminant transport like Monod degradation parameters, e.g.. The parameter identification is possible for the model extensions as well, which allows the identification of multiple complex parametrizations from suitable experiments (for example for source terms or microbially mediated degradation, sorption characteristics and hydraulic parameters). There is no need to impose a certain functional shape of these nonlinearities, the so-called form-free identification is also feasible, and furthermore a closed-flow experiment design can be accounted for. The sensitivity analysis is provided separately for the evaluation of the dependence of a key variable like the concentration of arbitrary model parameters, what represents a powerful tool in a transport simulation to identify controlling factors and evaluate uncertainties of the data.