Inhalt

### [ 460NATECP1V16 ] VL Computational Physics I

Versionsauswahl
Es ist eine neuere Version 2022W dieser LV im Curriculum Bachelor's programme Technical Physics 2022W vorhanden. 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 2020W
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