Scientific Computing Spring 2006

Peter Gottschling
Open Systems Lab
Indiana University

Course Overview

1. Introduction
   • Computing intensive applications
   • Limits of single-processor computers
   • Performance of modern computers
2. Floating point arithmetic
   • IEEE floating point arithmetic
   • Error analysis
   • Exception handling
   • Risks of parallel computation
3. Vector operations
   • Vector addition
   • Dot product
   • Matrix vector product
4. Matrix multiplication
   • Simple multiplication
   • Memory efficient algorithms
   • Blocked methods
5. Simulations of discrete objects
   • Discrete systems, i.e. discrete objects with discrete states
   • Particle systems, i.e. discrete objects with continuous states
   • Barnes-Hut algorithm
6. Solution of partial differential equations
   • PDE in physical processes
   • Grids
   • Discretization
   • Matrices
   • Overview of solvers for linear equations
7. Sparse matrices and their distributed storing
   • Storing structured and unstructured matrices
   • Matrix vector product sequential with performance analysis
8. Introduction into generic programming
9. Janus: Generic handling of data structures
   • Same handling of structured and unstructured matrices
   • Realization implicitly in matrix vector operations
   • Sample programs
10. Direct solvers for linear equations
    • Gaussian elimination
    • Equivalence with LU factorization
    • Parallel Gaussian elimination
    • Band matrices
    • Direct solvers for sparse systems
11. Linear solvers for sparse systems I
    • Cyclic reduction of tri-diagonal matrices
    • Jacobi method
    • Gauß-Seidel method
    • Blocked Gauß-Seidel method
12. Linear solvers for sparse systems II
    • Over-relaxation
    • CG method
    • Preconditioning: Jacobi, SSOR, red-black method
13. Multigrid methods (based on a tutorial from Klaus Stüben)
    • Why multigrid?
    • Basic principles
    • Full multigrid
    • Local refinements
14. Graph algorithms I
    • Terminology
    • Hamiltonian cycles
    • Depth-First search
    • Breadth-First search
15. Graph algorithms II
    • Shortest path
    • Spanning trees
    • Maximum flow

The content can be slightly changed. But not very much.