Vorträge
Computational routes towards materials discovery
06. Feb. 2013
Sprecher: Dr. Claudia Draxl
Ort: Humboldt-Kabinett Johann-von-Neumann-Haus, Rudower Chaussee 25
Beginn: 15:00
Finding novel functional materials is crucial for many aspects of our daily life. Solid-state theory combined with computational materials science can provide detailed insight into properties and processes and thus contribute to the discovery of new materials. Based on a variety of examples, I will show that ab initio calculations, comprising density-functional theory and methods going beyond, are a powerful tool to comprehensively describe condensed matter – from composition and geometry to opto-electronic excitations. In this context, I will introduce the basic formalisms of our methodology together with the conceptual and numerical challenges we are facing to make forefront methods being applied to complex nano-structures.
Nano-Plasmonics: Material Model and Computational Methods
04. Jul. 2012
Sprecher: Prof. Dr. Kurt Busch (Max-Born-Institut)
Ort: Humboldt-Kabinett
Beginn: 15:00
Finite element methods for fourth order elliptic problems
02. Jul. 2012
Sprecher: Prof. Dr. Neela Nataraj (Indian Institute of Technology Bombay, Department of Mathematics)
Ort: Humboldt-Kabinett, Johann von Neumann-Haus, Rudower Chaussee 2
Beginn: 13:00
Ende: 15:00 Uhr
After a brief introduction to conforming, non-conforming, discontinuous Galerkin methods and mixed finite element methods, a mixed discontinuous Galerkin method for the biharmonic equation will be presented. The biharmonic equation $DeltaDelta u = f$ is split into a system of two second order equations by introducing an auxiliary variable $v = Delta u$ and an hp-mixed discontinuous Galerkin method is applied to the resulting system. A $mathcal C^0$ interior penalty method will also be proposed and analyzed for general fourth order problems on polygonal domains. Error estimates and the results of some numerical experiments to illustrate the theoretical results will be discussed.
Computing correlation energies with guaranteed precision: Multi-resolution analysis for the helium atom.
27. Jun. 2012
Sprecher: Dr. Florian Bischoff (Humboldt-Universität Berlin, Institut für Chemie)
Ort: Rud25, 3
Beginn: 9:00
Ende: 11:00
We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly-correlated R12-type terms in the wave function in regularize the Coulomb electron-electron singularities of the Hamiltonian. Numerical performance of the method is highlighted by computing the first-order Møller-Plesset (MP1) wave function of a helium atom. The computed second-order (MP2) energy is precise to $sim$2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. The approach does not assume special geometric symmetries, hence application to molecules is straightforward.
Importance sampling techniques in finance
06. Feb. 2012
Sprecher: Dr. Stanislaw Shcheredin (KPMG)
Ort: Institut für Physik, 1
Beginn: 16:00
The credit crisis of 2008-2009 has highlighted structural problems in risk management of global financial institutions. The complexity in the global capital markets calls for application of mathematical modeling and thus cannot solely rely on intuition and expert judgment by finance professionals. The resulting mathematical models are computationally intensive and require innovative techniques to make the calculations accessible in the real time in the business environment. One of such techniques is the importance sampling as applied in the context of the credit portfolio risk. In the presentation we briefly review the ideas behind the importance sampling methods put forward in the leading industry journals by professionals and academics working in the field and establish the connection with analogous methods used in theoretical physics.