@article{Pieper2009,
  author    = {Pieper, Martin},
  title     = {Vector hyperinterpolation on the sphere},
  series = {Journal of approximation theory. 156 (2009), H. 2},
  journal   = {Journal of approximation theory. 156 (2009), H. 2},
  isbn      = {0021-9045},
  pages     = {173 -- 186},
  year      = {2009},
  language  = {en}
}
@book{Pieper2007,
  author    = {Pieper, Martin},
  title     = {Spektralrandintegralmethoden zur Maxwell-Gleichung},
  publisher = {Der Andere Verl.},
  address   = {T{\"o}nning [u.a.]},
  isbn      = {978-3-89959-635-9},
  pages     = {144 S. : graph. Darst.},
  year      = {2007},
  language  = {de}
}
@article{PieperKlein2011,
  author    = {Pieper, Martin and Klein, Peter},
  title     = {A simple and accurate numerical network flow model for bionic micro heat exchangers},
  series = {Heat mass transfer},
  volume    = {47},
  journal   = {Heat mass transfer},
  number    = {5},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {0947-7411},
  pages     = {491 -- 503},
  year      = {2011},
  language  = {en}
}
@article{PieperKlein2012,
  author    = {Pieper, Martin and Klein, Peter},
  title     = {Application of simple, periodic homogenization techniques to non-linear heat conduction problems in non-periodic, porous media},
  series = {Heat mass transfer},
  volume    = {48},
  journal   = {Heat mass transfer},
  number    = {2},
  publisher = {Springer},
  address   = {Berlin},
  issn      = {0947-7411},
  doi       = {10.1007/s00231-011-0879-4},
  pages     = {291 -- 300},
  year      = {2012},
  abstract  = {Often, detailed simulations of heat conduction in complicated, porous media have large runtimes. Then homogenization is a powerful tool to speed up the calculations by preserving accurate solutions at the same time. Unfortunately real structures are generally non-periodic, which requires unpractical, complicated homogenization techniques. We demonstrate in this paper, that the application of simple, periodic techniques to realistic media, that are just close to periodic, gives accurate, approximative solutions. In order to obtain effective parameters for the homogenized heat equation, we have to solve a so called "cell problem". In contrast to periodic structures it is not trivial to determine a suitable unit cell, which represents a non-periodic media. To overcome this problem, we give a rule of thumb on how to choose a good cell. Finally we demonstrate the efficiency of our method for virtually generated foams as well as real foams and compare these results to periodic structures.},
  language  = {en}
}
@article{Pieper2008,
  author    = {Pieper, Martin},
  title     = {Nonlinear integral equations for an inverse electromagnetic scattering problem},
  series = {Journal of Physics Conference Series. 124 (2008)},
  journal   = {Journal of Physics Conference Series. 124 (2008)},
  isbn      = {1742-6596},
  year      = {2008},
  language  = {en}
}
@article{PieperIvanyshyn2008,
  author    = {Pieper, Martin and Ivanyshyn, Olha},
  title     = {Nonlinear integral equations for a 3D inverse acoustic scattering problem : abstract / O. Ivanyshyn and M. Pieper},
  year      = {2008},
  language  = {en}
}
@article{EweKleinPieperetal.2009,
  author    = {Ewe, Hendrik and Klein, Peter and Pieper, Martin and F{\"u}ldner, G.},
  title     = {Heat conductivity in sintered aluminium fibers},
  series = {Cellular metals for structural and functional applications : CELLMET 2008 ; proceedings of the International Symposium on Cellular Metals for Structural and Functional Applications held October 8 - 10, 2008 in Dresden, Germany / ed. by G{\"u}nter Stephani},
  journal   = {Cellular metals for structural and functional applications : CELLMET 2008 ; proceedings of the International Symposium on Cellular Metals for Structural and Functional Applications held October 8 - 10, 2008 in Dresden, Germany / ed. by G{\"u}nter Stephani},
  publisher = {Fraunhofer IFAM},
  address   = {Dresden},
  pages     = {187 -- 193},
  year      = {2009},
  language  = {en}
}
@article{Pieper2011,
  author    = {Pieper, Martin},
  title     = {Multiobjective optimization with expensive objectives applied to a thermodynamic material design problem},
  series = {Proceedings in applied mathematics and mechanics : PAMM. 11 (2011), H. 1},
  journal   = {Proceedings in applied mathematics and mechanics : PAMM. 11 (2011), H. 1},
  publisher = {Wiley},
  address   = {Weinheim},
  isbn      = {1617-7061},
  pages     = {733 -- 734},
  year      = {2011},
  language  = {en}
}
@inproceedings{PieperKonopka2013,
  author    = {Pieper, Martin and Konopka, Mahnaz},
  title     = {Umgestaltung der Mathematik Anf{\"a}ngervorlesungen im Fachbereich Energietechnik},
  series = {Mathematik im {\"U}bergang Schule/Hochschule und im ersten Studienjahr : extended abstracts zur 2. khdm-Arbeitstagung 20.02. - 23.02.2013. (khdm-Report ; 13-01)},
  booktitle = {Mathematik im {\"U}bergang Schule/Hochschule und im ersten Studienjahr : extended abstracts zur 2. khdm-Arbeitstagung 20.02. - 23.02.2013. (khdm-Report ; 13-01)},
  pages     = {115 -- 116},
  year      = {2013},
  language  = {de}
}
@article{AlebouyehSamamiPieperBreitbachetal.2014,
  author    = {Alebouyeh Samami, Behzad and Pieper, Martin and Breitbach, Gerd and Hodapp, Josef},
  title     = {Heat production in the windings of the stators of electric machines under stationary condition},
  series = {Heat and mass transfer},
  volume    = {50},
  journal   = {Heat and mass transfer},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0947-7411 (Print) ; 1432-1181 (E-Journal)},
  doi       = {10.1007/s00231-014-1371-8},
  pages     = {1707 -- 1716},
  year      = {2014},
  abstract  = {In electric machines due to high currents and resistive losses (joule heating) heat is produced. To avoid damages by overheating the design of effective cooling systems is required. Therefore the knowledge of heat sources and heat transfer processes is necessary. The purpose of this paper is to illustrate a good and effective calculation method for the temperature analysis based on homogenization techniques. These methods have been applied for the stator windings in a slot of an electric machine consisting of copper wires and resin. The key quantity here is an effective thermal conductivity, which characterizes the heterogeneous wire resin-arrangement inside the stator slot. To illustrate the applicability of the method, the analysis of a simplified, homogenized model is compared with the detailed analysis of temperature behavior inside a slot of an electric machine according to the heat generation. We considered here only the stationary situation. The achieved numerical results are accurate and show that the applied homogenization technique works in practice. Finally the results of simulations for the two cases, the original model of the slot and the homogenized model chosen for the slot (unit cell), are compared to experimental results.},
  language  = {en}
}
@inproceedings{PieperSchulz2014,
  author    = {Pieper, Martin and Schulz, Silvia},
  title     = {Teaching Simulation Methods with COMSOL Multiphysics},
  organization    = {COMSOL Conference <2014, Cambridge>},
  pages     = {7},
  year      = {2014},
  abstract  = {This paper describes two courses on simulation methods for graduate students: "Simulation Methods" and "Simulation and Optimization in Virtual Engineering" The courses were planned to teach young engineers how to work with simulation software as well as to understand the necessary mathematical background. As simulation software COMSOL is used. The main philosophy was to combine theory and praxis in a way that motivates the students. In addition "soft skills" should be improved. This was achieved by project work as final examination. As underlying didactical principle the ideas of Bloom's revised taxonomy were followed. The paper basically focusses on educational aspects, e.g. how to structure the course, plan the exercises, organize the project work and include practical COMSOL examples.},
  language  = {en}
}
@article{JildehWagnerSchoeningetal.2015,
  author    = {Jildeh, Zaid B. and Wagner, Torsten and Sch{\"o}ning, Michael Josef and Pieper, Martin},
  title     = {Simulating the electromagnetic-thermal treatment of thin aluminium layers for adhesion improvement},
  series = {Physica status solidi (a)},
  volume    = {Vol. 212},
  journal   = {Physica status solidi (a)},
  number    = {6},
  publisher = {Wiley},
  address   = {Weinheim},
  issn      = {1862-6319},
  doi       = {10.1002/pssa.201431893},
  pages     = {1234 -- 1241},
  year      = {2015},
  abstract  = {A composite layer material used in packaging industry is made from joining layers of different materials using an adhesive. An important processing step in the production of aluminium-containing composites is the surface treatment and consequent coating of adhesive material on the aluminium surface. To increase adhesion strength between aluminium layer and the adhesive material, the foil is heat treated. For efficient heating, induction heating was considered as state-of-the-art treatment process. Due to the complexity of the heating process and the unpredictable nature of the heating source, the control of the process is not yet optimised. In this work, a finite element analysis of the process was established and various process parameters were studied. The process was simplified and modelled in 3D. The numerical model contains an air domain, an aluminium layer and a copper coil fitted with a magnetic field concentrating material. The effect of changing the speed of the aluminium foil (or rolling speed) was studied with the change of the coil current. Statistical analysis was used for generating a general control equation of coil current with changing rolling speed.},
  language  = {en}
}
@inproceedings{KremersPieper2015,
  author    = {Kremers, Alexander and Pieper, Martin},
  title     = {Simulation and Verification of Bionic Heat Exchangers with COMSOL Multiphysics® Software},
  series = {COMSOL Conference 2015 User Presentations ; COMSOL Conference 2015 Grenoble October 14 - 16, 2015 - World Trade Center, Grenoble, France},
  booktitle = {COMSOL Conference 2015 User Presentations ; COMSOL Conference 2015 Grenoble October 14 - 16, 2015 - World Trade Center, Grenoble, France},
  publisher = {COMSOL},
  address   = {G{\"o}ttingen ; Berlin},
  pages     = {6 Seiten},
  year      = {2015},
  language  = {en}
}
@inproceedings{StollenwerkRiekeDahmenetal.2016,
  author    = {Stollenwerk, Dominik and Rieke, C. and Dahmen, Markus and Pieper, Martin},
  title     = {Biogas Production Modelling : A Control System Engineering Approach},
  series = {IOP Conference Series: Earth and Environmental Science. Bd. 32},
  booktitle = {IOP Conference Series: Earth and Environmental Science. Bd. 32},
  issn      = {1755-1315},
  doi       = {10.1088/1755-1315/32/1/012008},
  pages     = {012008/1 -- 012008/4},
  year      = {2016},
  language  = {en}
}
@incollection{GeislerPieper2017,
  author    = {Geisler, Simon and Pieper, Martin},
  title     = {Mathematik PLuS als E-Book. Kann ein E-Book zur Ingenieursmathematik alle Lerntypen ansprechen?},
  series = {Das elektronische Schulbuch 2016},
  booktitle = {Das elektronische Schulbuch 2016},
  publisher = {LIT Verlag},
  address   = {Berlin},
  isbn      = {978-3-643-13475-2},
  pages     = {99 -- 111},
  year      = {2017},
  language  = {de}
}
@incollection{PieperWaehlisch2017,
  author    = {Pieper, Martin and W{\"a}hlisch, Georg},
  title     = {Mehrwert von E-Learning durch f{\"a}cher{\"u}bergreifenden Einsatz},
  series = {Teaching is Touching the Future \& ePS 2016 - Kompetenzorientiertes Lehren, Lernen und Pr{\"u}fen},
  booktitle = {Teaching is Touching the Future \& ePS 2016 - Kompetenzorientiertes Lehren, Lernen und Pr{\"u}fen},
  publisher = {UVW Universit{\"a}tsverlag Webler},
  address   = {Bielefeld},
  isbn      = {978-3-946017-05-9},
  pages     = {193 -- 196},
  year      = {2017},
  language  = {de}
}
@book{Pieper2017,
  author    = {Pieper, Martin},
  title     = {Mathematische Optimierung: Eine Einf{\"u}hrung in die kontinuierliche Optimierung mit Beispielen},
  publisher = {Springer Fachmedien},
  address   = {Wiesbaden},
  isbn      = {978-3-658-16975-6},
  doi       = {10.1007/978-3-658-16975-6},
  pages     = {IX, 53 S. 20 Abb.},
  year      = {2017},
  language  = {de}
}
@article{RiekeStollenwerkDahmenetal.2018,
  author    = {Rieke, Christian and Stollenwerk, Dominik and Dahmen, Markus and Pieper, Martin},
  title     = {Modeling and optimization of a biogas plant for a demand-driven energy supply},
  series = {Energy},
  volume    = {145},
  journal   = {Energy},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0360-5442},
  doi       = {10.1016/j.energy.2017.12.073},
  pages     = {657 -- 664},
  year      = {2018},
  abstract  = {Due to the Renewable Energy Act, in Germany it is planned to increase the amount of renewable energy carriers up to 60\%. One of the main problems is the fluctuating supply of wind and solar energy. Here biogas plants provide a solution, because a demand-driven supply is possible. Before running such a plant, it is necessary to simulate and optimize the process. This paper provides a new model of a biogas plant, which is as accurate as the standard ADM1 model. The advantage compared to ADM1 is that it is based on only four parameters compared to 28. Applying this model, an optimization was installed, which allows a demand-driven supply by biogas plants. Finally the results are confirmed by several experiments and measurements with a real test plant.},
  language  = {en}
}
@inproceedings{Pieper2018,
  author    = {Pieper, Martin},
  title     = {Digitale Hochschullehre in mathematischen und mathematikdidaktischen Veranstaltungen},
  series = {Beitr{\"a}ge zum Mathematikunterricht 2018 : Vortr{\"a}ge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung GDM und DMV 2018 (52. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik). Bd. 1},
  booktitle = {Beitr{\"a}ge zum Mathematikunterricht 2018 : Vortr{\"a}ge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung GDM und DMV 2018 (52. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik). Bd. 1},
  publisher = {WTM-Verlag},
  address   = {M{\"u}nster},
  isbn      = {978-3-95987-089-4},
  pages     = {105 -- 106},
  year      = {2018},
  language  = {de}
}
@inproceedings{Pieper2018,
  author    = {Pieper, Martin},
  title     = {Lernzielorientierte Kurse und Stack Aufgaben in der Mathematikausbildung},
  series = {Beitr{\"a}ge zum Mathematikunterricht 2018 : Vortr{\"a}ge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung GDM und DMV 2018 (52. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik). Bd. 3},
  booktitle = {Beitr{\"a}ge zum Mathematikunterricht 2018 : Vortr{\"a}ge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung GDM und DMV 2018 (52. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik). Bd. 3},
  publisher = {WTM-Verlag},
  address   = {M{\"u}nster},
  isbn      = {978-3-95987-089-4},
  pages     = {1399 -- 1402},
  year      = {2018},
  language  = {de}
}
@book{Pieper2019,
  author    = {Pieper, Martin},
  title     = {Quantenmechanik : Einf{\"u}hrung in die mathematische Formulierung},
  publisher = {Springer Spektrum},
  address   = {Wiesbaden},
  isbn      = {978-3-658-28329-2},
  doi       = {10.1007/978-3-658-28329-2},
  year      = {2019},
  language  = {de}
}
@article{KahmannRauschPluemeretal.2022,
  author    = {Kahmann, Stephanie L. and Rausch, Valentin and Pl{\"u}mer, Jonathan and M{\"u}ller, Lars P. and Pieper, Martin and Wegmann, Kilian},
  title     = {The automized fracture edge detection and generation of three-dimensional fracture probability heat maps},
  series = {Medical Engineering \& Physics},
  volume    = {2022},
  journal   = {Medical Engineering \& Physics},
  number    = {110},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1350-4533},
  pages     = {7 Seiten},
  year      = {2022},
  abstract  = {With proven impact of statistical fracture analysis on fracture classifications, it is desirable to minimize the manual work and to maximize repeatability of this approach. We address this with an algorithm that reduces the manual effort to segmentation, fragment identification and reduction. The fracture edge detection and heat map generation are performed automatically. With the same input, the algorithm always delivers the same output. The tool transforms one intact template consecutively onto each fractured specimen by linear least square optimization, detects the fragment edges in the template and then superimposes them to generate a fracture probability heat map. We hypothesized that the algorithm runs faster than the manual evaluation and with low (< 5 mm) deviation. We tested the hypothesis in 10 fractured proximal humeri and found that it performs with good accuracy (2.5 mm ± 2.4 mm averaged Euclidean distance) and speed (23 times faster). When applied to a distal humerus, a tibia plateau, and a scaphoid fracture, the run times were low (1-2 min), and the detected edges correct by visual judgement. In the geometrically complex acetabulum, at a run time of 78 min some outliers were considered acceptable. An automatically generated fracture probability heat map based on 50 proximal humerus fractures matches the areas of high risk of fracture reported in medical literature. Such automation of the fracture analysis method is advantageous and could be extended to reduce the manual effort even further.},
  language  = {en}
}
@book{Pieper2019,
  author    = {Pieper, Martin},
  title     = {Quantenmechanik: Einf{\"u}hrung in die mathematische Formulierung},
  publisher = {Springer Spektrum},
  address   = {Wiesbaden},
  isbn      = {978-3-658-28328-5},
  doi       = {10.1007/978-3-658-28329-2},
  pages     = {XI, 33 Seiten},
  year      = {2019},
  language  = {de}
}
@book{Pieper2021,
  author    = {Pieper, Martin},
  title     = {Quantum mechanics: Introduction to mathematical formulation},
  publisher = {Springer},
  address   = {Wiesbaden},
  isbn      = {978-3-658-32644-9},
  doi       = {10.1007/978-3-658-32645-6},
  pages     = {XIII, 33},
  year      = {2021},
  abstract  = {Anyone who has always wanted to understand the hieroglyphs on Sheldon's blackboard in the TV series The Big Bang Theory or who wanted to know exactly what the fate of Schr{\"o}dinger's cat is all about will find a short, descriptive introduction to the world of quantum mechanics in this essential. The text particularly focuses on the mathematical description in the Hilbert space. The content goes beyond popular scientific presentations, but is nevertheless suitable for readers without special prior knowledge thanks to the clear examples.},
  language  = {en}
}
@incollection{JordanKatzPieper2021,
  author    = {Jordan, Frank and Katz, Christiane and Pieper, Martin},
  title     = {Online-Kollaboration in der Mathematik: Ein Design-Based-Research-Projekt},
  series = {Forschungsimpulse f{\"u}r hybrides Lehren und Lernen an Hochschulen},
  booktitle = {Forschungsimpulse f{\"u}r hybrides Lehren und Lernen an Hochschulen},
  publisher = {TH K{\"o}ln},
  address   = {K{\"o}ln},
  url       = {http://nbn-resolving.de/urn:nbn:de:hbz:832-cos4-9465},
  pages     = {245 -- 261},
  year      = {2021},
  abstract  = {Die Studie er{\"o}rtert anhand eines Fallbeispiels aus der Mathematik f{\"u}r Ingenieur*innen, wie didaktische Gestaltungsprinzipien f{\"u}r Soziale Pr{\"a}senz, Kollaboration und das L{\"o}sen von praxisnahen Problemen mit mathematischem Denken in einer Online-Umgebung aussehen k{\"o}nnen. Hierf{\"u}r zieht der Beitrag den forschungsmethodologischen Rahmen Design-Based Research (DBR) hinzu und berichtet {\"u}ber Zwischenergebnisse. DBR wird an dieser Stelle als eine systematische Herangehensweise an kurzfristige Lehrver{\"a}nderungen und als Chance auf dem Weg zu einer neuen Hochschullehre nach der COVID-19-Pandemie dargestellt, die theoretische und empirische Erkenntnisse mit Praxisverkn{\"u}pfung und -relevanz vereint.},
  language  = {de}
}
@inproceedings{NierlePieper2023,
  author    = {Nierle, Elisabeth and Pieper, Martin},
  title     = {Measuring social impacts in engineering education to improve sustainability skills},
  series = {European Society for Engineering Education (SEFI)},
  booktitle = {European Society for Engineering Education (SEFI)},
  doi       = {10.21427/QPR4-0T22},
  pages     = {9 Seiten},
  year      = {2023},
  abstract  = {In times of social climate protection movements, such as Fridays for Future, the priorities of society, industry and higher education are currently changing. The consideration of sustainability challenges is increasing. In the context of sustainable development, social skills are crucial to achieving the United Nations Sustainable Development Goals (SDGs). In particular, the impact that educational activities have on people, communities and society is therefore coming to the fore. Research has shown that people with high levels of social competence are better able to manage stressful situations, maintain positive relationships and communicate effectively. They are also associated with better academic performance and career success. However, especially in engineering programs, the social pillar is underrepresented compared to the environmental and economic pillars. In response to these changes, higher education institutions should be more aware of their social impact - from individual forms of teaching to entire modules and degree programs. To specifically determine the potential for improvement and derive resulting change for further development, we present an initial framework for social impact measurement by transferring already established approaches from the business sector to the education sector. To demonstrate the applicability, we measure the key competencies taught in undergraduate engineering programs in Germany. The aim is to prepare the students for success in the modern world of work and their future contribution to sustainable development. Additionally, the university can include the results in its sustainability report. Our method can be applied to different teaching methods and enables their comparison.},
  language  = {en}
}
@article{PieperKlein2010,
  author    = {Pieper, Martin and Klein, Peter},
  title     = {Numerical solution of the heat equation with non-linear, time derivative-dependent source term},
  series = {International Journal for Numerical Methods in Engineering},
  volume    = {84},
  journal   = {International Journal for Numerical Methods in Engineering},
  number    = {10},
  publisher = {Wiley},
  address   = {Chichester},
  issn      = {0029-5981},
  doi       = {10.1002/nme.2937},
  pages     = {1205 -- 1221},
  year      = {2010},
  abstract  = {The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non-linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non-linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi-implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley \& Sons, Ltd.},
  language  = {en}
}