Florian Rupp

Random differential equations in scientific computing

This book offers a hollistic approach to the theory and numerics of random differential equations from an interdisciplinary and problem-centered point of view. In this interdisciplinary work, the authors examine state-of-the-art concepts of both dynamical systems and scientific computing.

GPU Optimization of Pseudo Random Number Generators for Random Ordinary Differential Equations

Abstract Solving differential equations with stochastic terms involves a massive use of pseudo random numbers. We present an application for the simulation of wireframe buildings under stochastic earthquake excitation. The inherent potential for vectorization of the application is used to its full extent on GPU accelerator hardware. A representative set of pseudo random number gen- erators for uniformly and normally distributed pseudo random numbers has been implemented, optimized, and benchmarked. The resulting optimized variants outperform standard library implementations on GPUs. The techniques and improvements shown in this contribution using the Kanai-Tajimi model can be generalized to other random differential equations or stochastic models as well as other accelerators.

Driving student-centred calculus: results of a comprehensive case study for Kaizen learning in the Sultanate of Oman

The art of teaching freshmen students is undergoing a rapid paradigm change. Classical forms of teaching are not applicable any more and an unmanageable offer of new multimedia tools and concepts is glutting the market. Moreover, compared to previous courses, the class size triples. In view of these challenges, we implemented a new teaching concept best described as Kaizen learning. By Kaizen learning, we define a teaching philosophy that is based on a concise mix of short learning units (with feedback loops and tests) and of carefully chosen repetitions (also with feedback loops and tests) to calibrate a course for the students. Here, this intensive blended, student-centred learning paradigm is analysed together with its direct impact on the students’ performance. This case study leads to easy-to-implement key drivers for successfully teaching science in Oman, such as (1) human–human interaction, (2) clearly communicated expectations, (3) avoidance of a short-term learning attitude, (4) a no-calculator policy, (5) continuous Kaizen learning, and (6) balanced combination of traditional teaching and e-learning.

Solving Random Ordinary Differential Equations on GPU Clusters using Multiple Levels of Parallelism

Random ordinary differential equations (RODEs) perfectly describe classes of time-dependent problems with stochastic disturbances that are of utmost importance in science and engineering. Both their pathwise solution concept leading to a massive amount of simulations and the form of the numerical solvers for RODEs contain high potential for efficient parallelization approaches. We analyze for the first time a high performance computing parallelization relying on GPU clusters to exploit the underlying three levels of parallelism for the example of the Kanai--Tajimi earthquake model in its RODE form. We identify four basic building blocks of the application which are valid also for general RODE scenarios. We optimized and benchmarked the implementation of the four building blocks separately to be able to select the best individual parameter settings. This allows for a comparison of the total performance of the overall application which shows excellent scaling results also on large GPU clusters. The results ...

Kaizen teaching and the learning habits of engineering students in a freshman mathematics course

Which are the teaching methods that actually contribute to the learning of mathematics? The answer to this certainly is the holy grail of didactic and pedagogy, and should be supported by large scale statistical evidence. Our article aims at providing an initial step into this direction by first illustrating a teaching paradigm that is suited for the generation of large scale data sets: based on industry best practice quality assurance standards we introduce the Kaizen teaching paradigm which enforces Kolb’s reflective learning cycle on the students’ side. Second, we present and analyze the data we obtained through our pilot implementation at a engineering freshman mathematics course in the Sultanate of Oman. These emphasize the effectiveness of Kaizen teaching and once again show the necessity of continuous learning. A practice that seems to be forgotten in traditional university engineering courses due to the mere size of the audience. In particular it seems that a Markovian estimator for students’ performance may have to be considered.

Dynamical Systems, Number Theory and Applications: A Festschrift in Honor of Armin Leutbecher's 80th Birthday

This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning the chasm between abstract insight and actual application. Several of the articles are expected to be in the intersection of dynamical systems theory and number theory. One article will likely relate the topics presented to the academic achievements and interests of Prof. Leutbecher and shed light on common threads among all the contributions. Readership: Researchers in algebra and number theory, dynamical systems and analysis and differential equations.