Numerical analysis MATH 4329 - Pownuk...enough. More careful finite element analysis, made after the accident, predicted that failure would occur with this design at a depth of 62m,

Andrew Pownuk - http://www.pownuk.com- Math 4329 (Numerical Analysis)

1

Numerical analysis MATH 4329 Andrew Pownuk

The University of Texas at El Paso


2

1 Web page with notes

http://www.pownuk.com/group/2017-Summer-Math-4329-CRN-31543/notes/

2 Technical remarks

Equation editor:

Math Type http://www.dessci.com/en/products/mathtype/

3 Additional resources

Matlab code for the book

http://homepage.math.uiowa.edu/~atkinson/ena_master.html

http://www.pownuk.com/group/2017-Summer-Math-4329-CRN-31543/notes/

http://www.dessci.com/en/products/mathtype/

http://homepage.math.uiowa.edu/~atkinson/ena_master.html


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4 Motivation

Nonelementary integral

http://en.wikipedia.org/wiki/Nonelementary_integral

2

2 ?x

e dx

Liouville's theorem (differential algebra)

https://en.wikipedia.org/wiki/Liouville%27s_theorem_(differential_algebra)

Plot[{Exp[-x^2/2],0},{x,0,1}]

NIntegrate[Exp[-x^2/2],{x,0,1}]

0.855624

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

http://en.wikipedia.org/wiki/Nonelementary_integral

https://en.wikipedia.org/wiki/Liouville%27s_theorem_(differential_algebra)


4

2

2

2

2 2

1

2

0

2

0

2

2 2

0

( )

'( )

x

x t

x

xx t

e dx

F x e dt

F x e

e dx e dt C

F[x_]=NIntegrate[Exp[-t^2/2],{t,0,x}];

Plot[F[x],{x,0,1}]

Integrate[Exp[-x^2/2],x]

Erf[x/ ]

https://en.wikipedia.org/wiki/Error_function

Integrate[Sin[x]/x,x]

SinIntegral[x]

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

2 2

https://en.wikipedia.org/wiki/Error_function


5

0

sin sinxx tdx dt C

x t

2 2 2 2

0 0

0

2 2 2 2

xx t x xxdx tdt C C C C


6

5 Numerical library

GSL numerical library

http://www.gnu.org/software/gsl/manual/html_node/Linear-Algebra.html

NAG numerical library

http://www.nag.co.uk/numeric/CL/nagdoc_cl09/html/FRONTMATTER/manconts.html

Matlab

Octave

Maxima

Mathematica

Maple

http://www.gnu.org/software/gsl/manual/html_node/Linear-Algebra.html

http://www.nag.co.uk/numeric/CL/nagdoc_cl09/html/FRONTMATTER/manconts.html


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6 Applications of numerical analysis

6.1 FEM simulations

Example

http://www.youtube.com/watch?v=geUCvKayhHE

Commercial Programs related to the applications of numerical analysis

[source: http://homepage.usask.ca/~ijm451/finite/fe_resources/]:

▪ Adina R&D, Inc.

▪ Algor (Professional)

▪ Alstom (SLIM)

▪ Altair

▪ AMPS

▪ Amtec (Mesh Generator)

▪ Anker-Zemer (LINFLOW)

▪ Ansoft Corporation (HFSS)

▪ ANSYS

▪ ATIR (STRAP)

▪ Argus Interware, Inc. (Argus ONE)

▪ AutoFEA Software Co. (JL Analyzer)

▪ Automated Analysis Corporation (COMET)

▪ CAE PowerTools

▪ CADFEM

▪ CAST3M

▪ CEETRON (GLview)

▪ CIMNE (GiD)

▪ CivilFEM

▪ Cobus (FesaWin)

▪ Computational Mechanics Co. (ProPHLEX)

▪ Computational Mechanics Australia (Meshing)

▪ Computers and Structures Inc.

▪ COMSOL (FEMLAB)

▪ COMSOL (PDE Toolbox)

▪ Computing Objects (CM2)

▪ Concurrent Analysis Corporation (CAEFEM)

▪ CrossX

▪ Cyberlogic (FEMdesigner)

▪ DIANA

▪ D.I.E Software

▪ Dr. Software

▪ EDS (FEMAP)

▪ EDS PLM Solutions (I-DEAS Simulation)

http://homepage.usask.ca/~ijm451/finite/fe_resources/node394.html



































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▪ Electric Power Research Institute (Merlin, Spider)

▪ Engineering Mechanics Research Corporation

▪ ESI Group (PAM-SYSTEM)

▪ Fastflo

▪ ESRD (StressCheck)

▪ FEA Ltd. (LUSAS)

▪ FEMCOS (COSAR)

▪ Femsys (FEMGV)

▪ Field Precision (TriComp/AMaze/GamBet)

▪ FinitES-Plast

▪ Flexcom-3D (MCS)

▪ FLUENT (FLUENT/FIDAP)

▪ ForDyn animation

▪ FrameMaster

▪ GEO-SLOPE

▪ Hibbitt, Karlsson and Sorensen (ABAQUS)

▪ HOMARD

▪ ICEM CFD Engineering

▪ Integrated Design and Analysis Consultants (IDAC)

▪ Inter-CAD Ltd (AxisVM)

▪ Intuition Software (VisualFEA)

▪ INFOLYTICA

▪ Intelligent Light (FieldView)

▪ Intes (PERMAS)

▪ Laboratoire Central des Ponts et Chaussees (CESAR)

▪ Lawrence Livermore National Laboratory (DYNA3D/NIKE3D)

▪ LEAP (ANSYS)

▪ LIRA Finite Element Analysis Software

▪ LISA

▪ Livermore Software Technology Corp. (LS-DYNA3D)

▪ MacNeal-Schwendler Corporation (MSC/NASTRAN,

MSC/PATRAN)

▪ MACRO Industries (MI/NASTRAN)

▪ Macsyma (PDEase)

▪ Magsoft (ATILA, Flux2D)

▪ Makros-A

▪ Maple

▪ MARC

▪ Mathematica

▪ Mathworks (MATLAB)

▪ Mathworks (Simulink)

▪ MIDAS

▪ MSTR Technology (FEWaves)

▪ NM SESES (Centre for Computational Physics ZHW)

▪ Noran Engineering, Inc. (NEiNastran)

▪ Northwest Numerics and Modelling (Zebulon)
















































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▪ Numerical Objects (Diffpack)

▪ Open Engineering (Oofelie)

▪ PDE2D

▪ PDE Solutions Inc (FlexPDE)

▪ Parametric Technology Corporation (Pro/MECHANICA)

▪ PLAXIS

▪ Pointwise, Inc (Gridgen/FIELDVIEW)

▪ PVM Corp (FEVA)

▪ PVM Corp (SAGE)

▪ Radioss Consulting Corp.

▪ Research Engineers (STAAD)

▪ Robobat (Robot 97)

▪ Rockfield (ELFEN)

▪ Roensch & Associates

▪ SAGE CRISP

▪ SAMTECH (samcef)

▪ SDTools (Structural Dynamics Toolbox)

▪ SEPRA (SEPRAN)

▪ SIMULOG (TetMesh-GHS3D)

▪ Softing (Nolian)

▪ Softek Services Ltd. (P-FRAME, S-FRAME)

▪ Soilvision (SVFlux)

▪ SOLVIA

▪ SRT (FEA-Crack)

▪ Steer Engineering (AFEMS, FemForm, FemTool)

▪ Strand7

▪ Structural Analysis Inc (mTAB*STRESS)

▪ Structural Research & Analysis Corp (COSMOS/M)

▪ GT STRUDL

▪ Synaps (Epogy)

▪ T-Systems (MEDINA)

▪ Tera Analysis (QuickField)

▪ ThermoAnalytics (RadTherm)

▪ Thin-Walled Structures Software

▪ Third Wave Systems (AdvantEdge)

▪ TrueGrid

▪ Utah State University (VABS)

▪ Vector Fields (TOSCA, OPERA)

▪ VectorSpace Programming (vs.lib)

▪ Visual Kinematics Inc. (DevTools)

▪ Visual Numerics (PV-WAVE)

▪ VMA Engineering (GENESIS)

▪ Weidlinger Associates Inc.

▪ ZACE Services Ltd.

▪ Zentech International (Zencrack)















































10

Problems with numerical analysis

11

0 001

1 10

1lim ln ln1 lim ln 0

1 1

aa a

n

i

n

i i i

dx x ax

dx f x xx

n=500;

dx=1/n;

N[Sum[dx*(1/(i*dx)),{i,1,n}]]

6.79282

The sinking of the Sleipner A offshore platform (August 23, 1991). The failure involved a total economic

loss of about $700 million.

The post accident investigation traced the error to inaccurate finite element approximation of the linear

elastic model of the tricell (using the popular finite element program NASTRAN). The shear stresses were

underestimated by 47%, leading to insufficient design. In particular, certain concrete walls were not thick

enough. More careful finite element analysis, made after the accident, predicted that failure would occur

with this design at a depth of 62m, which matches well with the actual occurrence at 65m.

References

The Sleipner Platform Accident, by B. Jakobsen and F. Rosendahl, Structural Engineering International

4(3), August 1994, pp. 190-193.

The Failure of an Offshore Platform, by R. G. Selby, F. J. Vecchio, and M. P. Collins, Concrete International

19(8), August 1997, pp. 28-35.


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7 References 1) Kendall Atkinson, Weimin Han, Elementary Numerical Analysis, 3rd Edition

2) William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery

Numerical Recipes, http://www.nr.com/oldverswitcher.html

http://www.nr.com/oldverswitcher.html

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471433373.html


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8 Journals

8.1 Advances in Computational Mathematics

http://www.springer.com/mathematics/computational+science+%26+engineering/journal/10444

8.2 Advanced Modeling and Simulation in Engineering Sciences

http://www.springer.com/materials/mechanics/journal/40323

8.3 Applied Numerical Mathematics

http://www.journals.elsevier.com/applied-numerical-mathematics



http://www.journals.elsevier.com/applied-numerical-mathematics/

http://www.sciencedirect.com/science/journal/01689274


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8.4 BIT Numerical Mathematics


8.5 Computational Astrophysics and Cosmology

http://www.springer.com/astronomy/journal/40668

8.6 Computational Economics

http://www.springer.com/economics/economic+theory/journal/10614


http://www.springer.com/astronomy/journal/40668

http://www.springer.com/economics/economic+theory/journal/10614


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8.7 Computational Geosciences

http://www.springer.com/earth+sciences+and+geography/journal/10596

8.8 Computational Mathematics and Mathematical Physics http://www.springer.com/mathematics/computational+science+%26+engineering/journal/11470

8.9 Computational Mathematics and Modeling

http://www.springer.com/mathematics/journal/10598

8.10 Computational Mechanics http://link.springer.com/journal/466

http://www.springer.com/earth+sciences+and+geography/journal/10596



http://link.springer.com/journal/466

http://www.springer.com/mathematics/computational+science+&+engineering/journal/11470


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8.11 Computing

http://www.springer.com/computer/journal/607

8.12 Communications in Nonlinear Science and Numerical Simulation http://www.journals.elsevier.com/communications-in-nonlinear-science-and-numerical-simulation

8.13 Computers & Structures

http://www.journals.elsevier.com/computers-and-structures/

http://www.springer.com/computer/journal/607

http://www.journals.elsevier.com/communications-in-nonlinear-science-and-numerical-simulation/

http://www.journals.elsevier.com/computers-and-structures/

http://link.springer.com/article/10.1007/s00466-014-0980-x/lookinside/000.png



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8.14 Computer Methods in Applied Mechanics and Engineering

http://www.journals.elsevier.com/computer-methods-in-applied-mechanics-and-engineering/

8.15 Engineering Analysis with Boundary Elements http://www.journals.elsevier.com/engineering-analysis-with-boundary-elements/

8.16 Finite Elements in Analysis and Design

http://www.journals.elsevier.com/finite-elements-in-analysis-and-design/

http://www.journals.elsevier.com/computer-methods-in-applied-mechanics-and-engineering/

http://www.journals.elsevier.com/engineering-analysis-with-boundary-elements/

http://www.journals.elsevier.com/finite-elements-in-analysis-and-design/





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8.17 Foundations of Computational Mathematics


8.18 International Journal for Numerical Methods in Biomedical Engineering http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2040-7947

8.19 International Journal for Numerical Methods in Engineering

http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207




http://www.sciencedirect.com/science/journal/0168874X


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8.20 International Journal for Numerical Methods in Fluids


8.21 International Journal of Computational Fluid Dynamics

http://www.tandfonline.com/toc/gcfd20/current#.U7ybFk1OWrc

8.22 International Journal of Numerical Methods for Heat & Fluid Flow

http://www.emeraldgrouppublishing.com/products/journals/journals.htm?id=HFF

Emerald Insight


http://www.tandfonline.com/toc/gcfd20/current#.U7ybFk1OWrc

http://www.emeraldgrouppublishing.com/products/journals/journals.htm?id=HFF


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8.23 International Journal of Numerical Modelling: Electronic Networks, Devices and

Fields


8.24 Journal of Applied Mathematics and Computing


8.25 Journal of Computational and Applied Mathematics http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/



http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/


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8.26 Journal of Computational Science

http://www.journals.elsevier.com/journal-of-computational-science

8.27 Mathematical Models and Computer Simulations


8.28 Mathematics and Computers in Simulation

http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/

http://www.journals.elsevier.com/journal-of-computational-science


http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/


http://www.sciencedirect.com/science/journal/sample/18777503


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8.29 Numerical Algorithms

http://www.springer.com/computer/theoretical+computer+science/journal/11075

8.30 Numerical Analysis and Applications


8.31 Numerical Heat Transfer, Part A: Applications An International Journal of Computation and Methodology

http://www.tandfonline.com/toc/unht20/current#.U7rmHk1OWrc

http://www.springer.com/computer/theoretical+computer+science/journal/11075


http://www.tandfonline.com/toc/unht20/current#.U7rmHk1OWrc



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Taylor & Francis

8.32 Numerical Heat Transfer, Part B: Fundamentals

An International Journal of Computation and Methodology

http://www.tandfonline.com/toc/unhb20/current#.U7rmQk1OWrc

Taylor & Francis

8.33 Numerical Linear Algebra with Applications


8.34 Numerical Methods for Partial Differential Equations


http://www.tandfonline.com/toc/unhb20/current#.U7rmQk1OWrc




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8.35 Numerische Mathematik


8.36 Progress in Computational Fluid Dynamics, An International Journal

http://www.inderscience.com/jhome.php?jcode=pcfd

8.37 SIAM Journal on Numerical Analysis (SINUM)

http://www.siam.org/journals/sinum.php


http://www.inderscience.com/jhome.php?jcode=pcfd

http://www.siam.org/journals/sinum.php


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8.38 SIAM Journal on Scientific Computing

http://www.siam.org/journals/sisc.php

8.39 Theoretical and Computational Fluid Dynamics


http://www.siam.org/journals/sisc.php


Documents

Numerical analysis MATH 4329 - Pownuk...enough. More careful finite element analysis, made after the accident, predicted that failure would occur with this design at a depth of 62m,