Lecture: “Fundamentals of Simulation Methods”

Winter semester 2013/2014      (will be offered again by V. Springel in winter semester 2015/2016)

by Volker Springel

This lecture (MVComp1) is part of the new 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

Origanization

The lecture takes place weekly, Tuesdays and Thursdays, 9:15-11:00, in INF-227 / HS2 (KIP), with the first lecture taking place on October 15, 2013.

The exercises are Fridays, 14:15-16:00 in the CIP-Pool 1.401 at INF-227. 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).

Literature

(more to come)

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