Dr. Kersten Schmidt - TU Berlin · 2014. 10. 14. · earth-quake) sueddeutsche.de, VL Scienti c...

Lecture on

Scientific Computing

Dr. Kersten Schmidt

Lecture 1

http://www.tu-berlin.de/?scientific-computing

Technische Universitat BerlinInstitut fur Mathematik

Wintersemester 2014/2015

What is Scientific Computing ?

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VL Scientific Computing WS 2014/2015, Dr. K. Schmidt, 10/14/2014 2


Description and Prediction of nature: for curiosity, to enable technical progress

Experiments = empirical method (measurements, observations)

I to discover some effect in nature, e.g. Rontgen obtained the First Nobel prize in

Physics in 1901 for discovering X-rays in 1895

I to test/verify existing theories or hypotheses e.g. Eddington found in 1919 during a

solar eclipse (dt. Sonnenfinsternis) a shift of the apparent star positions close to the sun

which was an affirmation of Einstein’s relativity theory

I the effect shall be dominant in the way that other (known) effects can notexplain the measurements

Theory = Gedankenexperiment

I to explain observations of nature, e.g. Planck obtained the Nobel prize in Physics

from 1918 for the theory of the quantization which explains experimental results, which

are not explained by classical physics

I to predict by the supposed (theoretical) structure further effects, e.g. Einstein did

not obtained the Nobel prize in Physics for the relativity theory, but for his theory of the

photoelectric effect

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Description and Prediction of nature: for curiosity, to enable technical progress

Numerical simulation = computational experiment, models are given as equations,which one can use for computations

I to reconstruct known effects and verify and understand models in comparisonwith experiments, e.g. solving Schrodinger equation in quantum physics or Maxwell’s

equations in electromagnetics

I to find models better explaining experimental observations, e.g. turbulence models

or wall laws in fluid dynamics

I to predict future and unobserved situations, e.g. weather forecast, prediction of

properties of new materials/technical constructions

Model fitting and data analysis = inverse problems

I to tune models (guess the parameters) to accurately reflect observations e.g.

guess structure of soil to match with seismologic experiments, non-destructive testing

Computational optimization

I propose constructions/materials with optimal properties

B Scientific computing connects theoretical and experimental sciences, but can beseen as a third main pillar (Standbein) to discover nature and for technical progress.

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Examples

Statics and Dynamics of elastic bodiesI Building, Towers, Bridges, Tunnels, Dams (dt. Staudamme), Foundation (dt.

Fundament)I Where are weak points ?I How much load is possible ?I How behaves the construction due to dynamic loads (e.g. wind, moving persons,

earth-quake)

kaeuferportal.de,


Examples



earth-quake)

Tone V. V. Rosbach Jensen

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Examples



earth-quake)

A. Volkwein, ETH Zurich,


Examples

Statics and Dynamics of elastic bodies

I Building, Towers, Bridges, Tunnels, Dams (dt. Staudamme), Foundation (dt.Fundament)

I Where are weak points ?I How much load is possible ?I How behaves the construction due to dynamic loads (e.g. wind, moving persons,

earth-quake)

Oil Spill Solutions

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Examples

Statics and Dynamics of elastic bodies

I Building, Towers, Bridges, Tunnels, Dams (dt. Staudamme), Foundation (dt.Fundament)

I Where are weak points ?

I How much load is possible ?

I How behaves the construction due to dynamic loads (e.g. wind, moving persons,earth-quake)

sueddeutsche.de

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Examples

Electric and magnetic properties of electromagnetic devices

I Power generator, Power transformer (dt. Transformator), electric motors

I Electric circuits

openelectrial.org CST

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Examples

Electric and magnetic properties of electromagnetic devicesI Power generator, Power transformer (dt. Transformator), electric motorsI Electric circuits

wikipedia.org

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Examples

Semiconductor devicesI integrated circuits in computer hardware: storage media (RAM, cache),

processorsI light emitting diodes (LED), semiconductor lasers, solar cellsI movements of free charge carriers

Nature,


Examples

Semiconductor devicesI integrated circuits in computer hardware: storage media (RAM, cache),

processorsI light emitting diodes (LED), semiconductor lasers, solar cellsI movements of free charge carriers

Uni Stuttgart,


Examples

Photonic devices

I Filters for light, switches, fibers

I Photonic crystal devices

Matheon

,


Examples

Photonic devices

I Filters for light, switches, fibers

I Photonic crystal devices

Tech-X UK

,


Examples

Electromagnetic wave propagationI Telecommunication devices (mobile phone, wifi, bluetooth), radarI how to construct antenna for sending and/or receiving ?

CST,


Examples

Electromagnetic wave propagationI Telecommunication devices (mobile phone, wifi, bluetooth), radarI how to construct antenna for sending and/or receiving ?

wikipedia.org

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Examples

Acoustics

I Computation of noise emission (dt. Larmabstrahlung) and attenuation (dt.Larmreduktion)

I Computation of sound emitted by music instruments

compositesworld.com

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Examples

Fluid dynamics

I Computation of lift (dt. dynamischer Auftrieb) and drag (dt.Stromungswiderstand) of airplanes, cars or

I Computation of forces to wind wheels (dt. Windrader)I Computation of flow due to combustion or steam flow in turbines

Bazilevs et. al. 2010

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Examples

Fluid dynamics

I Computation of lift (dt. dynamischer Auftrieb) and drag (dt.Stromungswiderstand) of airplanes, cars or

I Computation of forces to wind wheels (dt. Windrader)

I Computation of flow due to combustion or steam flow in turbines

Apotheken-Umschau

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Scientific computing

Continuous ModelI Domain in space, possibly infinite, or/and timeI govering (differential) equation for the unknown functionI linear or non-linear material functionsI boundary conditions or conditions at infinity (e.g. decay, outflow or radiation

condition)I initial conditions

B hierarchy of simplified models

Discrete ModelI ansatz of discrete approximation of the unknown function (e.g. piecewise linear

continuous)I may need to generate a mesh to represent the solutionI discrete version of the governing equations (e.g. variational method)I solution procedure, e.g. linear direct or iterative solver, non-linear iterative solver,

time-integration, possibly on many computers in parallelI possibly refinement of the discrete model to obtain a more accurate solutionI post-processing, e.g. graphical output

B outer loop for optimization, optimal control or inverse problems,


Syllabus

I Linear Regression, Fast Fourier transformI Modelling by partial differential equations (PDEs)

I Maxwell, Helmholtz, Poisson, Linear elasticity, Navier-Stokes equationI boundary value problem, eigenvalue problemI boundary conditions (Dirichlet, Neumann, Robin)I handling of infinite domains (wave-guide, homogeneous exterior: DtN, PML)I boundary integral equations

I Computer aided-design (CAD)

I Mesh generatorsI Space discretisation of PDEs

I Finite difference methodI Finite element methodI Discontinuous Galerkin finite element method

I SolversI Linear Solvers (direct, iterative), preconditionerI Nonlinear Solvers (Newton-Raphson iteration)I Eigenvalue Solvers

I ParallelisationI SIMP: OpenMPI MIMP: MPI

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Dr. Kersten Schmidt - TU Berlin · 2014. 10. 14. · earth-quake) sueddeutsche.de, VL Scienti c...

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