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Math2089 Essay

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Computational Engineering/Science

Topic and contents

Four steps in engineering problem analysis

School of Mathematics and Statistics

Most engineering problems involve
Problem specification/description, simplifying assumptions;
Mathematical model: governing equations from physical laws

A/Prof Rob Womersley

MATH2089 – Numerical Methods

equilibrium equation
Newton’s laws of motion
conservation of mass
conservation of energy
chemical balances
...

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§

Week 01 – Computing with real numbers ¥

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1

Computational Engineering/Science
Why numerical methods?

2

Computers
Computer architecture
Units
Memory hierarchy
Numbers
Storage
Floating point numbers

MATH2089 (Numerical Methods)

3

4

5
6

IEEE extensions – Inf, NaN
Errors
Absolute and relative errors
Rounding error
Catastrophic cancellation
Efficiency - Time
Floating point operations
Estimating computation time
Risks
References and links

WK 01 – Computing with real numbers

Computational Engineering/Science

S1 2012

Solution techniques
analytical solutions
numerical solutions

Interpretation of the solution
Visualisation
Physical model
1 / 24

MATH2089 (Numerical Methods)

WK 01 – Computing with real numbers

Why numerical methods?

Computers

Analytical vs numerical solutions

S1 2012

2 / 24

Computer architecture

Computer architecture
Central Processing unit (CPU)
consists of one or more cores
running at a (variable) clock speed measured in GHz

Analytical solution is an exact answer
closed-form mathematical expression
involves the variables describing the problem being solved

1 GHz = 109 cycles per second

Very few practical problems have analytical solutions.
Numerical solution
obtained by using a calculation-intensive process.
cannot be given as a mathematical expression

Modern computers are essential
Efficient numerical methods: Time, Storage (memory, disk)
Modern computers: more memory,...

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