Outline About the course Introduction
Chapter 1
Introduction to Computational Methods
Computational Methods
(SECE)
November 7, 2022
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
1
About the course
2
Introduction
Applications
System investigation methods
Scientific computing
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Focus:
on algorithms (principles, scope, and limitations),
on (efficient, stable) implementations in Matlab and C++,
on numerical experiments (design and interpretation).
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Focus:
on algorithms (principles, scope, and limitations),
on (efficient, stable) implementations in Matlab and C++,
on numerical experiments (design and interpretation).
Goals:
Knowledge of the fundamental algorithms in numerical mathematics
Knowledge of the essential terms in numerical mathematics and the
techniques used for the analysis of numerical algorithms
Ability to choose the appropriate numerical method for concrete
problems
Ability to interpret numerical results
Ability to implement numerical algorithms efficiently in Matlab and
C++.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Introduction
Engineering:
=⇒
Solving practical technical problems
1
Using scientific and mathematical tools when available, and
2
Using experience and intuition otherwise.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Introduction
Engineering:
=⇒
Solving practical technical problems
1
Using scientific and mathematical tools when available, and
2
Using experience and intuition otherwise.
Numerical Methods:
Mathematical models: provide a priori estimates of performance very desirable when prototypes or experiments are costly.
Approximate solutions: for engineering applications where exact
analytical solutions are not available, allowing the use of
approximate numerical methods.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Quantitative Engineering Activities: Analysis and Design
Analysis: Predicting the response of a system given a fixed system
design and operating conditions.
Gain of an electromagnetic antenna (Electrical Engineering)
Power output of an electric motor (Electrical/Mechanical
Engineering)
0-60 mph acceleration time of a vehicle (Mechanical Engineering)
Maximum load a bridge can support (Civil Engineering)
Reaction time of a chemical process (Chemical Engineering)
Drag force of an airplane (Aerospace Engineering)
Expected return of a product portfolio (Industrial and Operations
Engineering)
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Design: Determining an ideal system design such that a desired response
is achieved.
Maximizing a vehicle’s fuel economy while maintaining adequate
performance levels by varying vehicle design parameters.
Minimizing the weight of a mountain bike while ensuring it will not
fail structurally by varying frame shape and thickness.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
System investigation methods
Approaches for obtaining knowledge on the properties of systems.
1
theoretical methods,
2
experimental investigations,
3
numerical simulations/scientific computation.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Theoretical methods: analytical considerations of the equations
describing the problems,
Only very conditionally applicable for practically relevant problems.
The equations, which have to be considered for a realistic
description of the processes, are usually so complex and are not
solvable analytically.
Simplifications, often are not valid and lead to inaccurate results
(and therefore probably to wrong conclusions).
More universally valid approximative formulas, as they are willingly
used by engineers, usually cannot be derived from purely analytical
considerations for complex systems.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Experimental investigations: aims to obtain the required system
information by means of tests (with models or with real objects) using
specialized apparatuses and measuring instruments.
Measurements at real objects often are difficult or even impossible.
For instance, the dimensions are too small or too large.
Experiments are prohibited due to safety or environmental reasons.
Experiments are often very expensive and time consuming.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Then what should we use?
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Then what should we use?
Numerical Simulation
The modern development of numerical computing is driven by the
rapid increase in computer performance.
Numerical results often can be obtained faster and at lower costs.
Parameter variations on the computer usually are easily realizable.
A numerical simulation often gives more comprehensive information
due to the global and simultaneous computation of different
problem-relevant quantities.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Scientific computing
Is a discipline concerned with the development and study of
numerical algorithms.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Scientific computing
Is a discipline concerned with the development and study of
numerical algorithms.
Procedures in scientific computing:
1
Mathematical model: formulated in an attempt to explain and
understand an observed phenomenon.
2
Algorithms: to solve the mathematical problem efficiently,
accurately, and reliably. Numerical analysis may be viewed as the
theory behind such algorithms.
3
Implementation: leads to questions involving programming
languages, data structures, computing architectures, etc.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
Figure: 1.1 Scientific computing.
Computational Methods (SECE)
Chapter 1
Outline About the course Introduction
Applications System investigation methods Scientific computing
End of Chapter 1
Questions?
Computational Methods (SECE)
Chapter 1