2016: Fundamentals of Simulation Methods

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”