EU Regional School - Higham Seminar
Prof. Nicholas Higham, Ph.D. - Multiprecision Algorithms
- IEEE standard arithmetic and availability in hardware and software. Motivation for low precision from applications, including machine learning. Applications requiring high precision. Simulating low precision for testing purposes. Software for high precision. Challenges of implementing algorithms in low precision.
- Basics of rounding error analysis. Examples of error analyses of algorithms, focusing on issues relating to low precision.
- Solving linear systems using mixed precision: iterative renement, hybrid direct-iterative methods. Multiprecision algorithms for matrix functions, focusing on the matrix logarithm.
CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Noble Seminar
Prof. Denis Noble, Ph.D. - From Pacing the Heart to the Pace of Evolution
Department of Physiology, Anatomy and Genetics, University of Oxford, England
Multi-mechanism interpretations of cardiac pacemaker function reveal the extent to which many physiological functions are buffered against genomic change. Contrary to Schrodinger's claim in What is Life? (1944) which led to the Central Dogma of Molecular Biology (Crick 1970), biological functions at higher levels harness stochasticity at lower levels. This harnessing of stochasticity is a prerequisite for the processes by which the pace of evolution can be accelerated through guided control of mutation rates and of buffering by regulatory networks in organisms.
Schrodinger E. 1944 What is life? Cambridge, UK: Cambridge University Press.
Crick FHC. 1970 Central dogma of molecular biology. Nature 227, 561 – 563. (doi:10.1038/227561a0)
Noble D. Dance to the Tune of Life. Biological Relativity. Cambridge University Press 2016
Noble D. Evolution viewed from physics, physiology and medicine. Interface Focus 2017, 7, 20160159.
Noble R & Noble D. Was the Watchmaker Blind? Or was she One-eyed? Biology, 2017, 6, 47.
I³MS - Kiendl Seminar
Dr. Josef Kiendl - Isogeometric Methods in Structural Analysis
, Norwegian University of Science and Technology, Norway
Isogeometric analysis is a novel method of computational analysis where functions used to describe geometries in Computer Aided Design (CAD) are adopted as basis for analysis. Due to this unified geometric representation, the model transfer from design to analysis, called mesh generation, is omitted providing a better integration of design and analysis. NURBS are the most widespread technology in today’s CAD modeling tools and therefore are adopted as basis functions for analysis. Apart from the geometrical advantages, NURBS-based isogeometric analysis has proven superior approximation properties compared to standard finite element analysis for many different applications. Furthermore, the high continuity between elements also allows the discretization of higher order PDEs, which is especially useful in structural mechanics, where the classical plate and shell theories, based on Kirchhoff’s kinematic assumption, can be implemented in a straightforward way.
We show an isogeometric shell analysis framework with formulations ranging from linear, geometrically nonlinear, and fully nonlinear shell models. All formulations are based on the Kirchhoff-Love shell theory and are rotation-free, i.e., using only displacement degrees of freedom. These formulations are then employed for the simulation of various problems of structural mechanics, including large deformations, buckling, elastoplasticity, and brittle fracture as well as for fluid-structure-interaction problems including high-fidelity FSI simulations of offshore wind turbine blades and bioprosthetic heart valves.
A further development of IGA are isogeometric collocation methods (IGA-C), where the partial differential equations are solved in the strong form. This avoids the need of computing integrals by numerical quadrature and, thus, reduces the computational costs by several orders. We show isogeometric collocation formulations for different problems in structural mechanics, like spatial beams, plates, and shells.
I³MS - Dedé Seminar
Prof. Dr. Luca Dedé - Isogeometric Analysis of High Order, Surface, and Geometric Partial Differential Equations with Applications
Department of Mathematics, Politecnico di Melano, Italy
In this talk, we consider the spatial approximation of high order, surface, and geometric Partial Differential Equations (PDEs) by means of Isogeometric Analysis (IGA). Specifically, we discretize the PDEs by means of NURBS-based IGA in the framework of the Galerkin method and we show that IGA is particularly suitable for approximating these classes of PDEs. Indeed, NURBS-basis IGA straightforwardly encapsulates the exact representation of the computational domain (the geometry) in the numerical approximation of the PDE, thus significantly enhancing the accuracy of the solution of surface and geometric PDEs. Moreover, we consider trial spaces of NURBS basis functions with high degree of continuity in the computational domain, a feature that is particularly efficient for approximating high order PDEs. We show the efficiency and accuracy of the method by solving high order PDEs on both open and closed surfaces and phase field problems driven by the Cahn-Hilliard and crystal growth equations. Moreover, we approximate by means of NURBS-based IGA some benchmark geometric PDEs, specifically the mean curvature and Willmore flow problems and the Canham-Helfrich curvature model. The latter is indeed suited to model the shape of biomembranes and vescicles as red blood cells. Finally, we present and discuss a dynamical model for the simulation of the interaction of the biomembranes with the fluid.
CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Cremers Seminar
Prof. Dr. Daniel Cremers - Novel Algorithms for 3D Computer Vision
Department of Computer Science, Technical University of Munich