@article{OezsoyluKizildagSchoeningetal.2020,
  author    = {{\"O}zsoylu, Dua and Kizildag, Sefa and Sch{\"o}ning, Michael Josef and Wagner, Torsten},
  title     = {Differential chemical imaging of extracellular acidification within microfluidic channels using a plasma-functionalized light-addressable potentiometric sensor (LAPS)},
  series = {Physics in Medicine},
  volume    = {10},
  journal   = {Physics in Medicine},
  number    = {100030},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {2352-4510},
  doi       = {10.1016/j.phmed.2020.100030},
  pages     = {8},
  year      = {2020},
  abstract  = {Extracellular acidification is a basic indicator for alterations in two vital metabolic pathways: glycolysis and cellular respiration. Measuring these alterations by monitoring extracellular acidification using cell-based biosensors such as LAPS plays an important role in studying these pathways whose disorders are associated with numerous diseases including cancer. However, the surface of the biosensors must be specially tailored to ensure high cell compatibility so that cells can represent more in vivo-like behavior, which is critical to gain more realistic in vitro results from the analyses, e.g., drug discovery experiments. In this work, O2 plasma patterning on the LAPS surface is studied to enhance surface features of the sensor chip, e.g., wettability and biofunctionality. The surface treated with O2 plasma for 30 s exhibits enhanced cytocompatibility for adherent CHO-K1 cells, which promotes cell spreading and proliferation. The plasma-modified LAPS chip is then integrated into a microfluidic system, which provides two identical channels to facilitate differential measurements of the extracellular acidification of CHO-K1 cells. To the best of our knowledge, it is the first time that extracellular acidification within microfluidic channels is quantitatively visualized as differential (bio-)chemical images.},
  language  = {en}
}
@inproceedings{SildatkeKarwanniKraftetal.2020,
  author    = {Sildatke, Michael and Karwanni, Hendrik and Kraft, Bodo and Schmidts, Oliver and Z{\"u}ndorf, Albert},
  title     = {Automated Software Quality Monitoring in Research Collaboration Projects},
  series = {ICSEW'20: Proceedings of the IEEE/ACM 42nd International Conference on Software Engineering Workshops},
  booktitle = {ICSEW'20: Proceedings of the IEEE/ACM 42nd International Conference on Software Engineering Workshops},
  publisher = {IEEE},
  address   = {New York, NY},
  doi       = {10.1145/3387940.3391478},
  pages     = {603 -- 610},
  year      = {2020},
  abstract  = {In collaborative research projects, both researchers and practitioners work together solving business-critical challenges. These projects often deal with ETL processes, in which humans extract information from non-machine-readable documents by hand. AI-based machine learning models can help to solve this problem. Since machine learning approaches are not deterministic, their quality of output may decrease over time. This fact leads to an overall quality loss of the application which embeds machine learning models. Hence, the software qualities in development and production may differ. Machine learning models are black boxes. That makes practitioners skeptical and increases the inhibition threshold for early productive use of research prototypes. Continuous monitoring of software quality in production offers an early response capability on quality loss and encourages the use of machine learning approaches. Furthermore, experts have to ensure that they integrate possible new inputs into the model training as quickly as possible. In this paper, we introduce an architecture pattern with a reference implementation that extends the concept of Metrics Driven Research Collaboration with an automated software quality monitoring in productive use and a possibility to auto-generate new test data coming from processed documents in production. Through automated monitoring of the software quality and auto-generated test data, this approach ensures that the software quality meets and keeps requested thresholds in productive use, even during further continuous deployment and changing input data.},
  language  = {en}
}
@article{EngelmannPourshahidiShalabyetal.2022,
  author    = {Engelmann, Ulrich M. and Pourshahidi, Mohammad Ali and Shalaby, Ahmed and Krause, Hans-Joachim},
  title     = {Probing particle size dependency of frequency mixing magnetic detection with dynamic relaxation simulation},
  series = {Journal of Magnetism and Magnetic Materials},
  volume    = {563},
  journal   = {Journal of Magnetism and Magnetic Materials},
  number    = {In progress, Art. No. 169965},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-8853},
  doi       = {10.1016/j.jmmm.2022.169965},
  year      = {2022},
  abstract  = {Biomedical applications of magnetic nanoparticles (MNP) fundamentally rely on the particles' magnetic relaxation as a response to an alternating magnetic field. The magnetic relaxation complexly depends on the interplay of MNP magnetic and physical properties with the applied field parameters. It is commonly accepted that particle core size is a major contributor to signal generation in all the above applications, however, most MNP samples comprise broad distribution spanning nm and more. Therefore, precise knowledge of the exact contribution of individual core sizes to signal generation is desired for optimal MNP design generally for each application. Specifically, we present a magnetic relaxation simulation-driven analysis of experimental frequency mixing magnetic detection (FMMD) for biosensing to quantify the contributions of individual core size fractions towards signal generation. Applying our method to two different experimental MNP systems, we found the most dominant contributions from approx. 20 nm sized particles in the two independent MNP systems. Additional comparison between freely suspended and immobilized MNP also reveals insight in the MNP microstructure, allowing to use FMMD for MNP characterization, as well as to further fine-tune its applicability in biosensing.},
  language  = {en}
}
@article{AchtsnichtToedterNiehuesetal.2019,
  author    = {Achtsnicht, Stefan and T{\"o}dter, Julia and Niehues, Julia and Tel{\"o}ken, Matthias and Offenh{\"a}usser, Andreas and Krause, Hans-Joachim and Schr{\"o}per, Florian},
  title     = {3D printed modular immunofiltration columns for frequency mixing-based multiplex magnetic immunodetection},
  series = {Sensors},
  volume    = {19},
  journal   = {Sensors},
  number    = {1},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {1424-8220},
  doi       = {10.3390/s19010148},
  pages     = {15 Seiten},
  year      = {2019},
  abstract  = {For performing point-of-care molecular diagnostics, magnetic immunoassays constitute a promising alternative to established enzyme-linked immunosorbent assays (ELISA) because they are fast, robust and sensitive. Simultaneous detection of multiple biomolecular targets from one body fluid sample is desired. The aim of this work is to show that multiplex magnetic immunodetection based on magnetic frequency mixing by means of modular immunofiltration columns prepared for different targets is feasible. By calculations of the magnetic response signal, the required spacing between the modules was determined. Immunofiltration columns were manufactured by 3D printing and antibody immobilization was performed in a batch approach. It was shown experimentally that two different target molecules in a sample solution could be individually detected in a single assaying step with magnetic measurements of the corresponding immobilization filters. The arrangement order of the filters and of a negative control did not influence the results. Thus, a simple and reliable approach to multi-target magnetic immunodetection was demonstrated.},
  language  = {en}
}
@article{EngelmannShalabyShashaetal.2021,
  author    = {Engelmann, Ulrich M. and Shalaby, Ahmed and Shasha, Carolyn and Krishnan, Kannan M. and Krause, Hans-Joachim},
  title     = {Comparative modeling of frequency mixing measurements of magnetic nanoparticles using micromagnetic simulations and Langevin theory},
  series = {Nanomaterials},
  volume    = {11},
  journal   = {Nanomaterials},
  number    = {5},
  publisher = {MDPI},
  address   = {Basel},
  isbn      = {2079-4991},
  doi       = {10.3390/nano11051257},
  pages     = {1 -- 16},
  year      = {2021},
  abstract  = {Dual frequency magnetic excitation of magnetic nanoparticles (MNP) enables enhanced biosensing applications. This was studied from an experimental and theoretical perspective: nonlinear sum-frequency components of MNP exposed to dual-frequency magnetic excitation were measured as a function of static magnetic offset field. The Langevin model in thermodynamic equilibrium was fitted to the experimental data to derive parameters of the lognormal core size distribution. These parameters were subsequently used as inputs for micromagnetic Monte-Carlo (MC)-simulations. From the hysteresis loops obtained from MC-simulations, sum-frequency components were numerically demodulated and compared with both experiment and Langevin model predictions. From the latter, we derived that approximately 90\% of the frequency mixing magnetic response signal is generated by the largest 10\% of MNP. We therefore suggest that small particles do not contribute to the frequency mixing signal, which is supported by MC-simulation results. Both theoretical approaches describe the experimental signal shapes well, but with notable differences between experiment and micromagnetic simulations. These deviations could result from Brownian relaxations which are, albeit experimentally inhibited, included in MC-simulation, or (yet unconsidered) cluster-effects of MNP, or inaccurately derived input for MC-simulations, because the largest particles dominate the experimental signal but concurrently do not fulfill the precondition of thermodynamic equilibrium required by Langevin theory.},
  language  = {en}
}
@article{AliaziziOezsoyluBakhshiSichanietal.2024,
  author    = {Aliazizi, Fereshteh and {\"O}zsoylu, Dua and Bakhshi Sichani, Soroush and Khorshid, Mehran and Glorieux, Christ and Robbens, Johan and Sch{\"o}ning, Michael Josef and Wagner, Patrick},
  title     = {Development and Calibration of a Microfluidic, Chip-Based Sensor System for Monitoring the Physical Properties of Water Samples in Aquacultures},
  series = {Micromachines},
  volume    = {15},
  journal   = {Micromachines},
  number    = {6},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2072-666X},
  doi       = {10.3390/mi15060755},
  year      = {2024},
  abstract  = {In this work, we present a compact, bifunctional chip-based sensor setup that measures the temperature and electrical conductivity of water samples, including specimens from rivers and channels, aquaculture, and the Atlantic Ocean. For conductivity measurements, we utilize the impedance amplitude recorded via interdigitated electrode structures at a single triggering frequency. The results are well in line with data obtained using a calibrated reference instrument. The new setup holds for conductivity values spanning almost two orders of magnitude (river versus ocean water) without the need for equivalent circuit modelling. Temperature measurements were performed in four-point geometry with an on-chip platinum RTD (resistance temperature detector) in the temperature range between 2 °C and 40 °C, showing no hysteresis effects between warming and cooling cycles. Although the meander was not shielded against the liquid, the temperature calibration provided equivalent results to low conductive Milli-Q and highly conductive ocean water. The sensor is therefore suitable for inline and online monitoring purposes in recirculating aquaculture systems.},
  language  = {en}
}
@article{ZhantlessovaSavitskayaKistaubayevaetal.2024,
  author    = {Zhantlessova, Sirina and Savitskaya, Irina and Kistaubayeva, Aida and Ignatova, Ludmila and Talipova, Aizhan and Pogrebnjak, Alexander and Digel, Ilya},
  title     = {Correction: Zhantlessova et al. advanced "Green" prebiotic composite of bacterial cellulose/pullulan based on synthetic biology-powered microbial coculture strategy. Polymers 2022, 14, 3224},
  series = {Polymers},
  volume    = {16},
  journal   = {Polymers},
  number    = {13},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2073-4360},
  doi       = {10.3390/polym16131802},
  pages     = {2 Seiten},
  year      = {2024},
  language  = {en}
}
@article{HarrisKleefeld2022,
  author    = {Harris, Isaac and Kleefeld, Andreas},
  title     = {Analysis and computation of the transmission eigenvalues with a conductive boundary condition},
  series = {Applicable Analysis},
  volume    = {101},
  journal   = {Applicable Analysis},
  number    = {6},
  publisher = {Taylor \& Francis},
  address   = {London},
  issn      = {1563-504X},
  doi       = {10.1080/00036811.2020.1789598},
  pages     = {1880 -- 1895},
  year      = {2022},
  abstract  = {We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber-Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.},
  language  = {en}
}
@inproceedings{JabbariBhattaraiAndingetal.2017,
  author    = {Jabbari, Medisa and Bhattarai, Aroj and Anding, Ralf and Staat, Manfred},
  title     = {Biomechanical simulation of different prosthetic meshes for repairing uterine/vaginal vault prolapse},
  series = {2nd YRA MedTech Symposium 2017 : June 8th - 9th / 2017 / Hochschule Ruhr-West},
  booktitle = {2nd YRA MedTech Symposium 2017 : June 8th - 9th / 2017 / Hochschule Ruhr-West},
  editor    = {Erni, Daniel and Fischerauer, Alice and Himmel, J{\"o}rg and Seeger, Thomas and Thelen, Klaus},
  publisher = {Universit{\"a}t Duisburg-Essen},
  address   = {Duisburg},
  organization    = {MedTech Symposium},
  isbn      = {978-3-9814801-9-1},
  doi       = {10.17185/duepublico/43984},
  pages     = {118 -- 119},
  year      = {2017},
  language  = {en}
}
@book{StaatDigelTrzewiketal.2024,
  author    = {Staat, Manfred and Digel, Ilya and Trzewik, J{\"u}rgen and Sielemann, Stefanie and Erni, Daniel and Zylka, Waldemar},
  title     = {Symposium Proceedings; 4th YRA MedTech Symposium 2024 : February 1 / 2024 / FH Aachen},
  publisher = {Universit{\"a}t Duisburg-Essen},
  address   = {Duisburg},
  organization    = {MedTech Symposium},
  isbn      = {978-3-940402-65-3},
  doi       = {10.17185/duepublico/81475},
  pages     = {40 Seiten},
  year      = {2024},
  language  = {en}
}
@inproceedings{FrotscherStaat2015,
  author    = {Frotscher, Ralf and Staat, Manfred},
  title     = {Homogenization of a cardiac tissue construct},
  series = {CMBE15 : 4th International Conference on Computational \& Mathematical Biomedical Engineering ; 29th June - 1st July 2015 ; {\´E}cole Normale Sup{\´e}rieure de Cachan ; Cachan (Paris), France},
  booktitle = {CMBE15 : 4th International Conference on Computational \& Mathematical Biomedical Engineering ; 29th June - 1st July 2015 ; {\´E}cole Normale Sup{\´e}rieure de Cachan ; Cachan (Paris), France},
  editor    = {Nithiarasu, Perumal},
  publisher = {CMBE},
  address   = {[s.l.]},
  issn      = {2227-9385},
  pages     = {645 -- 648},
  year      = {2015},
  language  = {en}
}
@inproceedings{SchmitzApandiSpillneretal.2024,
  author    = {Schmitz, Annika and Apandi, Shah Eiman Amzar Shah and Spillner, Jan and Hima, Flutura and Behbahani, Mehdi},
  title     = {Effect of different cannula positions in the pulmonary artery on blood flow and gas exchange using computational fluid dynamics analysis},
  series = {YRA MedTech Symposium (2024)},
  booktitle = {YRA MedTech Symposium (2024)},
  editor    = {Digel, Ilya and Staat, Manfred and Trzewik, J{\"u}rgen and Sielemann, Stefanie and Erni, Daniel and Zylka, Waldemar},
  publisher = {Universit{\"a}t Duisburg-Essen},
  address   = {Duisburg},
  organization    = {MedTech Symposium},
  isbn      = {978-3-940402-65-3},
  doi       = {10.17185/duepublico/81475},
  pages     = {29 -- 30},
  year      = {2024},
  abstract  = {Pulmonary arterial cannulation is a common and effective method for percutaneous mechanical circulatory support for concurrent right heart and respiratory failure [1]. However, limited data exists to what effect the positioning of the cannula has on the oxygen perfusion throughout the pulmonary artery (PA). This study aims to evaluate, using computational fluid dynamics (CFD), the effect of different cannula positions in the PA with respect to the oxygenation of the different branching vessels in order for an optimal cannula position to be determined. The four chosen different positions (see Fig. 1) of the cannulas are, in the lower part of the main pulmonary artery (MPA), in the MPA at the junction between the right pulmonary artery (RPA) and the left pulmonary artery (LPA), in the RPA at the first branch of the RPA and in the LPA at the first branch of the LPA.},
  language  = {en}
}
@inproceedings{KuhlenDigel2017,
  author    = {Kuhlen, Max and Digel, Ilya},
  title     = {Fluorescence signatures and detection limits of ubiquitous terrestrial bio-compounds},
  series = {2nd YRA MedTech Symposium 2017 : June 8th - 9th / 2017 / Hochschule Ruhr-West},
  booktitle = {2nd YRA MedTech Symposium 2017 : June 8th - 9th / 2017 / Hochschule Ruhr-West},
  editor    = {Erni, Daniel and Fischerauer, Alice and Himmel, J{\"o}rg and Seeger, Thomas and Thelen, Klaus},
  publisher = {Universit{\"a}t Duisburg-Essen},
  address   = {Duisburg},
  organization    = {MedTech Symposium},
  isbn      = {978-3-9814801-9-1},
  doi       = {10.17185/duepublico/43984},
  pages     = {102 -- 103},
  year      = {2017},
  language  = {en}
}
@inproceedings{KirchnerHenkelNaetheretal.2008,
  author    = {Kirchner, Patrick and Henkel, H. and N{\"a}ther, Niko and Spelthahn, H. and Schneider, A. and Berger, J. and Kolstad, J. and Friedrich, P. and Sch{\"o}ning, Michael Josef},
  title     = {RFID-basiertes Sensorsystem zur Realisierung intelligenter Verpackungen f{\"u}r die Nahrungsmittelindustrie},
  series = {KMU - innovativ: IKT 2008. CD-ROM : BMBF-Statustagung KMU - innovativ: IKT, Darmstadt, 17. - 18. Nov. 2008},
  booktitle = {KMU - innovativ: IKT 2008. CD-ROM : BMBF-Statustagung KMU - innovativ: IKT, Darmstadt, 17. - 18. Nov. 2008},
  number    = {CD-ROM-Ausg.},
  publisher = {BMBF},
  address   = {Berlin},
  pages     = {9 S.},
  year      = {2008},
  language  = {de}
}
@article{ZhenLiangStaatetal.2024,
  author    = {Zhen, Manghao and Liang, Yunpei and Staat, Manfred and Li, Quanqui and Li, Jianbo},
  title     = {Discontinuous fracture behaviors and constitutive model of sandstone specimens containing non-parallel prefabricated fissures under uniaxial compression},
  series = {Theoretical and Applied Fracture Mechanics},
  volume    = {131},
  journal   = {Theoretical and Applied Fracture Mechanics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-8442},
  doi       = {10.1016/j.tafmec.2024.104373},
  pages     = {Artikel 104373},
  year      = {2024},
  abstract  = {The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress-strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress-strain curves of the fissured sandstone specimens.},
  language  = {en}
}
@article{KeutmannStaatLaack2018,
  author    = {Keutmann, Sabine and Staat, Manfred and Laack, Walter van},
  title     = {Untersuchung der thermischen Auswirkung von therapeutischem Ultraschall},
  volume    = {7},
  number    = {10},
  publisher = {Deutscher {\"A}rzte-Verl.},
  address   = {K{\"o}ln},
  issn      = {2193-5793},
  pages     = {518 -- 522},
  year      = {2018},
  abstract  = {Zusammenfassung: In der Orthop{\"a}die z{\"a}hlt der therapeutische Ultraschall als Mittel zur Pr{\"a}vention und Therapiebegleitung. Er hat mechanische, thermische und physiko-chemische Auswirkungen auf den menschlichen K{\"o}rper. Um mehr Erkenntnisse {\"u}ber die thermischen Auswirkungen zu erlangen, wurden Versuche an einem Hydrogel-Phantom und an Probanden durchgef{\"u}hrt. Dabei entstand eine signifikante Erw{\"a}rmung des Gewebes, welche beim Probandenversuch an der Oberfl{\"a}che und beim Hydrogelversuch in der Tiefe gemessen wurde. Summary: In orthopaedics, therapeutic ultrasound is a tool of prevention and therapy support. It has mechanical, thermal and physico-chemical effects on the human body. Tests with a hydrogel phantom and with human probands have been performed in order to obtain more knowledge about their thermal effects. Both tests measured temperature increases in cell tissue, on the surface with the human proband test and in depth with the hydrogel phantom test.},
  language  = {de}
}
@article{DiktaReisselHarlass2016,
  author    = {Dikta, Gerhard and Reißel, Martin and Harlaß, Carsten},
  title     = {Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation},
  series = {Journal of multivariate analysis},
  journal   = {Journal of multivariate analysis},
  number    = {147},
  publisher = {Elsevier},
  address   = {Amsterdam},
  doi       = {10.1016/j.jmva.2016.02.008},
  pages     = {273 -- 284},
  year      = {2016},
  abstract  = {Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function F, we solve the corresponding estimating equation by an explicit and implicit Euler scheme. While the first approach results in some known estimators, the second one produces new semi-parametric and pre-smoothed Kaplan-Meier estimators which are real distribution functions rather than sub-distribution functions as the former ones are. This property of the new estimators is particular useful if one wants to estimate the expected lifetime restricted to the support of the observation time. Specifically, we focus on estimation under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. We show that some estimated linear functionals which are based on the new semi-parametric estimator are strong consistent, asymptotically normal, and efficient under SRCM. In a small simulation study, the performance of the new estimator is illustrated under moderate sample sizes. Finally, we apply the new estimator to a well-known real dataset.},
  language  = {en}
}
@inproceedings{MarinovaKerroumiLintermannetal.2016,
  author    = {Marinova, V. and Kerroumi, I. and Lintermann, A. and G{\"o}bbert, J.H. and Moulinec, C. and Rible, S. and Fournier, Y. and Behbahani, Mehdi},
  title     = {Numerical Analysis of the FDA Centrifugal Blood Pump},
  series = {NIC Symposium 2016},
  booktitle = {NIC Symposium 2016},
  isbn      = {978-3-95806-109-5},
  pages     = {355 -- 364},
  year      = {2016},
  language  = {de}
}
@article{MichaelMayerWeberetal.2017,
  author    = {Michael, Hackl and Mayer, Katharina and Weber, Mareike and Staat, Manfred and van Riet, Roger and Burkhart, Klau Josef and M{\"u}ller, Lars Peter and Wegmann, Kilian},
  title     = {Plate osteosynthesis of proximal ulna fractures : a biomechanical micromotion analysis},
  series = {The journal of hand surgery},
  volume    = {42},
  journal   = {The journal of hand surgery},
  number    = {10},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0363-5023},
  doi       = {10.1016/j.jhsa.2017.05.014},
  pages     = {834.e1 -- 834.e7},
  year      = {2017},
  language  = {en}
}
@article{ClausnitzerKleefeld2024,
  author    = {Clausnitzer, Julian and Kleefeld, Andreas},
  title     = {A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a C² boundary},
  series = {Discrete and Continuous Dynamical Systems - Series B},
  volume    = {29},
  journal   = {Discrete and Continuous Dynamical Systems - Series B},
  number    = {4},
  publisher = {AIMS},
  address   = {Springfield},
  issn      = {1531-3492},
  doi       = {10.3934/dcdsb.2023148},
  pages     = {1624 -- 1651},
  year      = {2024},
  abstract  = {We consider the numerical approximation of second-order semi-linear parabolic stochastic partial differential equations interpreted in the mild sense which we solve on general two-dimensional domains with a C² boundary with homogeneous Dirichlet boundary conditions. The equations are driven by Gaussian additive noise, and several Lipschitz-like conditions are imposed on the nonlinear function. We discretize in space with a spectral Galerkin method and in time using an explicit Euler-like scheme. For irregular shapes, the necessary Dirichlet eigenvalues and eigenfunctions are obtained from a boundary integral equation method. This yields a nonlinear eigenvalue problem, which is discretized using a boundary element collocation method and is solved with the Beyn contour integral algorithm. We present an error analysis as well as numerical results on an exemplary asymmetric shape, and point out limitations of the approach.},
  language  = {en}
}