introduction to scientific computing · what is scientific... what’s in a name? why numerical......
TRANSCRIPT
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 1 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
Introduction to Scientific Computing
What is Scientific Computing?
October 28, 2002
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 2 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
1. What is Scientific Computing?
• mathematical and informatical basis of numerical simulation
• reconstruction or prediction of phenomena and processes, esp.from science and engineering, on supercomputers
• third way to obtain knowledge apart from theory and experiment
?
Exp
erim
ent
Sim
ula
tio
n
Th
eory
• transdisciplinary: mathematics + informatics + field of applica-tion!!
• Objectives depend on concrete task of simulation:
– reconstructand understandknown scenarios (natural disas-ters)
– optimizeknown scenarios (technical processes)
– predictunknown scenarios (weather, new materials)
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 3 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
2. What’s in a Name?
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 3 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
2. What’s in a Name?
• Scientific computing?
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 3 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
2. What’s in a Name?
• Scientific computing?
• scientific and engineering computing?
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 3 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
2. What’s in a Name?
• Scientific computing?
• scientific and engineering computing?
• computational science and engineering?
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 3 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
2. What’s in a Name?
• Scientific computing?
• scientific and engineering computing?
• computational science and engineering?
• simulation?
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 3 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
2. What’s in a Name?
• Scientific computing?
• scientific and engineering computing?
• computational science and engineering?
• simulation?
A chemist’s provoking question:
What the hell is nonscientific computing?
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 3 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
2. What’s in a Name?
• Scientific computing?
• scientific and engineering computing?
• computational science and engineering?
• simulation?
A chemist’s provoking question:
What the hell is nonscientific computing?
The scientific computer’s answer:
What you do, for example!
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 4 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
3. Why Numerical Simulations?
3.1. since experiments are sometimes impossible:
• astrophysics: life cycle of galaxies etc.
• geophysics: displacement of the earth’s magnetic field
(movie)
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 5 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
• climate research: Gulf Stream, greenhouse effect etc.
• weather forecast: tornadoes – where, when, and how strong?
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 6 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
• security: 1993 bomb attack in the World Trade Center
• propagation of harmful substances
• economics: development of the stock market etc.
• medicine: adaptive materials in implants
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 7 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
3.2. since experiments are sometimes very unwelcome
• the bad guy: tests of nuclear weapons
• statics: stability of buildings etc.
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 8 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
3.3. since experiments are sometimes rather unwelcome
• natural disasters: avalanches
• security: effects of car bombs
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 9 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
3.4. since experiments are sometimes extremely costly
• influence of radiation on the genetic makeup
• analysis and study of proteins
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 10 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
• Molecular dynamics: crystal structure, macromolecules
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 11 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
3.5. since simulations are sometimes just cheaper or faster,resp.
• aerodynamics, turbulence: objects in a wind tunnel and so on
• process engineering: stirring and mixing processes
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 12 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
• car industry: vehicle dynamics, elk test
• car industry: crash tests
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 13 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
4. US Government: Grand Challenges
• climate research
• combustion
• automobile development
• aircraft design
• electronic design automation
• biology and medicine
• chemistry and physics
• material science
• financial engineering
• . . .
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
�����
HHHHj embedding
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
�����
HHHHj embedding
statement
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
�����
HHHHj embedding
statement tool
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
�����
HHHHj embedding
statement tool
-
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
�����
HHHHj embedding
statement tool
-
-
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
�����
HHHHj embedding
statement tool
-
-
-
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 14 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
5. From Phenomena to Predictions
phenomenon, process etc.
mathematical model?
modelling
numerical algorithm?
numerical treatment
simulation code?
implementation
results to interpret?
visualization
�����
HHHHj embedding
statement tool
-
-
-validation
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 15 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
6. Mathematical Modelling
model as a (simplifying) formal abstraction of reality
issues when deriving a mathematical model:
– Which quantities have some influence, and how importantis it?
– What relations exist between them? "Which type of mathe-matics?"
– What is the given task (solve, optimize, etc.)?
issues when analyzing a mathematical model:
– What can be said about existence and uniqueness of solu-tions?
– Do the results depend continuously on the input data?
– How accurate is the model, what can be represented?
– Is the model well-suited for a numerical treatment?
There is not one correct model, but several possible!
model hierarchy: accuracy vs. complexity
example: simulations concerning man
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 16 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
7. Simulating Men: Levels of Point of View
issue level of resolution model basis (e.g.!)global increasein population
countries, regions population dynamics
local increase inpopulation
villages, individuals population dynamics
man circulations, organs system simulatorblood circulation pump/channels/valves network simulatorheart blood cells continuumcell macro molecules continuummacromolecules
atoms molecular dynamics
atoms electrons or finer quantum mechanics
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 17 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
8. What else has to be done?
In practice, models can typically not be solved analytically
numerical (approximate and computer-based) methods!
the numerical part is non-trivial:
– often complicated geometries (seeping processes in soil)
– often changing geometries (a sail in the wind)
– accuracy requirements force a high resolution of the do-main
– also higher dimensional problems:
– quantum mechanics: d=6,9,12,... , finance: d=365
– time dependence (unsteady phenomena)
– high memory requirements
– often poor convergence of standard methods (long run times)
– multiscale phenomena (turbulent flows)
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 18 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
9. Numerical Treatment of Models
many approximations and compromises:
numbers fixed number of digits instead of real numbers
functions approximating polynomials instead of series
domains polygonally bounded, restriction to grid points
operators difference quotients instead of derivatives
function spacesonly finite-dimensional
requirements to be fulfilled by numerical algorithms:
efficient high accuracy with moderate storage investment
fast the approximate solution is computed in short time
stable no significant/qualitative errors in the results
robust can be applied for a large class of problems
main tasks:
– derive the discretized equations
– solve the resulting discrete system of equations
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 19 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
10. What else has to be done?
a numerical algorithm is not yet an efficient code
the implementation is crucial:
– platform microprocessor: pipelining, cache memory
– platform supercomputer: vector/parallel/vector-parallel/cluster,distributed/shared/virtually shared memory
– suitable data structures and organization principles (hierar-chy, recurrences)
– potential of (automated) parallelization, communication
– today: software engineering important in simulation con-text, too
“MATLAB-numerics” is not sufficient for doing relevant numeri-cal simulations!
we need “plug-and-play tools”: embedding
interpretation of tons of data requires visualization
What is Scientific . . .
What’s in a Name?
Why Numerical . . .
Grand Challenges
From Phenomena to . . .
Mathematical Modelling
Levels of Point of View
What else has to be . . .
Numerical Treatment . . .
What else has to be . . .
Literature
Page 20 of 20
Introduction to Scientific Computing
1. DefinitionMiriam Mehl
References
[1] Walter Gander and Jiri Hrebícek. Solving Problems in ScientificComputing Using Maple and MATLAB. Springer-Verlag, Berlin,Germany / Heidelberg, Germany / London, UK / etc., secondedition, 1995.
[2] Werner Krabs. Mathematische Modellierung. Eine Einführung indie Problematik. Teubner-Verlag, 1997.
[3] Gene H. Golub and James M. Ortega. Scientific Computing andDifferential Equations. Academic Press, Boston, MA, USA, 1992.
[4] Jack J. Dongarra, Iain S. Duff, Danny C. Sorensen, and Henk A.van der Vorst. Numerical linear algebra for high-performancecomputers. Society for Industrial and Applied Mathematics(SIAM), Philadelphia, PA, USA, 1998.
[5] Kai Hwang. Advanced Computer Architecture: Parallelism, Scal-ability, Programmability. McGraw-Hill, New York, 1993.
[6] Michael Griebel, Thomas Dornseifer, and Tilman Neunhoeffer.Numerical Simulation in Fluid Dynamics: A Practical Introduc-tion. Society for Industrial and Applied Mathematics (SIAM),Philadelphia, PA, USA, 1997.