Lehrstuhl Informatik V

Scientific Computing IModule 1: Introduction

Tobias Neckel

Winter 2015/2016

Tobias Neckel: Scientific Computing I

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What is Computational Science and Engineering?

Computational Science and Engineering (CSE)• is the

• multi-disciplinary field• of computer-based modelling and simulation• for studying scientific phenomena and engineering designs.

• requires skills in• computer science• and applied mathematics,• but also in the respective fields of application.

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Scientific Computing =

Science + Computing?

Science on Computers??

“Computational Science”???

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A Short Look into Wikipedia . . .Computational science (or scientific computing) is the field ofstudy concerned with

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

to analyze and solve scientific, social scientific and engineeringproblems.

[. . .] it is typically the application of computer simulation and otherforms of computation from numerical analysis and theoreticalcomputer science to problems in various scientific disciplines.

[. . .]The scientific computing approach is to gain understanding,mainly through the analysis of mathematical models implemented oncomputers.

[. . .]massive amounts of calculations (usually floating-point) and areoften executed on supercomputers or distributed computingplatforms.

[Wikipedia, Oct 06, 2014]Tobias Neckel: Scientific Computing I

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Part I: An Interdisciplinary Discipline

Gaining Scientific KnowledgeThe classical scientific processApproaches to science

The Third Approach – SimulationDrawbacks of Theory and ExperimentWhere Simulation is NeededTwo Large Examples – Molecular Dynamics and Blood Flow

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Part II: Tasks of Scientific Computing

The Simulation PipelineStages of the Simulation PipelineDisciplines Involved

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Part I

An Interdisciplinary Discipline

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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?

4. experiment• verification/falsification• discrepancies might lead to improved model

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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 outcome3. simulation

• Why would we need that?

Experiments

Theory

Science

Experiments

Theory

Sim

ulation

Science

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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 (in time/money)

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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)

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Where Simulation is Needed

Replacing Analytical Solvers:

Experiment

Reality

Theory

Validation

Simulation

• analytical solution impossible or hard tocompute

• use numerical approximation instead• application: validate a complex model

• understand processes• validate assumptions

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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

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Where Simulation is Needed (3)

Replacing Analytical Solvers and Experiments:

Reality

Simulation

Prediction

• detailed and accurate mathematicalmodel given

• use simulation only• requires real world scenario description• application: predict reality

• (wheather/climate/earthquake/...)forecasts

• design and optimization• uncertainty quantification

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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

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Where Experiments are Impossible

Meteorology:

• weather forecasts• simulation of hurricanes

and storm surges

Climate and Ocean Modelling:

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

Image source: Cooperative Institute for Meteorological Satellite Studies,Space Science and Engineering Center, University of Wisconsin-Madison;http://tropic.ssec.wisc.edu/

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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

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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

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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, . . .

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Example – PRACE Award 2013

World-record simulation with 4.125 · 1012 molecules as performancestudy anticipating large-scale experiments to investigate nano-fluids:

• size dependence of inter-facial quantities such as surface tension• behavior of droplets, interactions between droplets, nucleation

Drop of acetone in its vaporphase, used as model for fuel

6.3 µm

Simulated a cube of liquid Kryp-ton of edge length l = 6.3µm

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Example – PRACE Award 2013 (2)

Simulation – HPC-Related Data:• N-body simulation with N = 4.125 · 1012 molecules• 100 TB RAM required only to store particles positions and

velocities (single precision), ≈ 200 TB memory in total• Simulation on SuperMUC (LRZ, Munich): 9126 nodes (each 2x

eight-core Intel SandyBridge, i.e. 146016 cores total)• leight-weight hybrid parallelisation: MPI plus OpenMP• Runtime: 40 s per iteration; terminated after 10 time steps• parallel efficiency: 86 % and 9.4 % peak performance

Further info:http://www.tum.de/en/about-tum/news/press-releases/short/article/30922/

http://www5.in.tum.de/pub/eckhardt2013-isc.pdf

Video!

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Example – Gordon Bell Prize 2010

(Rahimian, . . . , Biros, 2010)

• direct simulation of blood flow• particulate flow simulation (coupled problem)• Stokes flow for blood plasma• red blood cells as immersed, deformable particles

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Example – Gordon Bell Prize 2010 (2)

Simulation – HPC-Related Data:• up to 260 Mio blood cells, up to 9 · 1010 unknowns• fast multipole method to compute Stokes flow

(octree-based; octree-level 4–24)• scalability: 327 CPU-GPU nodes on Keeneland cluster,

200,000 AMD cores on Jaguar (ORNL)• 0.7 Petaflops/s sustained performance on Jaguar• extensive use of GEMM routine (matrix multiplication)• runtime: ≈ 1 minute per time step

Article for Supercomputing conference:http://www.cc.gatech.edu/~gbiros/papers/sc10.pdf

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Part II

Components of ScientificComputing

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The Simulation Pipeline

phenomenon, process etc.

mathematical model?

modelling

numerical algorithm? numerical treatment

simulation code?

implementation

results to interpret? visualization

�����HHHHj embedding

statement tool

-

-

-

validation

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The Simulation Pipeline IITechnische Universität München

H.-J. Bungartz: Introduction to the BGCE www.bgce.de BGCE 2014 Opening Weekend and Annual Meeting, Bernried, April 11–13, 2014

The Simulation Pipeline Basis of Computational Engineering

Mathematical model Discretization & solver

Parallel implementation, HPC

Exploration

Validation

Software

Insight, Design

1

image courtesy: H.-J. Bungartz

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Disciplines Involved

• Mathematics(modelling, numerics)

• Computer Science(implementation, visualization)

• Engineering & Natural Sciences(expertise in application area, modelling, validation)

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Steps in the Simulation Pipeline

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

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

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Steps in the Simulation Pipeline (2)

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

Visualization• visualization techniques• computational steering• images first?

=⇒ Verif. & Valid., UQ

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Part III

Organisation

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Relation: SciComp1↔ other CSE courses

ODEs, PDEs, ...

Scientific Computing I Numerical Analysis

Scientific Computing Lab

Matlab/tools → “hands on”

Advanced Programming

C++

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Roadmap of the Lecture

1. Introduction: Discipline2. Population Modelling – Discrete Models3. Population Modelling – Continuous Models4. Numerical Methods for ODEs5. Heat Transfer – Discrete and Continuous Models6. Analytical and Numerical Solutions of the 1D Heat Equation7. Introduction to Finite Element Methods8. Case Study – Computational Fluid Dynamics

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ECTS, Modules, TutorialsECTS, Modules

• 5 ECTS (2+2 lectures/tutorials per week)• CSE: compulsory course• Biomed. Computing/Computer Science: elective/Master

catalogue• others?

Tutorials:• 2 groups, with 2 tutors each; starting Oct 26• Mon, 14:15-16:00• Mon, 16:05-17:50• tutors: Juan Carlos Medina, Severin Reiz, Benjamin Ruth, Anna

Yurova (supervised by Denis Jarema)• use free slots

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Exam & TUMOnline

Exam:• written exam at end of semester• based on exercises presented in the tutorials

ToDo• TUMOnline: register for lecture• TUMOnline: register for tutorial (free places!)• TUMOnline: register for exam

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