Supervised Theses
Doctoral theses
Altunay, Rabia
Mathematics of personalized medicine PhD Thesis Forthcoming
Forthcoming.
@phdthesis{AltunayPhD,
title = {Mathematics of personalized medicine},
author = {Rabia Altunay},
editor = {Eero Immonen and Lassi Roininen and Andreas Rupp},
keywords = {},
pubstate = {forthcoming},
tppubtype = {phdthesis}
}
Master’s theses
Kaushik, G Harish
Spatial Decomposition Methods for Modelling Multi-resolution European Electricity Systems with High Shares of Renewables Masters Thesis
Lappeenranta-Lahti University of Technology (LUT), 2023.
@mastersthesis{Kaushik23,
title = {Spatial Decomposition Methods for Modelling Multi-resolution European Electricity Systems with High Shares of Renewables},
author = {G Harish Kaushik},
editor = {Andreas Rupp and Martha Maria Frysztacki},
url = { https://urn.fi/URN:NBN:fi-fe20231205151496},
year = {2023},
date = {2023-12-04},
urldate = {2023-12-04},
school = {Lappeenranta-Lahti University of Technology (LUT)},
abstract = {Energy system modelling involves a technology-rich portfolio in high temporal and spatial resolution to properly estimate the impact of renewable energy variability and the role of storage technologies. Consequently, such models comprises tens of millions of variables and constraints, and demand vast computational resources for optimization. Thus, electricity networks are often coarsened to lower computational costs. However, this coarsening has a significant effect on the accuracy of the results. Another common approach is modelling only single regions and optimizing the cost of these isolated electricity networks. However, isolated electricity networks do not consider the power flows between countries, hence they have a large variance in electricity demand from renewable sources. These variances are especially undesirable in large networks and can only be smoothened by using an inter-regional network. The objective of this study is to investigate heuristic methods for spatial decomposition to improve results from isolated country models, while accounting for the benefits of international cooperation from the larger European electricity network. The study utilizes the existing high correlation between power flows from low- and high-resolution models to develop heuristics, and tests these methods by running simulations on isolated countries with disaggregated resources from low to high resolution and then optimizing these networks for minimal cost. The renewable electricity generated from the optimized isolated networks are compared to the benchmark European electricity network. Our study clearly indicates that spatial decomposition has a positive impact on the modelling results. Compared to an isolated model, the costs of the system stay within a ±8% range, while maintaining an accuracy in electricity output upto 5% of the European electricity model.},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
Energy system modelling involves a technology-rich portfolio in high temporal and spatial resolution to properly estimate the impact of renewable energy variability and the role of storage technologies. Consequently, such models comprises tens of millions of variables and constraints, and demand vast computational resources for optimization. Thus, electricity networks are often coarsened to lower computational costs. However, this coarsening has a significant effect on the accuracy of the results. Another common approach is modelling only single regions and optimizing the cost of these isolated electricity networks. However, isolated electricity networks do not consider the power flows between countries, hence they have a large variance in electricity demand from renewable sources. These variances are especially undesirable in large networks and can only be smoothened by using an inter-regional network. The objective of this study is to investigate heuristic methods for spatial decomposition to improve results from isolated country models, while accounting for the benefits of international cooperation from the larger European electricity network. The study utilizes the existing high correlation between power flows from low- and high-resolution models to develop heuristics, and tests these methods by running simulations on isolated countries with disaggregated resources from low to high resolution and then optimizing these networks for minimal cost. The renewable electricity generated from the optimized isolated networks are compared to the benchmark European electricity network. Our study clearly indicates that spatial decomposition has a positive impact on the modelling results. Compared to an isolated model, the costs of the system stay within a ±8% range, while maintaining an accuracy in electricity output upto 5% of the European electricity model.
Ballou, Ouraga Aime Cevert
Artificial Intelligence versus Statistical Methods in Parameter Estimation for Discrete Models Masters Thesis
African Institute for Mathematical Sciences (AIMS) Rwanda, 2023.
@mastersthesis{Ballou23,
title = {Artificial Intelligence versus Statistical Methods in Parameter Estimation for Discrete Models},
author = {Ouraga Aime Cevert Ballou},
editor = {Andreas Rupp},
year = {2023},
date = {2023-05-31},
urldate = {2023-05-31},
school = {African Institute for Mathematical Sciences (AIMS) Rwanda},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
Ashu, Valery
Identifying Hidden Parameters in Cellular Automata with Neural Networks Masters Thesis
Lappeenranta-Lahti University of Technology (LUT), 2023.
@mastersthesis{Ashu23,
title = {Identifying Hidden Parameters in Cellular Automata with Neural Networks},
author = {Valery Ashu},
editor = {Andreas Rupp and Heikki Haario},
url = {https://urn.fi/URN:NBN:fi-fe2023053049557},
year = {2023},
date = {2023-05-29},
urldate = {2023-05-29},
school = {Lappeenranta-Lahti University of Technology (LUT)},
abstract = {Cellular Automata models are commonly utilized in studying the dynamics of complex systems in physics, biology, and social sciences. However, the behavior of CAs is often influenced by hidden parameters, which are difficult to determine. Since a CA assigns discrete values to each cell in a domain, it is tempting to use neural networks to classify these hidden parameters as neural networks have been used extensively to classify images. In this thesis, we propose an approach to identify the hidden jump parameters, which affect the behavior of CA models, using neural networks.
This study’s findings indicate that neural networks are a powerful tool to identify hidden parameters in CA models. They have the potential to greatly increase the performance of parameter identification since the identification process is usually much faster than that of comparable statistical methods. We believe that our approach can be used in physics, biology, and social sciences, Complex systems are modeled using CA models.},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
Cellular Automata models are commonly utilized in studying the dynamics of complex systems in physics, biology, and social sciences. However, the behavior of CAs is often influenced by hidden parameters, which are difficult to determine. Since a CA assigns discrete values to each cell in a domain, it is tempting to use neural networks to classify these hidden parameters as neural networks have been used extensively to classify images. In this thesis, we propose an approach to identify the hidden jump parameters, which affect the behavior of CA models, using neural networks.
This study’s findings indicate that neural networks are a powerful tool to identify hidden parameters in CA models. They have the potential to greatly increase the performance of parameter identification since the identification process is usually much faster than that of comparable statistical methods. We believe that our approach can be used in physics, biology, and social sciences, Complex systems are modeled using CA models.
This study’s findings indicate that neural networks are a powerful tool to identify hidden parameters in CA models. They have the potential to greatly increase the performance of parameter identification since the identification process is usually much faster than that of comparable statistical methods. We believe that our approach can be used in physics, biology, and social sciences, Complex systems are modeled using CA models.
Mushimiyimana, Jean Modeste
Modelling Water Reinjection after Methane Extraction in Lake Kivu Masters Thesis
Lappeenranta-Lahti University of Technology (LUT), 2023.
@mastersthesis{Mushimiyimana23,
title = {Modelling Water Reinjection after Methane Extraction in Lake Kivu},
author = {Jean Modeste Mushimiyimana},
editor = {Bernardo Barbiellini and Andreas Rupp},
url = {https://urn.fi/URN:NBN:fi-fe2023052949000},
year = {2023},
date = {2023-05-19},
urldate = {2023-05-19},
school = {Lappeenranta-Lahti University of Technology (LUT)},
abstract = {The large amount of dissolved gases including carbon dioxide and methane in Lake Kivu poses a significant threat due to the potential for catastrophic gas eruption. To mitigate this risk, the implementation of the project to extract methane gas from the lake for electricity generation, and reduce the amount of dissolved gases in the lake has been initiated. However, the extraction imposes significant risks that could negatively impact the lake ecosystem and increase the probability of a gas eruption. This study aims at modelling water reinjection after methane extraction in Lake Kivu within 100 years by using the Kivu-Simstrat model, to identify the most effective and sustainable reinjection strategies for maintaining the stability and dissolved gas concentrations. Two cases are used, the first without methane extraction in the lake, and the other with 200 MW power production under the variation of extraction and reinjection depths to simulate methane, carbon dioxide, temperature, salinity, density and buoyancy frequency profiles. The results show that both extraction and reinjection depths have significant impacts on the physical and chemical properties of the lake, because they both affect the stability and concentration of dissolved gas. To mitigate these impacts, the results indicate the possible reinjection and extraction strategies: (1) reinjected water should be returned and restratified closely above the upper limit of the normal main chemocline at around 240 m depth to maintain a stable density stratification and optimal methane usage; (2) one should extract gas from the deepest layers of the lake to prevent the accumulation of dissolved gases and the formation of hazardous gas concentrations below the extraction depths.},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
The large amount of dissolved gases including carbon dioxide and methane in Lake Kivu poses a significant threat due to the potential for catastrophic gas eruption. To mitigate this risk, the implementation of the project to extract methane gas from the lake for electricity generation, and reduce the amount of dissolved gases in the lake has been initiated. However, the extraction imposes significant risks that could negatively impact the lake ecosystem and increase the probability of a gas eruption. This study aims at modelling water reinjection after methane extraction in Lake Kivu within 100 years by using the Kivu-Simstrat model, to identify the most effective and sustainable reinjection strategies for maintaining the stability and dissolved gas concentrations. Two cases are used, the first without methane extraction in the lake, and the other with 200 MW power production under the variation of extraction and reinjection depths to simulate methane, carbon dioxide, temperature, salinity, density and buoyancy frequency profiles. The results show that both extraction and reinjection depths have significant impacts on the physical and chemical properties of the lake, because they both affect the stability and concentration of dissolved gas. To mitigate these impacts, the results indicate the possible reinjection and extraction strategies: (1) reinjected water should be returned and restratified closely above the upper limit of the normal main chemocline at around 240 m depth to maintain a stable density stratification and optimal methane usage; (2) one should extract gas from the deepest layers of the lake to prevent the accumulation of dissolved gases and the formation of hazardous gas concentrations below the extraction depths.
Tyree, Juniper
Prudent Response Surface Models: Exploring a Framework for Approximating Simulations with Confidence and Certainty Masters Thesis
University of Helsinki, 2023.
@mastersthesis{Tyree23,
title = {Prudent Response Surface Models: Exploring a Framework for Approximating Simulations with Confidence and Certainty},
author = {Juniper Tyree},
editor = {Michael Boy and Andreas Rupp and Petri Clusius},
url = {http://urn.fi/URN:NBN:fi:hulib-202305151941},
year = {2023},
date = {2023-04-26},
urldate = {2023-04-26},
school = {University of Helsinki},
abstract = {Response Surface Models (RSM) are cheap, reduced complexity, and, usually, statistical models that are fit to the response of more complex models to approximate their outputs with higher computational efficiency. In atmospheric science, there has been a continuous push to reduce the amount of training data required to fit an RSM. With this reduction in costly data gathering, RSMs can be used more ad hoc and quickly adapted to new applications. However, with the decrease in diverse training data, the risk increases that the RSM is eventually used on inputs on which it cannot make a prediction. If there is no indication from the model that its outputs can no longer be trusted, trust in an entire RSM decreases. We present a framework for building prudent RSMs that always output predictions with confidence and uncertainty estimates. We show how confidence and uncertainty can be propagated through downstream analysis such that even predictions on inputs outside the training domain or in areas of high variance can be integrated.
Specifically, we introduce the Icarus RSM architecture, which combines an out-of-distribution detector, a prediction model, and an uncertainty quantifier. Icarus-produced predictions and their uncertainties are conditioned on the confidence that the inputs come from the same distribution that the RSM was trained on. We put particular focus on exploring out-of-distribution detection, for which we conduct a broad literature review, design an intuitive evaluation procedure with three easily-visualisable toy examples, and suggest two methodological improvements. We also explore and evaluate popular prediction models and uncertainty quantifiers.
We use the one-dimensional atmospheric chemistry transport model SOSAA as an example of a complex model for this thesis. We produce a dataset of model inputs and outputs from simulations of the atmospheric conditions along air parcel trajectories that arrived at the SMEAR II measurement station in Hyytiälä, Finland, in May 2018. We evaluate several prediction models and uncertainty quantification methods on this dataset and construct a proof-of-concept SOSAA RSM using the Icarus RSM architecture. The SOSAA RSM is built on pairwise-difference regression using random forests and an auto-associative out-of-distribution detector with a confidence scorer, which is trained with both the original training inputs and new synthetic out-of-distribution samples. We also design a graphical user interface to configure the SOSAA model and trial the SOSAA RSM.
We provide recommendations for out-of-distribution detection, prediction models, and uncertainty quantification based on our exploration of these three systems. We also stress-test the proof-of-concept SOSAA RSM implementation to reveal its limitations for predicting model perturbation outputs and show directions for valuable future research. Finally, our experiments affirm the importance of reporting predictions alongside well-calibrated confidence scores and uncertainty levels so that the predictions can be used with confidence and certainty in scientific research applications.},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
Response Surface Models (RSM) are cheap, reduced complexity, and, usually, statistical models that are fit to the response of more complex models to approximate their outputs with higher computational efficiency. In atmospheric science, there has been a continuous push to reduce the amount of training data required to fit an RSM. With this reduction in costly data gathering, RSMs can be used more ad hoc and quickly adapted to new applications. However, with the decrease in diverse training data, the risk increases that the RSM is eventually used on inputs on which it cannot make a prediction. If there is no indication from the model that its outputs can no longer be trusted, trust in an entire RSM decreases. We present a framework for building prudent RSMs that always output predictions with confidence and uncertainty estimates. We show how confidence and uncertainty can be propagated through downstream analysis such that even predictions on inputs outside the training domain or in areas of high variance can be integrated.
Specifically, we introduce the Icarus RSM architecture, which combines an out-of-distribution detector, a prediction model, and an uncertainty quantifier. Icarus-produced predictions and their uncertainties are conditioned on the confidence that the inputs come from the same distribution that the RSM was trained on. We put particular focus on exploring out-of-distribution detection, for which we conduct a broad literature review, design an intuitive evaluation procedure with three easily-visualisable toy examples, and suggest two methodological improvements. We also explore and evaluate popular prediction models and uncertainty quantifiers.
We use the one-dimensional atmospheric chemistry transport model SOSAA as an example of a complex model for this thesis. We produce a dataset of model inputs and outputs from simulations of the atmospheric conditions along air parcel trajectories that arrived at the SMEAR II measurement station in Hyytiälä, Finland, in May 2018. We evaluate several prediction models and uncertainty quantification methods on this dataset and construct a proof-of-concept SOSAA RSM using the Icarus RSM architecture. The SOSAA RSM is built on pairwise-difference regression using random forests and an auto-associative out-of-distribution detector with a confidence scorer, which is trained with both the original training inputs and new synthetic out-of-distribution samples. We also design a graphical user interface to configure the SOSAA model and trial the SOSAA RSM.
We provide recommendations for out-of-distribution detection, prediction models, and uncertainty quantification based on our exploration of these three systems. We also stress-test the proof-of-concept SOSAA RSM implementation to reveal its limitations for predicting model perturbation outputs and show directions for valuable future research. Finally, our experiments affirm the importance of reporting predictions alongside well-calibrated confidence scores and uncertainty levels so that the predictions can be used with confidence and certainty in scientific research applications.
Specifically, we introduce the Icarus RSM architecture, which combines an out-of-distribution detector, a prediction model, and an uncertainty quantifier. Icarus-produced predictions and their uncertainties are conditioned on the confidence that the inputs come from the same distribution that the RSM was trained on. We put particular focus on exploring out-of-distribution detection, for which we conduct a broad literature review, design an intuitive evaluation procedure with three easily-visualisable toy examples, and suggest two methodological improvements. We also explore and evaluate popular prediction models and uncertainty quantifiers.
We use the one-dimensional atmospheric chemistry transport model SOSAA as an example of a complex model for this thesis. We produce a dataset of model inputs and outputs from simulations of the atmospheric conditions along air parcel trajectories that arrived at the SMEAR II measurement station in Hyytiälä, Finland, in May 2018. We evaluate several prediction models and uncertainty quantification methods on this dataset and construct a proof-of-concept SOSAA RSM using the Icarus RSM architecture. The SOSAA RSM is built on pairwise-difference regression using random forests and an auto-associative out-of-distribution detector with a confidence scorer, which is trained with both the original training inputs and new synthetic out-of-distribution samples. We also design a graphical user interface to configure the SOSAA model and trial the SOSAA RSM.
We provide recommendations for out-of-distribution detection, prediction models, and uncertainty quantification based on our exploration of these three systems. We also stress-test the proof-of-concept SOSAA RSM implementation to reveal its limitations for predicting model perturbation outputs and show directions for valuable future research. Finally, our experiments affirm the importance of reporting predictions alongside well-calibrated confidence scores and uncertainty levels so that the predictions can be used with confidence and certainty in scientific research applications.
Kabuya, Désiré
Modeling the Temperature in Lake Kivu Masters Thesis
African Institute for Mathematical Sciences (AIMS) Rwanda, 2022.
@mastersthesis{Kabuya22,
title = {Modeling the Temperature in Lake Kivu},
author = {Désiré Kabuya},
editor = {Andreas Rupp},
year = {2022},
date = {2022-06-01},
urldate = {2022-06-01},
school = {African Institute for Mathematical Sciences (AIMS) Rwanda},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
Hauck, Moritz
Analysis and Implementation of an Enriched Galerkin Scheme for the Shallow Water Equations Masters Thesis
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2020.
@mastersthesis{Hauck20,
title = {Analysis and Implementation of an Enriched Galerkin Scheme for the Shallow Water Equations},
author = {Moritz Hauck},
editor = {Vadym Aizinger and Peter Knabner and Andreas Rupp},
year = {2020},
date = {2020-03-01},
urldate = {2020-03-01},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
Musch, Markus
A Hybridizable Discontinuous Galerkin Scheme with Different Orders of Approximation Spaces Capable of Dealing with Jump Conditions: Analysis and Implementation Masters Thesis
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2018.
@mastersthesis{Musch18,
title = {A Hybridizable Discontinuous Galerkin Scheme with Different Orders of Approximation Spaces Capable of Dealing with Jump Conditions: Analysis and Implementation},
author = {Markus Musch},
editor = {Florian Frank and Peter Knabner and Andreas Rupp},
year = {2018},
date = {2018-07-01},
urldate = {2018-07-01},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)},
keywords = {},
pubstate = {published},
tppubtype = {mastersthesis}
}
Bachelor’s theses
Lappalainen, Joona
Parameter Estimation for Cellular Automata Bachelor Thesis
Lappeenranta-Lahti University of Technology (LUT), 2023.
@bachelorthesis{Lappalainen23,
title = {Parameter Estimation for Cellular Automata},
author = {Joona Lappalainen},
editor = {Andreas Rupp and Heikki Haario},
url = {https://urn.fi/URN:NBN:fi-fe20230828110825},
year = {2023},
date = {2023-08-31},
urldate = {2023-08-31},
school = {Lappeenranta-Lahti University of Technology (LUT)},
abstract = {Cellular automaton (CA) is a discrete model that can be used in modelling self organizing complex systems. Usually, CA is illustrated in two-dimensional (2D) space as a square grid, which contains smaller squares. These squares are called cells and they move during CA iterations. The movement leads to patterns, which vary according to the model parameters. In this thesis, the CA model has only one parameter: jump parameter, which defines the biggest possible jumping distance for cells and agglomerates within their domain. The goal is to study a simple CA model and parameter estimation, implement multiple time steps method and analyze its results. The aim of this method is to enhance the results of the estimation algorithm. The method is implemented successfully, and the results are improved in general.},
keywords = {},
pubstate = {published},
tppubtype = {bachelorthesis}
}
Cellular automaton (CA) is a discrete model that can be used in modelling self organizing complex systems. Usually, CA is illustrated in two-dimensional (2D) space as a square grid, which contains smaller squares. These squares are called cells and they move during CA iterations. The movement leads to patterns, which vary according to the model parameters. In this thesis, the CA model has only one parameter: jump parameter, which defines the biggest possible jumping distance for cells and agglomerates within their domain. The goal is to study a simple CA model and parameter estimation, implement multiple time steps method and analyze its results. The aim of this method is to enhance the results of the estimation algorithm. The method is implemented successfully, and the results are improved in general.
Vahteristo, Ilmari
Man vs Machine: Beating Humans in a Multiplayer Card Game without Lookahead Bachelor Thesis
Lappeenranta-Lahti University of Technology (LUT), 2023.
@bachelorthesis{Vahteristo23,
title = {Man vs Machine: Beating Humans in a Multiplayer Card Game without Lookahead},
author = {Ilmari Vahteristo},
editor = {Andreas Rupp and Teemu Härkönen and Heikki Haario},
url = {https://urn.fi/URN:NBN:fi-fe2023051644576},
year = {2023},
date = {2023-05-15},
urldate = {2023-05-15},
school = {Lappeenranta-Lahti University of Technology (LUT)},
abstract = {Games offer a fun and challenging test bed for algorithms and artificial intelligence, due to their well-defined environment, potentially large complexity, and 'man vs machine' dichotomy. Since vacuum-tube computers, scientists have used games to test how intelligently they can make a computer play and to benchmark progress in hardware, computer science, and mathematics.
In this study, a representation for 'Team Machine' in the hidden information card game 'Moska' is created. Moska is a multiplayer, non-sequential, shedding-type card game with a large game tree complexity. It has similarities with the popular Russian card game 'Durak'.
We simulate Moska games and gather data from them to train a deep neural network to evaluate how good a position is from the player's perspective, i.e. with hidden information. We use this neural network for move selection with a look-ahead of one and test the performance of the agent by launching a website where people can play against the agent. We observe the agent successfully employ multiple strategies used by humans and reliably outplay even advanced human players.},
keywords = {},
pubstate = {published},
tppubtype = {bachelorthesis}
}
Games offer a fun and challenging test bed for algorithms and artificial intelligence, due to their well-defined environment, potentially large complexity, and 'man vs machine' dichotomy. Since vacuum-tube computers, scientists have used games to test how intelligently they can make a computer play and to benchmark progress in hardware, computer science, and mathematics.
In this study, a representation for 'Team Machine' in the hidden information card game 'Moska' is created. Moska is a multiplayer, non-sequential, shedding-type card game with a large game tree complexity. It has similarities with the popular Russian card game 'Durak'.
We simulate Moska games and gather data from them to train a deep neural network to evaluate how good a position is from the player's perspective, i.e. with hidden information. We use this neural network for move selection with a look-ahead of one and test the performance of the agent by launching a website where people can play against the agent. We observe the agent successfully employ multiple strategies used by humans and reliably outplay even advanced human players.
In this study, a representation for 'Team Machine' in the hidden information card game 'Moska' is created. Moska is a multiplayer, non-sequential, shedding-type card game with a large game tree complexity. It has similarities with the popular Russian card game 'Durak'.
We simulate Moska games and gather data from them to train a deep neural network to evaluate how good a position is from the player's perspective, i.e. with hidden information. We use this neural network for move selection with a look-ahead of one and test the performance of the agent by launching a website where people can play against the agent. We observe the agent successfully employ multiple strategies used by humans and reliably outplay even advanced human players.
Hauck, Moritz
Stabilization Techniques for the Finite Element Method Applied on Advection Dominated Problems Bachelor Thesis
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2018.
@bachelorthesis{Hauck18,
title = {Stabilization Techniques for the Finite Element Method Applied on Advection Dominated Problems},
author = {Moritz Hauck},
editor = {Florian Frank and Andreas Rupp},
url = {https://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-102581},
year = {2018},
date = {2018-12-14},
urldate = {2018-12-14},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)},
abstract = {This thesis in the mathematical field of numerics of partial differential equations deals with different stabilization techniques of finite element discretizations of advection-dominated problems. The underlying advection–diffusion equation is used, e.g., in hydrogeology, where it describes the transport of groundwater-dissolved matter through the porous soil matrix at an averaged scale. The transport is caused by the actual groundwater flow ("advection") as well as by Brownian particle motion and grain-structure-related dispersion ("diffusion"). Discretizing the advection–diffusion equation in space using the classical finite element method (FEM), unphysical oscillations occur if advection dominates diffusion. The quotient of these two quantities defines the Peclet number. For high Peclet numbers, the numerical solution also attains negative concentration values.
Three different stabilization techniques are considered in this thesis: The first one uses a finite volume discretization for the advective part. For equations of hyperbolic character, finite volume methods are known to have better properties than the FEM. The second method is the streamline diffusion method (streamline upwind Petrov–Galerkin, SUPG) for polynomial degrees one and two. Finally, a not yet widely-established method is considered: Algebraic flux correction (AFC). AFC limits the mass flux between degrees of freedom such that a given prescribed principle is preserved. For example, one can guarantee the discrete non-negativity of concentrations using the AFC method. This is desirable as negative concentrations are physically not meaningful. AFC is formulated on the algebraic level, not on the variational one, and introduces additional non-linearities. Those can be handled by a fixed-point iteration or an appropriate linearization. In any case, AFC turns out to have the highest computational costs compared to the other two stabilization methods. While one can apply SUGP for arbitrary polynomial degrees, the finite volume stabilization and AFC in the standard "linear mass lumping" version can only be applied using first-order polynomials.},
keywords = {},
pubstate = {published},
tppubtype = {bachelorthesis}
}
This thesis in the mathematical field of numerics of partial differential equations deals with different stabilization techniques of finite element discretizations of advection-dominated problems. The underlying advection–diffusion equation is used, e.g., in hydrogeology, where it describes the transport of groundwater-dissolved matter through the porous soil matrix at an averaged scale. The transport is caused by the actual groundwater flow ("advection") as well as by Brownian particle motion and grain-structure-related dispersion ("diffusion"). Discretizing the advection–diffusion equation in space using the classical finite element method (FEM), unphysical oscillations occur if advection dominates diffusion. The quotient of these two quantities defines the Peclet number. For high Peclet numbers, the numerical solution also attains negative concentration values.
Three different stabilization techniques are considered in this thesis: The first one uses a finite volume discretization for the advective part. For equations of hyperbolic character, finite volume methods are known to have better properties than the FEM. The second method is the streamline diffusion method (streamline upwind Petrov–Galerkin, SUPG) for polynomial degrees one and two. Finally, a not yet widely-established method is considered: Algebraic flux correction (AFC). AFC limits the mass flux between degrees of freedom such that a given prescribed principle is preserved. For example, one can guarantee the discrete non-negativity of concentrations using the AFC method. This is desirable as negative concentrations are physically not meaningful. AFC is formulated on the algebraic level, not on the variational one, and introduces additional non-linearities. Those can be handled by a fixed-point iteration or an appropriate linearization. In any case, AFC turns out to have the highest computational costs compared to the other two stabilization methods. While one can apply SUGP for arbitrary polynomial degrees, the finite volume stabilization and AFC in the standard "linear mass lumping" version can only be applied using first-order polynomials.
Three different stabilization techniques are considered in this thesis: The first one uses a finite volume discretization for the advective part. For equations of hyperbolic character, finite volume methods are known to have better properties than the FEM. The second method is the streamline diffusion method (streamline upwind Petrov–Galerkin, SUPG) for polynomial degrees one and two. Finally, a not yet widely-established method is considered: Algebraic flux correction (AFC). AFC limits the mass flux between degrees of freedom such that a given prescribed principle is preserved. For example, one can guarantee the discrete non-negativity of concentrations using the AFC method. This is desirable as negative concentrations are physically not meaningful. AFC is formulated on the algebraic level, not on the variational one, and introduces additional non-linearities. Those can be handled by a fixed-point iteration or an appropriate linearization. In any case, AFC turns out to have the highest computational costs compared to the other two stabilization methods. While one can apply SUGP for arbitrary polynomial degrees, the finite volume stabilization and AFC in the standard "linear mass lumping" version can only be applied using first-order polynomials.
Roith, Tim
Jacobian-Free Newton–Krylov Methods Applied to the Cahn–Hilliard Equa- tion with Degenerate Mobility Bachelor Thesis
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2018.
@bachelorthesis{Roith18,
title = {Jacobian-Free Newton–Krylov Methods Applied to the Cahn–Hilliard Equa- tion with Degenerate Mobility},
author = {Tim Roith},
editor = {Florian Frank and Andreas Rupp},
year = {2018},
date = {2018-12-01},
urldate = {2018-12-01},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)},
keywords = {},
pubstate = {published},
tppubtype = {bachelorthesis}
}