Inhalt

[ 460NATECP1V16 ] VL Computational Physics I

Versionsauswahl
Workload Education level Study areas Responsible person Hours per week Coordinating university
3 ECTS M1 - Master's programme 1. year Physics Stefan Janecek 2 hpw Johannes Kepler University Linz
Detailed information
Original study plan Master's programme Nanoscience and Technology 2016W
Objectives Introduction to numerical Methods in Physics; solving initial value problems for systems of ordinary differential equations (ODEs); solving boundary- and eigenvalue problems for ODEs with finite differences and finite elements; linear algebra: iterative solution of linear systems and eigenvalue problems; introduction to partial differential equations.
Subject
  • Numerical errors, floating-point numbers
  • Basic numerical analysis: Interpolation, differentiation, finding roots, quadrature (newton-cotes, Gauss quadrature)
  • Solution of initial value problems for systems of ODEs: Euler-, Runge-Kutta-, Predictor-corrector methods, symplectic integrators
  • Three-body problem, introduction to classical chaos
  • Boundary- and Eigenvalue problems
  • Finite difference discretization
  • Finite element discretization
  • Iterative solution of linear systems (Jacobi, Gauss-Seidel, SOR, Conjugate Gradient methods, preconditioning)
  • Iterative solution of eigenvalue problems (Inverse iterations, Rayleigh quotient iterations, subspace iteration method, Lanczos method, generalized eigenvalue problems)
  • Introduction partial differential equations
Criteria for evaluation 2 term papers:

  • celestial mechanics problem (chaotic motion in the 3-body problem, Lagrange points)
  • finite element simulation (Schrödinger equation of a quantum dot)

The grade for the lecture is based on quality and "scientific soundness" of the papers turned in.

Language English
Study material Material distributed in class:

  • Lecture notes as pdf
  • Mathematica Example Notebooks/CDF files

Literature:

  • Paul DeVries, "A first course in computational physics", Wiley 1994
  • Josef Stör, Roland Bulirsch, "Numerische Mathematik 1" and "Numerische Mathematik 2", Springer (also available in English)
  • Gene H. Golub, Charles F. Loan, "Matrix Computations", John Hopkins University Press
  • Z. Bai, J. Demmel, J. Dongarra et al, "Templates for the Solution of Algebraic Eigenvalue Problems", SIAM 2000
  • R. Barrett, M. Berry, T.F. Chan et al, "Templates for the Solution of Linear Systems", SIAM 200g
Changing subject? No
On-site course
Maximum number of participants -
Assignment procedure Direct assignment