Browsing 2  Snapshots of Modern Mathematics from Oberwolfach by Snapshot Mathematical Subject "Numerics and Scientific Computing"
Now showing items 120 of 26

The adaptive finite element method
[SNAP2016013EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other ... 
Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
[SNAP2019012EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191121)Throughout the history of dynamical systems, instruments have been used to calculate and visualize (approximate) solutions of differential equations. Here we describe the approach of a group of physicists and engineers ... 
Chaos and chaotic fluid mixing
[SNAP2015005EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Very simple mathematical equations can give rise to surprisingly complicated, chaotic dynamics, with behavior that is sensitive to small deviations in the initial conditions. We illustrate this with a single recurrence ... 
Computational Optimal Transport
[SNAP2017008EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171221)Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; ... 
Computing the long term evolution of the solar system with geometric numerical integrators
[SNAP2017009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171227)Simulating the dynamics of the Sun–Earth–Moon system with a standard algorithm yields a dramatically wrong solution, predicting that the Moon is ejected from its orbit. In contrast, a well chosen algorithm with the ... 
Darcy's law and groundwater flow modelling
[SNAP2015007EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, ... 
Data assimilation: mathematics for merging models and data
[SNAP2018011EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180710)When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a selfdriving car, you typically have two sources of information. The first is a mathematical model, and the ... 
Deep Learning and Inverse Problems
[SNAP2019015EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191121)Big data and deep learning are modern buzz words which presently infiltrate all fields of science and technology. These new concepts are impressive in terms of the stunning results they achieve for a large variety of ... 
Drugs, herbicides, and numerical simulation
[SNAP2014010EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)[also available in German] The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the EcuadorColombia border became an international issue. We developed a ... 
Fast Solvers for Highly Oscillatory Problems
[SNAP2018006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180626)Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial for speech, mobile phones, and other communication technologies. Elastic waves propagating through the Earth bounce ... 
High performance computing on smartphones
[SNAP2016006EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Nowadays there is a strong demand to simulate even realworld engineering problems on small computing devices with very limited capacity, such as a smartphone. We explain, using a concrete example, how we can obtain a ... 
Is it possible to predict the far future before the near future is known accurately?
[SNAP2019021EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191218)It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict ... 
Mathematics plays a key role in scientific computing
[SNAP2017011EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171229)I attended a very interesting workshop at the research center MFO in Oberwolfach on “Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws”. The title sounds a bit technical, but in plain language ... 
Mathematische Modellierung von Krebswachstum
[SNAP2017004DE] (Mathematisches Forschungsinstitut Oberwolfach, 20171017)Krebs ist eine der größten Herausforderungen der modernen Medizin. Der WHO zufolge starben 2012 weltweit 8,2 Millionen Menschen an Krebs. Bis heute sind dessen molekulare Mechanismen nur in Teilen verstanden, was eine ... 
Mixeddimensional models for realworld applications
[SNAP2019014EN] (Mathematisches Forschungsinstitut Oberwolfach, 20191121)We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixeddimensional models. We first give several examples, and ... 
Modeling communication and movement: from cells to animals and humans
[SNAP2015006EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species ... 
Modelling the spread of brain tumours
[SNAP2015013EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment ... 
Molecular Quantum Dynamics
[SNAP2017006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171024)We provide a brief introduction to some basic ideas of Molecular Quantum Dynamics. We discuss the scope, strengths and main applications of this field of science. Finally, we also mention open problems of current ... 
The mystery of sleeping sickness – why does it keep waking up?
[SNAP2015015EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about ... 
On radial basis functions
[SNAP2019002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190313)Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a ...