Post on 24-Aug-2020
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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What is Scientific Computing ?
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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What is Scientific Computing ?
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,
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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)
Tone V. V. Rosbach Jensen
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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)
A. Volkwein, ETH Zurich,
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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)
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,
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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
Uni Stuttgart,
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Examples
Photonic devices
I Filters for light, switches, fibers
I Photonic crystal devices
Matheon
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Examples
Photonic devices
I Filters for light, switches, fibers
I Photonic crystal devices
Tech-X UK
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Examples
Electromagnetic wave propagationI Telecommunication devices (mobile phone, wifi, bluetooth), radarI how to construct antenna for sending and/or receiving ?
CST,
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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,
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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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