Inhalt

### [ 460NATECP1U16 ] UE 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
1,5 ECTS M1 - Master's programme 1. year Physics Stefan Janecek 1 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 and French
Study material
• Lecture notes as pdf
• 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 25
Assignment procedure Assignment according to priority