Podcasts about numerical analysis

José Mario Martínez was born in Cangas del Narcea, Asturias, Spain in 1948, but he moved to Argentina in 1951. He received the B. S. degree in Mathematics from the University of Buenos Aires in 1971 and the Ph. D. degree in Systems Engineering and Computation from the University of Rio de Janeiro in 1978. Since 1978 he is a Professor at the Applied Mathematics Department of the University of Campinas, Brazil. Since 2020 he has been Emeritus Professor with the University of Campinas. He is the author of two books, around 200 papers and several software packages for Optimization. His research interests include Applied Mathematics, Optimization and Numerical Analysis. Currently, he is part of the Editorial Board of the journals Numerical Algorithms, Optimization Methods and Software and European Journal on Operations Research. Mario was a recipient of the Order of Scientific Merit of the Brazilian Ministry of Science. He is a member of the Brazilian Academy of Sciences and SIAM Fellow. In 2023, he received the Su Buchin Prize from the International Council for Industrial and Applied Mathematics. Dr. Martínez was a recipient of the Order of Scientific Merit of the Brazilian Ministry of Science. He is a member of the Brazilian Academy of Sciences and SIAM Fellow. In 2023 he received the Su Buchin Prize from the Institute of Computational and Industrial Mathematics, ICIAM.

"Energy transition is everywhere. It is an underlying trend, and sustainability is something that we have to incorporate into every company's strategy." Sophie Zurquiyah, CEO of Viridien, discusses the transformation of CGG into Viridien. In this episode, we talk about: > The reasons behind CGG's rebranding to Viridien > The significance of technology and quality of service in differentiation in the marketplace > The role of AI and machine learning in enhancing product offerings > The impact of the energy transition on Viridien's goals and strategies > Key trends shaping the future of the oil and gas sector > The influence of being based in the EU on Viridien's business approach > Strategies for attracting and retaining top talent in a competitive industry > Sophie's vision for Viridien's future and its evolution over the next decade In this conversation with host Andrew Geary, Sophie highlights the impact of the energy transition on Viridien's strategies and goals and shares her insights on key trends in the oil and gas sector. Listeners will gain valuable insights into the significance of technology in addressing energy security and Sophie's vision for the company's future. This episode is a must-listen for anyone interested in the evolving landscape of the oil and gas industry and the role of technology and sustainability in shaping its future. THIS EPISODE SPONSORED BY VIRIDIEN Viridien, formerly CGG, is an advanced technology, digital and Earth data company that pushes the boundaries of science for a more prosperous and sustainable future. Building on a track record of innovation, Viridien continues to serve the energy industry as it accelerates its growth in the low-carbon markets of minerals & mining and carbon storage, as well as in high-performance computing and infrastructure monitoring. Learn how Viridien's insights, innovations, and solutions can help resolve your complex challenges efficiently and responsibly - and see things differently at https://www.viridiengroup.com/. THIS EPISODE SPONSORED BY BLUWARE Bluware is revolutionizing interpretation workflows with its cutting-edge interactive AI technology. Designed for geoscientists, the tool enables rapid and precise seismic interpretation, significantly enhancing decision-making processes. Reduce the time and effort required for repetitive interpretation tasks. Instead, increase operational efficiency and drive better outcomes in exploration and production. Discover the future of geoscience interpretation with Bluware InteractivAI - where advanced technology meets unparalleled performance. Learn more at https://bluware.com. GUEST BIOGRAPHY Sophie Zurquiyah is the Director and Chief Executive Officer of Virdien. She is a graduate of the École Centrale of Paris. She holds a Master's in Numerical Analysis from Pierre et Marie Curie University (Paris VI) and a Master's in Aerospace Engineering from the University of Colorado. LINKS * Visit https://seg.org/podcasts/episode-228-key-trends-that-will-shape-the-oil-and-gas-industry-w-sophie-zurquiyah/ for Sophie's complete biography and the interview transcript. SHOW CREDITS Andrew Geary at TreasureMint hosted, edited, and produced this episode. The SEG podcast team comprises Jennifer Cobb, Kathy Gamble, and Ally McGinnis.

Glenn Hefferan and Jacob Dahlin sit down and go in depth (sorry for the length) in USA hockey and do a deep dive into what the numbers are telling us where D1 commits are coming from in USA Hockey.  

When looking at buying an RV park, there are three units of mathematical comparison that are the most important: 1) cap rate 2) cash-on-cash, and 3) cash flow. In this RV Park Mastery podcast, we will drill down on what these are, how to calculate them, and what they mean when acquiring an RV park property.

In this interview, Dr. Nader sits down with Dr. Anirban Bandyopadhyay to discuss the nature of consciousness and microtubule vibrations. From Dr. Bandyopadhyay's perspective, treating the brain with microtubule vibrations could benefit a host of mental, neurological, and cognitive conditions. Microtubule quantum vibrations appear to interfere and produce much slower EEG "beat frequencies" says Dr. Bandyopadhyay, and despite a century of clinical use the underlying origins of EEG rhythms have remained a mystery. Dr. Bandyopadhyay is a Senior Researcher at the National Institute for Materials Science in Tsukuba, Japan. He possesses a Masters of Science in Condensed Matter Physics, Computer, Numerical Analysis, and Astrophysics from North Bengal University, as well as a PhD in Physics from Jadavpur University, where he worked on supramolecular electronics and multi-level switching. Make sure to listen to Part 1! Dr Bandyopadhyay | LinkedIn https://jp.linkedin.com/in/anirbanbandyopadhyay Dr Tony Nader | Instagram http://instagram.com/drtonynader Dr Tony Nader | Twitter http://twitter.com/drtonynader Dr Tony Nader | YouTube https://www.youtube.com/user/DrTonyNader Dr Tony Nader | Facebook http://facebook.com/DrTonyNader

Global dynamics and architecture of the Kepler-444 system by M. Stalport et al. on Thursday 15 September S-type planets, which orbit one component of multiple-star systems, place strong constraints on the planet formation and evolution models. A notable case study is Kepler-444, a triple-star system whose primary is orbited by five planets smaller than Venus in a compact configuration, and for which the stellar binary companion revolves around the primary on a highly eccentric orbit. Having access to the most precise up-to-date masses and orbital parameters is highly valuable to understand formation and evolution processes. We provide the first full dynamical exploration of this system, with the goal to refine those parameters. The planetary system does not appear in any of low-order two or three-planet mean-motion resonances (MMR). We provide the most precise up-to-date dynamical parameters for the planets and the stellar binary companion, using an approach that makes use of the Numerical Analysis of Fundamental Frequencies (NAFF) fast chaos indicator. The orbit of the latter is constrained by new observations from HIRES and Gaia, and also by the stability analysis. This update further challenges the planets formation processes. We also test the dynamical plausibility of a sixth planet in the system, following hints observed in the Hubble Space Telescope (HST) data. We find that this putative planet could exist over a broad range of masses, and with an orbital period roughly comprised between 12 and 20 days. We note an overall good agreement of the system with short-term orbital stability. This suggests that a diverse range of planetary system architectures could be found in multiple-star systems, potentially further challenging the planet formation models. arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2209.06810v1

Global dynamics and architecture of the Kepler-444 system by M. Stalport et al. on Thursday 15 September S-type planets, which orbit one component of multiple-star systems, place strong constraints on the planet formation and evolution models. A notable case study is Kepler-444, a triple-star system whose primary is orbited by five planets smaller than Venus in a compact configuration, and for which the stellar binary companion revolves around the primary on a highly eccentric orbit. Having access to the most precise up-to-date masses and orbital parameters is highly valuable to understand formation and evolution processes. We provide the first full dynamical exploration of this system, with the goal to refine those parameters. The planetary system does not appear in any of low-order two or three-planet mean-motion resonances (MMR). We provide the most precise up-to-date dynamical parameters for the planets and the stellar binary companion, using an approach that makes use of the Numerical Analysis of Fundamental Frequencies (NAFF) fast chaos indicator. The orbit of the latter is constrained by new observations from HIRES and Gaia, and also by the stability analysis. This update further challenges the planets formation processes. We also test the dynamical plausibility of a sixth planet in the system, following hints observed in the Hubble Space Telescope (HST) data. We find that this putative planet could exist over a broad range of masses, and with an orbital period roughly comprised between 12 and 20 days. We note an overall good agreement of the system with short-term orbital stability. This suggests that a diverse range of planetary system architectures could be found in multiple-star systems, potentially further challenging the planet formation models. arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2209.06810v1

Global dynamics and architecture of the Kepler-444 system by M. Stalport et al. on Thursday 15 September S-type planets, which orbit one component of multiple-star systems, place strong constraints on the planet formation and evolution models. A notable case study is Kepler-444, a triple-star system whose primary is orbited by five planets smaller than Venus in a compact configuration, and for which the stellar binary companion revolves around the primary on a highly eccentric orbit. Having access to the most precise up-to-date masses and orbital parameters is highly valuable to understand formation and evolution processes. We provide the first full dynamical exploration of this system, with the goal to refine those parameters. The planetary system does not appear in any of low-order two or three-planet mean-motion resonances (MMR). We provide the most precise up-to-date dynamical parameters for the planets and the stellar binary companion, using an approach that makes use of the Numerical Analysis of Fundamental Frequencies (NAFF) fast chaos indicator. The orbit of the latter is constrained by new observations from HIRES and Gaia, and also by the stability analysis. This update further challenges the planets formation processes. We also test the dynamical plausibility of a sixth planet in the system, following hints observed in the Hubble Space Telescope (HST) data. We find that this putative planet could exist over a broad range of masses, and with an orbital period roughly comprised between 12 and 20 days. We note an overall good agreement of the system with short-term orbital stability. This suggests that a diverse range of planetary system architectures could be found in multiple-star systems, potentially further challenging the planet formation models. arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2209.06810v1

Global dynamics and architecture of the Kepler-444 system by M. Stalport et al. on Thursday 15 September S-type planets, which orbit one component of multiple-star systems, place strong constraints on the planet formation and evolution models. A notable case study is Kepler-444, a triple-star system whose primary is orbited by five planets smaller than Venus in a compact configuration, and for which the stellar binary companion revolves around the primary on a highly eccentric orbit. Having access to the most precise up-to-date masses and orbital parameters is highly valuable to understand formation and evolution processes. We provide the first full dynamical exploration of this system, with the goal to refine those parameters. The planetary system does not appear in any of low-order two or three-planet mean-motion resonances (MMR). We provide the most precise up-to-date dynamical parameters for the planets and the stellar binary companion, using an approach that makes use of the Numerical Analysis of Fundamental Frequencies (NAFF) fast chaos indicator. The orbit of the latter is constrained by new observations from HIRES and Gaia, and also by the stability analysis. This update further challenges the planets formation processes. We also test the dynamical plausibility of a sixth planet in the system, following hints observed in the Hubble Space Telescope (HST) data. We find that this putative planet could exist over a broad range of masses, and with an orbital period roughly comprised between 12 and 20 days. We note an overall good agreement of the system with short-term orbital stability. This suggests that a diverse range of planetary system architectures could be found in multiple-star systems, potentially further challenging the planet formation models. arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2209.06810v1

In this interview, Dr. Nader sits down with Dr. Anirban Bandyopadhyay to discuss the nature of consciousness and microtubule vibrations. From Dr. Bandyopadhyay's perspective, treating the brain with microtubule vibrations could benefit a host of mental, neurological, and cognitive conditions. Microtubule quantum vibrations appear to interfere and produce much slower EEG "beat frequencies" says Dr. Bandyopadhyay, and despite a century of clinical use the underlying origins of EEG rhythms have remained a mystery. Dr. Bandyopadhyay is a Senior Researcher at the National Institute for Materials Science in Tsukuba, Japan. He possesses a Masters of Science in Condensed Matter Physics, Computer, Numerical Analysis, and Astrophysics from North Bengal University, as well as a PhD in Physics from Jadavpur University, where he worked on supramolecular electronics and multi-level switching. Part 2 Coming Soon! Dr Anirban | LinkedIn https://jp.linkedin.com/in/anirbanbandyopadhyay Dr Tony Nader | Instagram http://instagram.com/drtonynader Dr Tony Nader | Twitter http://twitter.com/drtonynader Dr Tony Nader | YouTube https://www.youtube.com/user/DrTonyNader Dr Tony Nader | Facebook http://facebook.com/DrTonyNader

Alfio Quarteroni is Professor of Numerical Analysis and Director of of the Laboratory for Modeling and Scientific Computing -- otherwise known as MOX -- at the Polytechnic University of Milan in Italy. He is the founder (and first director) of MOX and of MATHICSE at EPFL, Lausanne, where he is Emeritus Professor. He is co-founder (and President) of MOXOFF, a spin-off company. His research interests concern Mathematical Modelling, Numerical  Analysis, Scientific Computing, and applications in fluid mechanics, geophysics, medicine, epidemiology, and the improvement of sports performance. His research group at EPFL has contributed to the preliminary design of Solar Impulse, the Swiss, long-range experimental solar-powered aircraft project; they also carried out the mathematical simulation optimising the performances of the Alinghi yacht, twice winner of the America's Cup. He authored or edited 37 books and contributed more than 400 articles to international scientific journals and conference proceedings. He also serves on many editorial boards of journals and book series.He is a plenary speaker at ECM 2021, where he will give a talk on Mathematical Modeling of the Cardiac FunctionRelated Books and Journals and Springer homepage of the podcast: https://www.springer.com/gp/campaign/mathematics-podcasts

Entrevista a Ignacio Urteaga, Fundador del "Instituto para el uso ético de la Ciencia de Datos". Profesor MBA-SUNY-USAL. Profesor de la Diplomatura en Business Intelligence UTN.BA. Compartimos su historia profesional y como lo llevó a ahondar sobre la ética en la ciencia de datos, en relación al impacto que tienen los datos e información en la toma de decisiones, como así también el impacto de las nuevas tecnologías con el futuro del ser humano. DETALLE DE LA ENTREVISTA 00:00 Historia profesional de Ignacio Urteaga, del lado y del otro de informática (el lado oscuro?) 04:10 Pionero en inteligencia artificial aplicada, no es magia es matemática. 06:10 El renacer y descubrir el propósito de vida personal (me he reconvertido a la coronavida) 07:40 Las raíces por la preocupación del #Etica y la #CienciaDeDatos - La ética de la ciencia de datos (privacidad, investigación y construcción científica). - Historia basada en los hechos, empezando por la imprenta. - Frente a una situación cambiante ¿Prohibir es siempre la primera respuesta? 10:36 ¿La tecnología nos impulsa o nos empuja a una nueva realidad? - La historia que conlleva el presente, anhelando un futuro diferente. 12:40 ¿Cuales son los límites y acuerdos en la ciencia de datos? La autoregulación. 14:21 Hay alguna meta-metodología para generar soluciones disruptivas para tomar decisiones estratégicas? 18:30 ¿Los expertos serán reemplazados por los datos? Inteligencia humana versus inteligencia artificial. 21:00 ¿Existen liderazgos inspiradores para estos contextos desafiantes? 23:50 El caso actual de covid19 entre los falso, lo real y lo necesario. - La habilidad humana de obtener información y proyectar el futuro. 28:45 ¿Las personas están preparadas para manejar datos exponenciales? 32:00 La intuición y el pensamiento sistémico. La causa y el efecto inmediato. 35:05 La información nunca es completa, y si lo es no estaríamos seguros. 36:01 De aquí en más ¿que? El futuro de la ciencia de datos. 38:15 Frases fuerzas finales y reflexiones para inspirar IGNACIO URTEAGA: Linkedin: https://www.linkedin.com/in/ignaciourteaga/ Fundador del "Instituto para el uso ético de la Ciencia de Datos". Profesor MBA-SUNY-USAL. Profesor de la Diplomatura en Business Intelligence UTN.BA. Licenciado Fïsico. Especialidades:Data Science, Systems development, Numerical Analysis, Presentations, Financial Analysis, Recruiting.

Click to view slideshow. A aquatic jetpack designed by Archie O’Brien “I want this to be something so cool that you’re wearing it when you’re not even using it,” O’Brien said. “You feel like James Bond.” O’Brien has created a aquatic jetpack; The CUDA jetpack was made using a 3D printer and took several months. The creation, for a final year project in his product design class at the U.K’s Loughborough University. He plans to sell the aquatic jetpack for around $6,000. “By this time next year, I’m planning on having the production model,” he said. “I’ll be going around doing promo videos around the world. I plan to get sponsored by GoPro and Red Bull… The idea is to be able to produce this one, get enough funding to reinvest it into the company, and try and make a much cheaper model. That’s almost working it like Tesla did, with something that really grabs people’s attention, and then bringing that price down to something people can afford more.” THE PATH TO GET HERE O’Brien’s journey to the potential Elon Musk of the watersport propulsion world began when he saw a promotional video for the SEABOB, a handheld aqua scooter that’s half jet-ski and half one of those foam floats they used to give the kids at school who couldn’t swim properly. He liked what he saw — at least, with the exception of its $17,000 price tag. Fortunately, O’Brien had just found out about 3D printing, and the idea occurred to him that, if he couldn’t afford a SEABOB, he might just be able to build his own. “I was so surprised to find that there really wasn’t anything like this that you could wear on your back.” He began poring over research papers like “Numerical Analysis of a Waterjet Propulsion System,” cover to cover. He hooked up with 3D Hubs, a manufacturing platform that provides affordable and fast 3D printing, CNC machining and injection-molding services. He studied the design of high-end cars made by Lamborghini, Mclaren, and Aston Martin, which he wanted his product to resemble aesthetically. Things were progressing nicely until a friend gave him a copy of Daniel Wilson’s 2007 non-fiction book Where’s My Jetpack: A Guide to the Amazing Science Fiction Future that Never Arrived. Suddenly the project parameters changed. Handheld devices were out. Underwater jetpacks were in. “I’ve always wanted to fly, and I just thought that if you can make the experience hands-free it’s a lot better for many reasons,” O’Brien said. “I was so surprised to find that there really wasn’t anything like this that you could wear on your back.” “Think of it like an airplane. If it’s not moving you can’t turn. It kind of feels like you’re a little underwater airplane.” The final CUDA is almost exclusively 3D printed, with the exception of the battery and electronics. Because he wasn’t able to get permission to test it in public spaces, he’s so far put it through its paces in private swimming pools — although he hopes this will change in the future. He hasn’t yet been able to decisively measure a top speed, either, due to the lack of a speedometer and limited testing space. It’s definitely faster than regular swimming, though. “Oh yeah,” he assured us. “Yeah, yeah, yeah.” It needs to go fast because it won’t steer properly unless you’re going quickly. “I’m still learning how to use it,” he admitted. “It seems that the faster you go the easier it is to turn. Think of it like an airplane. If it’s not moving you can’t turn. It kind of feels like you’re a little underwater airplane.” The commercial version will be even faster, he explained, since the current prototype doesn’t have the more powerful battery pack he’s hoping to add. “It would have taken me an extra week and I didn’t have a week to do it,” he said. THE LEADER IN WATERSPORTS PROPULSION Archie O’Brien has big plans for his product. As noted, he’s currently targeting Q2 2019 for the first CUDA production models. It won’t stop there, though. This is just product one of a larger water sports brand. “I’ve got man...

Gudrun had two podcast conversations at the FEniCS18 workshop in Oxford (21.-23. March 2018). FEniCS is an open source computing platform for solving partial differential equations with Finite Element methods. This is the first of the two episodes from Oxford in 2018. Roisin Hill works at the National University of Ireland in Galway on the west coast of Ireland. The university has 19.000 students and 2.000 staff. Roisin is a PhD student in Numerical Analysis at the School of Mathematics, Statistics & Applied Mathematics. Gudrun met her at her poster about Balanced norms and mesh generation for singularly perturbed reaction-diffusion problems. This is a collaboration with Niall Madden who is her supervisor in Galway. The name of the poster refers to three topics which are interlinked in their research. Firstly, water flow is modelled as a singularly perturbed equation in a one-dimensional channel. Due to the fact that at the fluid does not move at the boundary there has to be a boundary layer in which the flow properties change. This might occur very rapidly. So, the second topic is that depending on the boundary layer the problem is singularly perturbed and in the limit it is even ill-posed. When solving this equation numerically, it would be best, to have a fine mesh at places where the error is large. Roisin uses a posteriori information to see where the largest errors occur and changes the mesh accordingly. To choose the best norm for errors is the third topic in the mix and strongly depends on the type of singularity. More precisely as their prototypical test case they look for u(x) as the numerical solution of the problem for given functions b(x) and f(x). It is singularly perturbed in the sense that the positive real parameter ε may be arbitrarily small. If we formally set ε = 0, then it is ill-posed. The numercial schemes of choice are finite element methods - implemented in FEniCS with linear and quadratic elements. The numerical solution and its generalisations to higher-dimensional problems, and to the closely related convection-diffusion problem, presents numerous mathematical and computational challenges, particularly as ε → 0. The development of algorithms for robust solution is the subject of intense mathematical investigation. Here “robust” means two things: The algorithm should yield a “reasonable” solution for all ranges of ε, including resolving any layers present; The mathematical analysis of the method should be valid for all ranges of ε. In order to measure the error, the energy norm sounds like a good basis - but as ε^2 → 0 the norm → 0 with order ε . They were looking for an alternative which they found in the literature as the so-called balanced norm. That remains O(1) as ε → 0. Therefore, it turns out that the balanced norm is indeed a better basis for error measurement.After she finished school Roisin became an accountant. She believed what she was told: if you are good at mathematics, accountancy is the right career. Later her daughter became ill and had to be partially schooled at home. This was the moment when Roisin first encountered applied mathematics and fell in love with the topic. Inspired by her daughter - who did a degree in general science specialising in applied mathematics - Roisin studied mathematics and is a PhD student now (since Sept. 2017). Her enthusiasm has created impressive results: She won a prestigious Postgraduate Scholarship from the Irish Research Council for her four year PhD program. References R. Lin, M. Stynes: A balanced finite element method for singularly perturbed reaction diffusion problems. SIAM J. Numer. Anal., 50(5):2729–2743, 2012. T. Linß: Layer-adapted meshes for reaction-convection-diffusion problems, volume 1985 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2010. H.-G. Roos, M. Stynes, L. Tobiska: Robust Numerical Methods for Singularly Perturbed Differential Equations, volume 24 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 2nd edition, 2008. Podcasts M. E. Rognes: Cerebral Fluid Flow, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 134, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.

Gudrun had two podcast conversations at the FEniCS18 workshop in Oxford (21.-23. March 2018). FEniCS is an open source computing platform for solving partial differential equations with Finite Element methods. This is the first of the two episodes from Oxford in 2018. Roisin Hill works at the National University of Ireland in Galway on the west coast of Ireland. The university has 19.000 students and 2.000 staff. Roisin is a PhD student in Numerical Analysis at the School of Mathematics, Statistics & Applied Mathematics. Gudrun met her at her poster about Balanced norms and mesh generation for singularly perturbed reaction-diffusion problems. This is a collaboration with Niall Madden who is her supervisor in Galway. The name of the poster refers to three topics which are interlinked in their research. Firstly, water flow is modelled as a singularly perturbed equation in a one-dimensional channel. Due to the fact that at the fluid does not move at the boundary there has to be a boundary layer in which the flow properties change. This might occur very rapidly. So, the second topic is that depending on the boundary layer the problem is singularly perturbed and in the limit it is even ill-posed. When solving this equation numerically, it would be best, to have a fine mesh at places where the error is large. Roisin uses a posteriori information to see where the largest errors occur and changes the mesh accordingly. To choose the best norm for errors is the third topic in the mix and strongly depends on the type of singularity. More precisely as their prototypical test case they look for u(x) as the numerical solution of the problem for given functions b(x) and f(x). It is singularly perturbed in the sense that the positive real parameter ε may be arbitrarily small. If we formally set ε = 0, then it is ill-posed. The numercial schemes of choice are finite element methods - implemented in FEniCS with linear and quadratic elements. The numerical solution and its generalisations to higher-dimensional problems, and to the closely related convection-diffusion problem, presents numerous mathematical and computational challenges, particularly as ε → 0. The development of algorithms for robust solution is the subject of intense mathematical investigation. Here “robust” means two things: The algorithm should yield a “reasonable” solution for all ranges of ε, including resolving any layers present; The mathematical analysis of the method should be valid for all ranges of ε. In order to measure the error, the energy norm sounds like a good basis - but as ε^2 → 0 the norm → 0 with order ε . They were looking for an alternative which they found in the literature as the so-called balanced norm. That remains O(1) as ε → 0. Therefore, it turns out that the balanced norm is indeed a better basis for error measurement.After she finished school Roisin became an accountant. She believed what she was told: if you are good at mathematics, accountancy is the right career. Later her daughter became ill and had to be partially schooled at home. This was the moment when Roisin first encountered applied mathematics and fell in love with the topic. Inspired by her daughter - who did a degree in general science specialising in applied mathematics - Roisin studied mathematics and is a PhD student now (since Sept. 2017). Her enthusiasm has created impressive results: She won a prestigious Postgraduate Scholarship from the Irish Research Council for her four year PhD program. References R. Lin, M. Stynes: A balanced finite element method for singularly perturbed reaction diffusion problems. SIAM J. Numer. Anal., 50(5):2729–2743, 2012. T. Linß: Layer-adapted meshes for reaction-convection-diffusion problems, volume 1985 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2010. H.-G. Roos, M. Stynes, L. Tobiska: Robust Numerical Methods for Singularly Perturbed Differential Equations, volume 24 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 2nd edition, 2008. Podcasts M. E. Rognes: Cerebral Fluid Flow, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 134, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.

Das Gespräch mit Susanne Höllbacher von der Simulationsgruppe an der Frankfurter Goethe-Universität war ein Novum in unserer Podcastgeschichte. Das erste mal hatte sich eine Hörerin gemeldet, die unser Interesse an Partikeln in Strömungen teilte, was sofort den Impuls in Gudrun auslöste, sie zu einem Podcastgespräch zu diesem Thema einzuladen. Susanne hat in der Arbeitsgruppe von Gabriel Wittum in Frankfurt promoviert. Dort werden Finite-Volumen-Verfahren zur Lösung von Partiellen Differentialgleichungen benutzt. Das Verfahren betrifft hier insbesondere die räumliche Diskretisierung: Das Rechengebiet wird in Kontrollvolumen aufgeteilt, in denen durch das Verfahren sichergestellt wird, dass bestimmte Größen erhalten bleiben (z.B. die Masse). Diese Verfahren stammen aus dem Umfeld hyperbolischer Probleme, die vor allem als Erhaltungsgesetze modelliert sind. Diese Gleichungen haben die Eigenschaft, dass Fehler nicht automatisch geglättet werden und abklingen sondern potentiell aufgeschaukelt werden können. Trotzdem ist es möglich, diese numerischen Verfahren ähnlich wie Finite-Elemente-Verfahren als Variationsprobleme zu formulieren und die beiden Familien in der Analyse etwas näher zusammenrücken zu lassen. Gemeinsam ist ihnen ja ohnehin, dass sie auf große Gleichungssysteme führen, die anschließend gelöst werden müssen. Hier ist eine billige und doch wirkungsvolle Vorkonditionierung entscheidend für die Effizienz und sogar dafür, ob die Lösungen durch das numerische Verfahren überhaupt gefunden werden. Hier hilft es, schon auf Modell-Ebene die Eigenschaften des diskreten Systems zu berücksichtigen, da ein konsistentes Modell bereits als guter Vorkonditionierer fungiert. Das Promotionsprojekt von Susanne war es, eine Methode zur direkten numerischen Simulation (DNS) von Partikeln in Fluiden auf Basis eines finite Volumen-Verfahrens zu entwickeln. Eine grundsätzliche Frage ist dabei, wie man die Partikel darstellen möchte und kann, die ja winzige Festkörper sind und sich anders als die Strömung verhalten. Sie folgen anderen physikalischen Gesetzen und man ist geneigt, sie als Kräfte in die Strömung zu integrieren. Susanne hat die Partikel jedoch als Teil des Fluides modelliert, indem die Partikel als finite (und nicht infinitesimal kleine) Volumen mit zusätzlicher Rotation als Freiheitsgrad in die diskreten Gleichungen integriert werden. Damit fügen sich die Modelle für die Partikel natürlich und konsistent in das diskrete System für die Strömung ein. Vorhandene Symmetrien bleiben erhalten und ebenso die Kopplung der Kräfte zwischen Fluid und Partikel ist gewährleistet. Die Nebenbedingungen an das System werden so formuliert, dass eine Sattelpunkt-Formulierung vermieden wird. Die grundlegende Strategie dabei ist, die externen Kräfte, welche bedingt durch die Partikel und deren Ränder wirken, direkt in die Funktionenräume des zugrundeliegenden Operators zu integrieren. In biologischen Systemen mit hoher Viskotität des Fluides fungiert die Wirkung der Partikel auf das Fluid als Informationstransport zwischen den Partikeln und ist sehr wichtig. In der Umsetzung dieser Idee verhielten sich die Simulationen des Geschwindigkeitsfeldes sehr gutartig, aber Susanne beobachtete Oszillationen im Druck. Da sie sich nicht physikalisch erklären ließen, musste es sich um numerische Artekfakte handeln. Bei näherem Hinsehen zeigte sich, dass es vor allem daran lag, dass die Richtungen von Kraftwirkungen auf dem Rand der Partikel im diskreten System nicht sinnvoll approximiert wurden. In den berechneten Lösungen für das Geschwindigkeitsfeld hat sich dies kaum messbar niedergeschlagen. Im Druck zeigte sich jedoch, dass es sich lohnt, hier das numerische Verfahren zu ändern, so dass die Normalenrichtungen auf dem Rand jeweils korrekt sind. Mathematisch heißt das, dass die Ansatzfunktionen so geändert werden, dass deren Freiheitsgrade auf dem Rand liegen. Der Aufwand dafür ist vergleichsweise gering und die Resultate sind überzeugend. Die Oszillationen verschwinden komplett. Der Nachweis der Stabilität des entstehenden Gleichungssystems lässt sich über die inf-sup-Bedingung des orginalen Verfahrens erbringen, da die Konstruktion den Raum in der passenden Weise erweitert. Literatur und weiterführende Informationen S. V. Apte, M. Martin, N. A. Patankar: A numerical method for fully resolved simulation (FRS) of rigid particle–flow interactions in complex flows, Journal of Computational Physics 228, S. 2712–2738, 2009. R. E. Bank, D. J. Rose: Some Error Estimates for the Box Method, SIAM Journal on Numerical Analysis 24, S. 777–787, 1987. Glowinski, R.: Finite element methods for incompressible viscous flow, P. G. Ciarlet, J. L. Lions (Eds.), Handbook of Numerical Analysis IX (North-Holland, Amsterdam), S. 3–1176, 2003. Strang, G.: Wissenschaftlisches Rechnen, Springer-Verlag Berlin Heidelberg, 2010. A. Vogel, S. Reiter, M. Rupp, A. Naegel, G. Wittum: UG 4: A novel flexible software system for simulating PDE based models on high performance computers, Computing and Visualization in Science 16, S. 165–179, 2013. G. J. Wagner, N. Moes, W. K. Liu, T. Belytschko: The extended finite element method for rigid particles in Stokes flow, International Journal for Numerical Methods in Engineering 51, S. 293–313, 2001. D. Wan, S. Turek: Fictitious boundary and moving mesh methods for the numerical simulation of rigid particulate flows, Journal of Computational Physics 222, S. 28–56, 2007. P. Wessling: Principles of Computational Fluid Dynamics, Springer, Series in Computational Mathematics, 2001. J. Xu, Q. Zou: Analysis of linear and quadratic simplicial finite volume methods for elliptic equations, Numerische Mathematik 111, S. 469–492, 2009. X. Ye: On the Relationship Between Finite Volume and Finite Element Methods Applied to the Stokes Equations, Numerical Methods for Partial Differential Equations 17, S. 440–453, 2001. Podcasts T. Henn: Partikelströmungen, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 115, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2016. http://modellansatz.de/partikelstroemungen L.L.X. Augusto: Filters, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 112, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2016. http://modellansatz.de/filters L. Adlung: Systembiologie, Gespräch mit G. Thäter und S. Ritterbusch im Modellansatz Podcast, Folge 39, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2014. http://modellansatz.de/systembiologie

Strömungen beobachten wir fast jeden Tag. Die Meeresbrandung fasziniert uns und eine gut funktionierende Klimaanlage ist ein wunderbarer Luxus, egal ob sie wärmt oder kühlt. Strömungen zu beherrschen ist aber auch in vielen verfahrenstechnischen Zusammenhängen wichtig. Insofern haben Gleichungen, die Strömungen beschreiben, eine große praktische Relevanz und gleichzeitig eine fast emotionale Anziehungskraft. Das einfachste mathematische Modell, das auch für viele Computersimulationen genutzt wird, sind die inkompressiblen Navier-Stokes Gleichungen (INS). Hier ist die strömende Substanz dem Wasser ähnlich genug, dass nur in der Materialkonstante Viskosität verschiedene Fließfähigkeiten unterschieden werden. Als Lösungen des Systems von partiellen Differentialgleichungen suchen wir das Geschwindigkeitsfeld und den Druck als Funktionen von Raum und Zeit . Im 3d-Fall ist das ein System von vier Gleichungen. Drei davon sind eine Vektorgleichung, die aus der Impulserhaltung abgeleitet wird und die vierte ist die Erhaltung der Masse. Im inkompressiblen Fall vereinfacht sich diese aus die Forderung, dass die Divergenz des Geschwindigkeitsfeldes verschwindet. Die komplexer aussehende Gleichung ist die Vektorgleichung, weil hier die zweiten räumlichen Ableitungen des Geschwindigkeitsfeldes, der Druckgradient, die zeitliche Ableitung der Geschwindigkeit und ein nichtlinearer Term vorkommen. Die Gleichungen müssen im Strömungsgebiet gelten. Die Lösungen müssen sich aus dem Anfangszustand entwickeln (Anfangsbedingung) und am räumlichen Rand vorgeschriebenen Werten, den Randwerten (meist fordert man, dass die Geschwindigkeit Null ist) genügen. Dieses Modell ist in einem längeren Prozess entwickelt worden. Ein großer Durchbruch bei der mathematischen Analyse gelang dem französischen Mathematiker Leray im Jahr 1934. Er hatte die geniale Idee, sich von dem Wunsch zu verabschieden, für diese komplizierte Gleichung eine punktweise zutreffende Lösung zu konstruieren. Statt dessen verallgemeinerte er den Lösungsbegriff und führte den Begriff der schwachen Lösung ein. Diese erfüllt die Gleichung nur im Sinne eines ausgeklügelten Systems von unendlich vielen Integralgleichungen. Er zeigte mit Hilfe von abstrakten Argumenten, dass die INS immer solche schwachen Lösungen haben. Heute ist bekannt, dass falls eine punktweise Lösung existiert (sogenannte starke Lösung), diese eindeutig ist (also insbesondere mit der schwachen übereinstimmt), es in 2d immer eine punktweise Lösung gibt, die für alle Zeiten existiert (unter geringfügigen Bedingungen an den Rand), und es unter Kleinheitsbedingungen an die Daten und bei glattem geometrischen Rand des Gebietes auch in 3d punktweise Lösungen gibt.Wir wissen jedoch in 3d nicht, ob die gefundenen schwache Lösung regulär bzw. stark ist (d.h. eine punktweise Lösung ist.) In Vorbereitung auf den Jahrtausendwechsel gab es in der Mathematik die Bestrebung, so wie dies 100 Jahre zuvor von Hilbert geschehen war, die wichtigsten mathematischen Problemstellungen in den Fokus zu nehmen. Das Ergebnis waren sieben sogenannte Milleniumsprobleme der Clay Foundation, für deren Lösung jeweils ein Preisgeld von einer Millionen Dollar ausgelobt wurde. Eines dieser für so wichtig angesehenen Probleme ist die offene Frage der Regularität der schwachen Lösungen der INS. Woran liegt das? Eine Eigenschaft der INS, die sie schwierig macht, ist ihre Nichtlinearität. Sie ist nur quadratisch und hat eine besondere Struktur. Diese Struktur verdanken wir es z.B., dass die schwache Theorie erfolgreich ist. Es besteht Hoffnung, dass wir auch die Lücke zur starken Theorie unter Ausnutzung der Struktur schließen können. Der Standardweg im linearen Fall (z.B. beim Laplace-Problem) ist es, für die schwachen Lösungen mit einem Münchhausen-Prinzip (Elliptic Bootstrapping) Stück für Stück mehr Regularität zu zeigen. Man kann so zeigen, dass die Lösung immer so gut ist, wie die es Daten erlauben. Man nennt das maximale Regularität. Leider ist für die INS das Wachstum in der Nichtlinearität zu schnell, um im 3d-Fall mit diesen Standardmethoden zu argumentieren (im 2d Fall geht es aber). Im 3d-Fall geht es aber unter bestimmten Zusatzbedingungen, z.B. einer höheren Integrierbarkeit des Geschwindigkeitsfeldes als die schwachen Lösungen von vornherein haben. Man fand dies über Skalierungs-Eigenschaften der Gleichung heraus. Grob gesagt, muss man fordern dass die Lösung zu einem Raum gehört, der Skalierungsinvariant ist. Eine weitere zusätzliche Forderung ist die Gültigkeit der Energiegleichung (Erhaltung der kinetischen Energie), denn leider weiß man bisher von schwachen Lösungen nur, dass sie eine Energieungleichung erfüllen. Eine zweite Schwierigkeit der INS ist der Zusammenhang zwischen Druck und Divergenzgleichung. Ein Trick der schwachen Theorie ist, dass wir uns von Anfang an auf Funktionen beschränken, die schwach divergenzfrei sind (also die Gleichung in Integralmittel erfüllen. Was in der Theorie sehr gut funktioniert, ist blöd für die Numerik, weil man Divergenzfreiheit immer wieder herstellen muss wegen der Rechenfehler im Prozess. Unter den Forschern gibt es zwei Richtungen: Entweder man sucht nach Blow-up Lösungen, also schwachen Lösungen, die keine punktweisen Lösungen sein können, oder man versucht die Zusatzforderungen aufzuweichen (um sie am Ende ganz weglassen zu können). Dabei gibt es ständig kleine Fortschritte. Es gibt auch zwei Wege, für allgemeinere Modelle Theorien zu entwickeln, die dann im Spezialfall auch etwas über INS sagen. Ein durch O.A. Ladyzenskaya vorgeschlagener Zugang geht über den p-Laplace-Operator. Hier findet man starke Lösungen für alle p>2,5, die INS ist jedoch der Fall p=2. Als Materialgesetz interessant für Ingenieure ist aber der noch schwierigere Fall 1

In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences.

In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms?

In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants

In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT.

In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions.

In this lecture, Professor Trefethen discusses order of accuracy and reaction-diffusion equations and other stiff PDEs.

In this lecture, Professor Trefethen discusses Chebyshev spectral discretization.

In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences.

In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun.

In this lecture, Professor Trefethen discusses planetary motions, chaos and Lyapunov exponents, the Lorenz equations, and lastly Sinai billiards and the SIAM 100-digit challenge.

In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes.

In this lecture, Professor Trefethen discusses ODEs and IVPs, Runge-Kutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun.

In this lecture, Professor Trefethen discusses matrix factorizations and SVD.

In this lecture, Professor Trefethen provides a demonstration of Chebfun.

In this lecture, Professor Trefethen discusses Newton's methods for 1) a single equation, 2) a system of equations, and 3) minimizing a function of 1 variable.

In this lecture, Professor Trefethen first provides an overview of the field of linear algebra and optimization. Secondly, he discusses the question of how fast we can solve Ax=3Db? Thirdly, he discusses sparse matrices

In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG.

In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners

In this lecture, Professor Trefethon provides a definition of numerical analysis and provides an overview of matrix iterations, including a discussion on the Lanczos iteration. He also reviews various numerical software tools and information sources.

In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices.

In this lecture, Professor Trefethen discusses Newton's methods for minimizing a function of several variables. He then moves on from Newton's method to practical optimization.

In this lecture, Professor Trefethen discusses NEOS and COIN-OR, constraints and linear programming, and quadratic programming and linear constraints.

In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis.

In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear least-squares.

To separate one single instrument from the acoustic sound of a whole orchestra- just by knowing its exact position- gives a good idea of the concept of wave splitting, the research topic of Marie Kray. Interestingly, an approach for solving this problem was found by the investigation of side-effects of absorbing boundary conditions (ABC) for time-dependent wave problems- the perfectly matched layers are an important example for ABCs. Marie Kray works in the Numerical Analysis group of Prof. Grote in Mathematical Department of the University of Basel. She did her PhD 2012 in the Laboratoire Jacques-Louis Lions in Paris and got her professional education in Strasbourg and Orsay. Since boundaries occur at the surface of volumes, the boundary manifold has one spatial dimension less than the actual regarded physical domain. Therefore, the treatment of normal derivatives as in the Neumann boundary condition needs special care. The implicit Crank-Nicolson method turned out to be a good numerical scheme for integrating the time derivative, and an upwinding scheme solved the discretized hyperbolic problem for the space dimension. An alternative approach to separate the signals from several point sources or scatterers is to apply global integral boundary conditions and to assume a time-harmonic representation. The presented methods have important applications in medical imaging: A wide range of methods work well for single scatterers, but Tumors often tend to spread to several places. This serverely impedes inverse problem reconstruction methods such as the TRAC method, but the separation of waves enhances the use of these methods on problems with several scatterers. Literature and additional material F. Assous, M. Kray, F. Nataf, E. Turkel: Time-reversed absorbing condition: application to inverse problems, Inverse Problems, 27(6), 065003, 2011. F. Assous, M. Kray, F. Nataf: Time reversal techniques for multitarget identification, in Ultrasonics Symposium (IUS), IEEE International (pp. 143-145). IEEE, 2013. M. Grote, M. Kray, F. Nataf, F. Assous: Wave splitting for time-dependent scattered field separation, Comptes Rendus Mathematique, 353(6), 523-527, 2015.

To separate one single instrument from the acoustic sound of a whole orchestra- just by knowing its exact position- gives a good idea of the concept of wave splitting, the research topic of Marie Kray. Interestingly, an approach for solving this problem was found by the investigation of side-effects of absorbing boundary conditions (ABC) for time-dependent wave problems- the perfectly matched layers are an important example for ABCs. Marie Kray works in the Numerical Analysis group of Prof. Grote in Mathematical Department of the University of Basel. She did her PhD 2012 in the Laboratoire Jacques-Louis Lions in Paris and got her professional education in Strasbourg and Orsay. Since boundaries occur at the surface of volumes, the boundary manifold has one spatial dimension less than the actual regarded physical domain. Therefore, the treatment of normal derivatives as in the Neumann boundary condition needs special care. The implicit Crank-Nicolson method turned out to be a good numerical scheme for integrating the time derivative, and an upwinding scheme solved the discretized hyperbolic problem for the space dimension. An alternative approach to separate the signals from several point sources or scatterers is to apply global integral boundary conditions and to assume a time-harmonic representation. The presented methods have important applications in medical imaging: A wide range of methods work well for single scatterers, but Tumors often tend to spread to several places. This serverely impedes inverse problem reconstruction methods such as the TRAC method, but the separation of waves enhances the use of these methods on problems with several scatterers. Literature and additional material F. Assous, M. Kray, F. Nataf, E. Turkel: Time-reversed absorbing condition: application to inverse problems, Inverse Problems, 27(6), 065003, 2011. F. Assous, M. Kray, F. Nataf: Time reversal techniques for multitarget identification, in Ultrasonics Symposium (IUS), IEEE International (pp. 143-145). IEEE, 2013. M. Grote, M. Kray, F. Nataf, F. Assous: Wave splitting for time-dependent scattered field separation, Comptes Rendus Mathematique, 353(6), 523-527, 2015.

Vikhansky, A (QMUL) Friday 16 December 2011, 09:00-09:30

This presentation demonstrates the importance of long-range strain in quantum dotsNumerical analysis of the importance of the buffer around the central quantum dot - local band edges – vertical and horizontal extension of the bufferControlled overgrowth can tune the electron energies in the systemLearning Objectives:Strain is the source of the creation of the InAs QDs on GaAsStrain is a long range phenomenonStrain reaches further vertically than horizontallyQuantum dots will grow on top of each otherElectron wavefunctions are confined to the central quantum dots and can be computed in a smaller domain

This presentation demonstrates the importance of long-range strain in quantum dotsNumerical analysis of the importance of the buffer around the central quantum dot - local band edges – vertical and horizontal extension of the bufferControlled overgrowth can tune the electron energies in the systemLearning Objectives:Strain is the source of the creation of the InAs QDs on GaAsStrain is a long range phenomenonStrain reaches further vertically than horizontallyQuantum dots will grow on top of each otherElectron wavefunctions are confined to the central quantum dots and can be computed in a smaller domain