### Numerical Linear Algebra for Scientific High Performance Computing (Winter Semester 2021/22)

• Lecturer:
• Classes: Lecture (2400138), Problem class (2400140)
• Weekly hours: 2+2

Given the current situation, we will realize this lecture as a hybrid event.
The lecture will take place in SR -1.009 (20.30) and will be streamed on
https://kit-lecture.zoom.us/j/62012337519

We will use C / C++ for programming. You are free to use Java or FORTRAN, if you prefer (I recommend C/C++, though!).

The lecture slides will be collected in the git repo
https://gitlab.com/nla4hpc/fall-2021/lecture-slides.git

The homework assignments will be available in the git repo
https://gitlab.com/nla4hpc/fall-2021/exercises.git

Schedule
Lecture: Thursday 12:00-13:30 SR -1.009 (20.30)
Problem class: Tuesday 10:00-11:30 SR -1.009 (20.30)

Content we will cover:

• Fundamentals of Parallel Processing
• Parallel Architectures (SIMD/SIMT/MIMD)
• Roofline Model,
• Arithmetic Intensity, Machine Balance
• Amdahl’s Law
• Data dependency/Flow dependency/Resource dependency
• Fork-Join, Bulk-Synchronous Programming Model (BSP), Task-based Model
• BLAS routines
• LAPACK
• LU Decomposition
• Cholesky Decomposition
• QR Decomposition
• Fix-Point Iterations
• Krylov Methods
• ILU Preconditioning
• Finite Differences
• Domain Decomposition Methods (Additive/Multiplicative Schwarz)
• Shared Memory / Distributed Memory
• Synchronization, Mutex, One-sided-Communication
• MPI, OpenMP, GPU programming (CUDA)
• Precision Formats and Mixed Precision Numerics

# Examination

The success control takes place in the form of a project presentation and an oral exam of at least 30 minutes duration and evaluation of the written project report and grading of the performance in the exercises.

The overall grade for a different type of examination is formed as follows:
A total of 200 points can be achieved, that compose of
• a maximum of 60 points for the exercise sheets (10 per exercise sheet),
• a maximum of 60 points for the final presentation including an oral examination,
• A maximum of 80 points for the project implementation and project report.
To pass the success control, at least 140 points must be collected.

# References

The Sourcebook of Parallel Computing, Edited by Jack Dongarra, Ian Foster, Geoffrey Fox, William Gropp, Ken Kennedy, Linda Torczon, Andy White, 2002, 760 pages, ISBN 1-55860-871-0, Morgan Kaufmann Publishers.

Introduction to High-Performance Computing for Scientists and Engineers, by Georg Hager, Gerhard Wellein, CRC Press, 2010.

Introduction to High-Performance Scientific Computing, Victor Eijkhout, https://pages.tacc.utexas.edu/~eijkhout/istc/istc.html