Inhalt
[ 460NATECP1U16 ] UE Computational Physics I





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, floatingpoint numbers
 Basic numerical analysis: Interpolation, differentiation, finding roots, quadrature (newtoncotes, Gauss quadrature)
 Solution of initial value problems for systems of ODEs: Euler, RungeKutta, Predictorcorrector methods, symplectic integrators
 Threebody problem, introduction to classical chaos
 Boundary and Eigenvalue problems
 Finite difference discretization
 Finite element discretization
 Iterative solution of linear systems (Jacobi, GaussSeidel, 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 3body 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 



Onsite course 
Maximum number of participants 
25 
Assignment procedure 
Assignment according to priority 


