# TMA4280: Introduction to Supercomputing

# Practical notes

This exam lets you (as of 2014 at least) bring most printed and hand-written examination aids, which means that if you print and bring:

- All lecture notes, slides, codes, exercises and suggested solutions from the TMA4280 course material.
- Rottmann: Mathematical formulas.
- Earlier exams+suggested solutions in TMA4280.
- LINPACK specification and FAQ.
- All handwritten notes, including annotations on printed material.
- Simple, approved calculator.

you should be pretty alright on the exam.

# Introduction

Some of the theory on parallelisation is covered by TDT4200: Parallel Computing, relevant parts are the distributed memory and shared memory parallisation as well as the parallelisation theory.

In addition to topics covered by TDT4200, TMA4280 covers some mathematical theory behind solutions to the problems typically solved by supercomputers and efficient ways of finding said solutions.

# The maths used in this course

TMA4280 is a maths course, but most of the curriculum is centered around parallel computing. Nevertheless, some actual knowledge of maths is required.

## Elliptic partial differential equation

An elliptic partial differential equation is a general partial differential equation of second order of form

$$ Au_{xx} + 2Bu_{xy} + Cu_{yy} + Du_x + Eu_y + F = 0 $$ that satisfies the condition$$ B^2 - AC < 0 $$ (assuming implicitly that$ u_{xy} = u_{yx} $ ).

### The Poisson problem

The Poisson equation is an elliptic partial differential equation. The Poisson problem is the solution of the Poisson equation given boundary conditions. The poisson equation is typically denoted as

## Speedup

To determine the speedup from 1 to