2016: Fundamentals of Simulation Methods

17.10.2016

Winter semester 2016/2017

by Frauke Gräter and Rüdiger Pakmor

This lecture (MVComp1) is part of the specialization in Computational Physics within the physics masters degree at Heidelberg University. The objectives of this course are to endow students with the capacity to identify and classify common numerical problems, to reach an active understanding of applicable numerical methods and algorithms, to solve basic physical problems with adequate numerical techniques, and to recognize the range of validity of numerical solutions.

TOPICS

  • Basic concepts of numerical simulations, continuous and discrete simulations
  • Discretization of ordinary differential equations, integration schemes of different order
  • N-body problems, molecular dynamics, collisionless systems
  • Discretization of partial differential equations
  • Finite element and finite volume methods
  • Lattice methods
  • Adaptive mesh refinement and multi-grid methods
  • Matrix solvers and FFT methods
  • Monte Carlo methods, Markov chains, applications in statistical physics

Examples will include molecular and astrophysics problems.

LECTURE DATES AND TOPICS

Date     Lecturer           Topic
oct
18            FG                   intro
20            FG               1. intro
25            RP               2. ODEs
27            RP               2. ODEs
nov
3              RP               3. collisionless systems
8              RP               3. collisionless cystems
10            RP               4. trees
25            FG               5. Particle-mesh
17            FG               5. Particle-mesh
22            FG               6. FT
24            FG               6. FT
29            FG               7. iterative solvers
dec
1              FG               7. iterative solvers
6              FG               8. MD
8              FG               8. MD
13            RP               8. MD
15            FG               8. BD
20            FG               9. MC
22            FG               9. MC
jan
10            RP             10. Gas dynamics
12            RP             10. Gas dynamics
17            RP             11. PDEs
19            RP             11. PDEs
24            RP             12. SPH
26            RP             13. FEM
31            RP             13. FEM
feb
2              RP             14. Parallelization
7              RP             14. Parallelization
9                                 exam
march
9                                 2nd exam

ORGANIZATION

The lecture takes place weekly, Tuesdays and Thursdays, 9:30-11:00, in INF-227 / HS2 (KIP), with the first lecture taking place on October 18, 2016.

The exercises are Fridays:

group 1: 11:15-13:00 in the CIP-Pool Philos.-weg 12 ( by Csaba Daday)
group 2: 14:15-16:00 in the CIP-Pool 1.401 at INF-227 (by Christopher Zapp)

Prior knowledge in a programming language and experience with plotting software is highly recommended for the course. There will be a short written examination at the end, and active and successful participation in the homework/exercises is a prerequisite for participation in the final exam and obtaining the credit points for the lecture. The use of Moodle is foreseen for the lecture. Those of you who wish to acquire the credit points should please register to the Moodle (password will be announced at the first lecture).

Access to the script and exercises are provided through Moodle here.

LITERATURE

(more to come)

  • W. Hockney and J.W. Eastwood, “Computer Simulation using Particles”
  • P. Allen and D. J. Tildesley, “Computer Simulation of Liquids“
  • Randall J. LeVeque, “Finite Volume Methods for Hyperbolic Problems”
  • Toro, E.F. “Riemann Solvers and Numerical Methods for Fluid Dynamics”

Über das HITS

Das Heidelberger Institut für Theoretische Studien (HITS) wurde 2010 von dem Physiker und SAP-Mitgründer Klaus Tschira (1940-2015) und der Klaus Tschira Stiftung als private, gemeinnützige Forschungseinrichtung ins Leben gerufen. Das HITS betreibt Grundlagenforschung in den Naturwissenschaften, der Mathematik und der Informatik. Dabei werden große, komplexe Datenmengen verarbeitet, strukturiert und analysiert und computergestützte Methoden und Software entwickelt. Die Forschungsfelder reichen von der Molekularbiologie bis zur Astrophysik. Die HITS Stiftung, eine Tochter der Klaus Tschira Stiftung, stellt die Grundfinanzierung der HITS gGmbH auf Dauer sicher. Die Mittel dafür erhält sie von der Klaus Tschira Stiftung. Gesellschafter des HITS sind neben der HITS Stiftung die Universität Heidelberg und das Karlsruher Institut für Technologie (KIT). Das HITS arbeitet außerdem mit weiteren Universitäten und Forschungsinstituten sowie mit industriellen Partnern zusammen. Die wichtigsten externen Mittelgeber sind das Bundesministerium für Bildung und Forschung (BMBF), die Deutsche Forschungsgemeinschaft (DFG) und die Europäische Union.

Zur englischen Seite wechseln oder auf dieser Seite bleiben.