Course No.：S070101XJ014
Course Category：Basic course of subject
Period/Credits：40/2
Prerequisites：advanced mathematics, computational methods, differential equations, elementary linear functional analysis.
Aims & Requirements：
This is one of the speciality foundation courses for master degree candidates majoring in computational mathematics and applied mathematics, and it can also be taken as an elective course for those majoring in physics, mechanics, chemistry and engineering fields. It mainly includes: 1. computational methods for quantum systems；2. Computational methods in composite material and structural mechanics；3. Computational fluid dynamics；4. parallel matrix computation.
Participants of this course are expected to have a general understanding of fundamental problems and main methods of scientific and engineering computations, and to lay the foundation for future research in related fields.
Primary Coverage：
Chapter 1 Introduction
Background problems in physical mechanics；mathematical models；fundamental problems of scientific computing；computer languages and algorithms
Chapter 2 Basic numerical methods
Interpolation and numerical quadraturre；Runge-Kutta methods；computational methods for linear and non-linear algebraic equation systems; numerical methods for eigenvalue problems.
Chapter 3 Computational methods for quantum systems
Kohn-Sham equation；first principle calculation；potential function；MD simulation method；random numbers；Monte-Carlo method；numerical renormalization group method
Chapter 4 Computational methods in composite materials and structural mechanics
Variational principle；finite element method; micmmechanics model；homogenization method；multi-scale algorithms；symplectic geometric algorithms
Chapter 5 Computational fluid dynamics
Euler equation；Navier-Stokes equation；convective-diffusion equation；Liouville and Boltzmann equation；finite difference methods；finite volume methods；Boltzmann lattice gas method.
Chapter 6 Parallel matrix computation
Basic concepts；matrix multiplication；matrix decomposition.
Textbook：
1. K. H. Hoffmann, M.Schreiber, Computational Physics, Springer-Verlag, 1996.
2. Tao Wenquan，Numerical heat transfer theory (2 ed. ), Xi’an Jiaotong University Press. 2001.
3. O.A.Oleinik et al., Mathematical Problems in Elasticity and Homogenization, North-Holland, 1992.
References：
Gene H. Golub, Charles F. Van Loan (translated by YUAN Yaxiang et al.), Matrix Computations, Science Press, Beijing, 2001.
Author ：Cao Liqun（Academy of Mathematics and Systems Science）
Date ：November, 2001.
