Scientific Computing I Module 1: Introduction Miriam Mehl based on - - PowerPoint PPT Presentation

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Lehrstuhl Informatik V Scientific Computing I Module 1: Introduction Miriam Mehl based on Slides by Michael Bader (Winter 09/10) Winter 2011/2012 Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1:

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Lehrstuhl Informatik V

Scientific Computing I

Module 1: Introduction

Miriam Mehl based on Slides by Michael Bader (Winter 09/10)

Winter 2011/2012

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 1

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Lehrstuhl Informatik V

Scientific Computing =

Science + Computing?

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 2

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Lehrstuhl Informatik V

Scientific Computing =

Science + Computing? Science on Computers??

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 2

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Lehrstuhl Informatik V

Scientific Computing =

Science + Computing? Science on Computers?? “Computational Science”???

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 2

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A Short Look into Wikipedia . . .

Not to be confused with computer science. Computational science (or scientific computing) is the field of study concerned with

  • constructing mathematical models
  • and quantitative analysis techniques
  • and using computers

to analyze and solve scientific, social scientific and engineering problems. [. . .]The scientific computing approach is to gain understanding, mainly through the analysis of mathematical models implemented on computers. [. . .]massive amounts of calculations (usually floating-point) and are

  • ften executed on supercomputers or distributed computing

platforms.

[Wikipedia, Sep 21, 2011]

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 3

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Part I An Interdisciplinary Discipline

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 4

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Gaining Scientific Knowledge

The Classical Scientific Process

  • 1. characterization
  • observation
  • quantification/measurement

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 5

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Gaining Scientific Knowledge

The Classical Scientific Process

  • 1. characterization
  • observation
  • quantification/measurement
  • 2. hypothesis
  • theory
  • model

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 5

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Gaining Scientific Knowledge

The Classical Scientific Process

  • 1. characterization
  • observation
  • quantification/measurement
  • 2. hypothesis
  • theory
  • model
  • 3. prediction
  • consequences/logical deducation from hypothesis/model?

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 5

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Lehrstuhl Informatik V

Gaining Scientific Knowledge

The Classical Scientific Process

  • 1. characterization
  • observation
  • quantification/measurement
  • 2. hypothesis
  • theory
  • model
  • 3. prediction
  • consequences/logical deducation from hypothesis/model?
  • 4. experiment
  • verification/falsification
  • discrepancies might lead to improved model

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 5

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Gaining Scientific Knowledge (2)

Approaches to Science:

  • 1. theoretical investigation
  • hypothesis / models
  • analytical calculations
  • Gedankenexperiments

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 6

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Gaining Scientific Knowledge (2)

Approaches to Science:

  • 1. theoretical investigation
  • hypothesis / models
  • analytical calculations
  • Gedankenexperiments
  • 2. experimentation
  • build model scenarios
  • compare observations with

predicted theoretical results

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 6

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Lehrstuhl Informatik V

Gaining Scientific Knowledge (2)

Approaches to Science:

  • 1. theoretical investigation
  • hypothesis / models
  • analytical calculations
  • Gedankenexperiments
  • 2. experimentation
  • build model scenarios
  • compare observations with

predicted theoretical results

Sience

Experiments Theory

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 6

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Lehrstuhl Informatik V

Gaining Scientific Knowledge (2)

Approaches to Science:

  • 1. theoretical investigation
  • hypothesis / models
  • analytical calculations
  • Gedankenexperiments
  • 2. experimentation
  • build model scenarios
  • predict theoretical results

and compare with outcome

  • 3. simulation
  • Why would we need that?

Sience

Experiments Theory Simulation

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 7

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Drawbacks of Theory and Experiment

Theoretical Investigation:

  • analytical solutions for simple scenarios, only,
  • models usually very complicated or even impossible to solve

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 8

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Drawbacks of Theory and Experiment

Theoretical Investigation:

  • analytical solutions for simple scenarios, only,
  • models usually very complicated or even impossible to solve

Experiments:

  • might be impossible to do
  • might be dangerous or unwelcome
  • might be very expensive

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 8

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The Scientific Process Revisited

Scientific/Engineering Tasks:

Experiment Reality Theory Solution Validation

scientific/engineering tasks:

  • understand processes (model)
  • verify/validate hypotheses/models

(experiment)

  • design and optimize (model or

experiment)

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 9

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Where Simulation is Needed

Replacing Analytical Solvers:

Experiment Reality Theory Validation Simulation

  • analytical solution impossible or hard to

compute

  • use numerical approximation instead
  • application: validate a complex model
  • understand processes
  • validate assumptions

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 10

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Where Simulation is Needed (2)

Replacing Experiments:

Reality Theory Solution Validation Simulation

  • analytical theoretical solution available
  • replace experiments by simulation of a

more detailed model

  • application: develop a simple model
  • neglecting non-relevant effects
  • with reduced dimensionality
  • reduced-order models

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 11

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Where Simulation is Needed (3)

Replacing Analytical Solvers and Experiments:

Reality Simulation Prediction

  • detailed and accurate mathematical

model given

  • use simulation only
  • requires real world scenario description
  • application: predict reality
  • (wheather/climate/earthquake/...)

forecasts

  • design and optimization
  • uncertainty quantification

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 12

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Where Experiments are Impossible

Astrophysics:

  • “life cycle” of stars, galaxies, . . .
  • motion of planets, asteroids, comets, . . .

Geophysics:

  • displacement of the earth’s magnetic field
  • continental drift

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 13

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Where Experiments are Impossible

Meteorology:

  • weather forecasts
  • tornado prediction

Climate Research:

  • greenhouse effect
  • ocean currents (gulf stream, etc.)

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 14

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When There is No Second Try

Stability of Buildings:

  • large span bridges or skyscrapers
  • consider wind loads, earthquakes, . . .

Astronautics

  • flight path of space crafts or satellites
  • re-entry of space crafts

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 15

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Where Experiments have Harmful Side-effects

Propagation of Pollutants:

  • pollutants in air, water, or soil
  • predict long-term behaviour

Nuclear Research:

  • security of nuclear power plants
  • nuclear weapons

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 16

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Where Experiments are Expensive

Car Industry:

  • aerodynamics
  • crash tests
  • assembly of parts
  • build prototypes or rather simulate?

also combustion processes, vehicle dynamics, . . .

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 17

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Part II Components of Scientific Computing

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 18

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The Simulation Pipeline

phenomenon, process etc. mathematical model ❄ modelling numerical algorithm ❄ numerical treatment simulation code ❄ implementation results to interpret ❄ visualization ✟ ✟ ✟ ✟ ✙ ❍❍❍ ❍ ❥ embedding statement tool ✲ ✲ ✲ v a l i d a t i

  • n

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 19

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Disciplines Involved

  • Mathematics

(modelling, numerics)

  • Computer Science

(implementation, visualization)

  • Engineering & Natural Sciences

(expertise in application area, modelling, validation)

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 20

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Mathematical Modelling

  • classification, types of models
  • differential equations
  • population models
  • heat equations

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 21

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Numerical Treatment

  • discretization
  • grid generation, time stepping
  • numerical integration of ODE/PDE
  • continuous vs. discretized model

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 22

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Implementation

  • data structures and algorithms
  • platform-aware programming
  • parallel programming
  • embedding

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 23

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Visualization

  • visualization techniques
  • computational steering
  • images first?

Miriam Mehl based on Slides by Michael Bader (Winter 09/10): Scientific Computing I Module 1: Introduction, Winter 2011/2012 24