Computational Electromagnetics in Antenna Analysis and Design
|
|
- Cathleen Gardner
- 5 years ago
- Views:
Transcription
1 Computatonal Electromagnetcs n Antenna Analyss and Desgn Introducton It s rare for real-lfe EM problems to fall neatly nto a class that can be solved by the analytcal methods presented n the precedng lectures. Classcal approaches may fal f: the materal s not lnear and cannot be lnearzed wthout serously affectng the result the soluton regon s complex (.e. the varous boundares do not concde wth any well descrbed coordnate system). the boundary condtons are tme-dependent the medum s nhomogeneous or ansotropc Whenever a problem wth such complexty arses numercal solutons must be employed. Fortunately there are a large number of very good commercal programs avalable for solvng antenna problems.
2 Computatonal Electromagnetcs computatonal electromagnetcs rgorous methods Hgh frequency IE DE VM TD FD TD FD feld based current based MoM FEM FDTD TLM GO/GTD PO/PTD
3
4
5 Comparson of Methods Doman Generalty Accuracy Memory N= number of elements MoM Frequency Homogeneous or dscretely homogeneous regons FDTD Tme (all frequences n one run) Very general. nhomogeneous dspersve ansotropc FEM Frequency Very general. nhomogeneous dspersve ansotropc Hgh Frequency Methods Frequency Only good for structures much larger than the wavelength Antenna Types Very ) All but harder for large reflector antennas Moderately All but harder for large reflector antennas Very log N) All but harder for large reflector antennas Only accurate for large Only good for large antennas (mostly used for reflectors)
6 Goal of all of these methods Approxmate these B D E = M H = t t D = ρ B = ρ Wth ths m J [ A ] [ x] = [ b]
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26 Fnte Dfference Tme Doman FDTD
27 Reason for nterest n FDTD In the tme doman Maxwell s equatons gve rse to PDEs nvolvng tme and spatal dervatves. Some good reasons for dealng wth PDE s are: Complex-value materals easly accommodated. Computer resources are adequate. PDE solutons are robust. Tme doman PDE methods usually have no matrces. Geometres to be solved can be more vared.
28 Some bg advantages Broadband response wth a sngle exctaton. 3D models easly. Memory requrement scales lnearly wth problem sze Frequency dependent materals accommodated. Most parameters can be generated e.g. Scattered felds antenna patters RCS S-parameters etc..
29 How does t wor? Based on the two Maxwell curl equatons n dervatve form. These are lnearzed by central fnte dfferencng. We only consder nearest neghbor nteractons because all the felds are advanced temporally n dscrete tme steps over spatal cells. e we sample n space & tme embeddng of an antenna n a FDTD space lattce (note that the whole volume s meshed!)
30 Dscretze Obects n Space usng Cartesan Grd D Dscretzaton 3D Dscretzaton z x D Dscretzaton Z z = 0 Ex () zt z = Z
31 Defne Locatons of Feld Components: FDTD Cell called Yee Cell Fnte-Dfference Space s dvded nto small cells One Cell: (dx)(dy)(dz) E and H components are dstrbuted n space around the Yee cell (note: feld components are not collocated) FDTD: Yee K. S.: Numercal soluton of ntal boundary value problems nvolvng Maxwell's equatons n sotropc meda. IEEE Transactons on Antennas Propagaton Vol. AP-4 pp
32 3D formulaton y x z x y x z y y x z z E H E H t z y H E E H t x z E E H H t y x ρ µ ρ µ ρ µ = = = y x z x y x z y y x z z H E H E t y z E H H E t z x H H E E t x y σ ε σ ε σ ε = = = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = z E E x E E H H y E E z E E H H n x n x n z n z r n x n x n z n z n y n y r n x n x 0 0 µ µ µ µ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = 0 0 E E z H H y H H t E E x E E y E E t H H n x n x n y n y n z n z r n x n x n y n y n x n x r n z n z σ ε ε µ µ Convert equatons le these To ones le these
33 QucWave ( Commercal FDTD pacage wth CAD nterface Uses conformal FDTD mesh Many specal features for antenna problems Wrtten and supported by QWED Poland Runs under 3/x64 bt Wndows platforms and Lnux
34 QucWave ( Examples:
35 QucWave ( Examples:
36 XFdtd ( /) Commercal FDTD pacage wth CAD nterface Probably the most popular FDTD pacage for antenna problems Many specal features for antenna problems ncludng full human body mesh Wrtten and supported by Remcom USA Runs under 3/x64 bt Wndows Mac OS X and Lnux
37 XFdtd ( /)
38 Lumercal ( /) Commercal FDTD pacage wth CAD nterface Popular FDTD pacage for the optcs fols (.e. ntegrated optcs lght scatterng plasmoncs) Large lbrary of materals at optcal wavelengths Has very nce scrptng language for defnng large complcated problems. Has nce bult n optmzaton Runs under 3/x64 bt Wndows Mac OS X and Lnux
39 Lumercal ( /)
40 Fnte Element Method
41 Fnte Element Method
42 Varatonal Approach In solvng problems arsng n physcs and engneerng t s often possble to replace the problem of ntegratng a dfferental equaton by the equvalent problem of seeng a functon that gves a mnmum value of some ntegral. Problems of ths type are called varatonal problems. The methods that allow us to reduce the problem of ntegratng a dfferental equaton to the equvalent varatonal problem are usually called varatonal methods.
43 Varatonal Approach Name of equatons PDE Varatonal prncple Homogeneous wave equaton wth sources Homogeneous wave equaton wthout sources Dffuson equaton Posson s equaton Homogenous Laplace s equaton Φ Φ = Φ Φ Φ = Φ t Φ = Φ = g 0 = g 0 0 [ I( Φ) = Φ Φ gφ]dv v I( Φ) = v [ Φ Φ ]dv Φ I( Φ) = Φ Φ dvdt t t v [ I( Φ) = Φ gφ]dv v I( Φ) = v [ Φ ]dv
44 Fnte Element Method The fnte element method (FEM) has ts orgn n the feld of structural analyss. However snce then the method has been employed n nearly all areas of computatonal physcs and engneerng. The FEM method whle more dffcult to program than ether the fnte dfference (FD) or method of moments (MOM) s a more powerful and versatle numercal technque for handlng problems nvolvng complex geometres and nhomogeneous meda.
45 Basc concept Although the behavour may be complex when vewed over a large regon a smple approxmaton may suffce over a small subregon. The regon s dvded up nto fnte elements. (usually trangles or squares but can be more complcated) Regardless of the shape the feld s approxmated by a dfferent expresson over each element mantanng contnuty at adonng elements.
46 Soluton Strategy: Varatonal Approach The equatons to be solved are usually stated not n terms of feld the varables but n terms of an ntegral-type functonal such as energy. The functonal s chosen such that the feld soluton maes the functonal statonary The total functonal s the sum of the ntegral over each element
47 Fnte Element Method The fnte element method (FEM) nvolves bascally four steps: () Dscretze the soluton regon nto a fnte number of subregons or elements () Derve the governng equatons for each element based on ether a varatonal approach or Galern s method (3) Assemble all the elements together n the soluton space. (4) Solve the resultng system of equatons
48 HFSS ( Commercal FEM pacage wth CAD nterface Uses adaptve meshng Probably the most popular commercal pacage for antenna applcatons. Wrtten and supported by Ansoft USA Runs under 3/x64 bt Wndows platforms Redhat Lnux Solars (Sun worstatons). Has ntegrated hybrd fnte element / boundary ntegral methods (MoM) Knd of expensve! Optonal optmzaton pacage (optmetrcs)
49 HFSS (
50 CST Mcrowave Studo ( Commercal FEM MoM and TLM pacage wth CAD nterface Mature and easy to use nterface Popular program for mcrowave crcut applcatons but also very useful for antennas. Wrtten and supported by CST Internatonal Runs under 3/x64 bt Wndows platforms and Redhat Lnux Knd of expensve! Has a specfc antenna desgn opton called Magus
51 CST Mcrowave Studo (
52 Comsol Multphyscs( Commercal FEM pacage wth CAD nterface Is best nown for ts ablty to solve multphyscs problems Becomng a very popular program. Lns ncely wth Matlab Easy to learn nterface Runs under 3/x64 bt Wndows platforms Moderately prces
53 Comsol Multphyscs(
54 References:. Clemson ste lsts all the free EM modelng tools Clemson ste lsts all the commercal EM modelng tools
Numerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationAppendix B. The Finite Difference Scheme
140 APPENDIXES Appendx B. The Fnte Dfference Scheme In ths appendx we present numercal technques whch are used to approxmate solutons of system 3.1 3.3. A comprehensve treatment of theoretcal and mplementaton
More informationFormal solvers of the RT equation
Formal solvers of the RT equaton Formal RT solvers Runge- Kutta (reference solver) Pskunov N.: 979, Master Thess Long characterstcs (Feautrer scheme) Cannon C.J.: 970, ApJ 6, 55 Short characterstcs (Hermtan
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationInterconnect Modeling
Interconnect Modelng Modelng of Interconnects Interconnect R, C and computaton Interconnect models umped RC model Dstrbuted crcut models Hgher-order waveform n dstrbuted RC trees Accuracy and fdelty Prepared
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationAnalytical Gradient Evaluation of Cost Functions in. General Field Solvers: A Novel Approach for. Optimization of Microwave Structures
IMS 2 Workshop Analytcal Gradent Evaluaton of Cost Functons n General Feld Solvers: A Novel Approach for Optmzaton of Mcrowave Structures P. Harscher, S. Amar* and R. Vahldeck and J. Bornemann* Swss Federal
More informationA constant recursive convolution technique for frequency dependent scalar wave equation based FDTD algorithm
J Comput Electron (213) 12:752 756 DOI 1.17/s1825-13-479-2 A constant recursve convoluton technque for frequency dependent scalar wave equaton bed FDTD algorthm M. Burak Özakın Serkan Aksoy Publshed onlne:
More informationHybrid FDTD/FETD Technique Using Parametric Quadratic Programming for Nonlinear Maxwell s Equations
Progress In Electromagnetcs Research M, Vol. 54, 113 123, 217 Hybrd FDTD/FETD Technque Usng Parametrc Quadratc Programmng for Nonlnear Maxwell s Equatons Hongxa L 1,BaoZhu 2 and Jefu Chen 3, * Abstract
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationCHAPTER 14 GENERAL PERTURBATION THEORY
CHAPTER 4 GENERAL PERTURBATION THEORY 4 Introducton A partcle n orbt around a pont mass or a sphercally symmetrc mass dstrbuton s movng n a gravtatonal potental of the form GM / r In ths potental t moves
More informationIntegrals and Invariants of Euler-Lagrange Equations
Lecture 16 Integrals and Invarants of Euler-Lagrange Equatons ME 256 at the Indan Insttute of Scence, Bengaluru Varatonal Methods and Structural Optmzaton G. K. Ananthasuresh Professor, Mechancal Engneerng,
More informationOne-sided finite-difference approximations suitable for use with Richardson extrapolation
Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,
More informationB. H. Jung Department of Information and Communication Engineering Hoseo University Asan, Chungnam , Korea
Progress In Electromagnetcs Research, PIER 79, 339 352, 2008 SOLVING TIME DOMAIN HELMHOLTZ WAVE EQUATION WITH MOD-FDM B. H. Jung Department of Informaton and Communcaton Engneerng Hoseo Unversty Asan,
More informationConsistency & Convergence
/9/007 CHE 374 Computatonal Methods n Engneerng Ordnary Dfferental Equatons Consstency, Convergence, Stablty, Stffness and Adaptve and Implct Methods ODE s n MATLAB, etc Consstency & Convergence Consstency
More information2 Finite difference basics
Numersche Methoden 1, WS 11/12 B.J.P. Kaus 2 Fnte dfference bascs Consder the one- The bascs of the fnte dfference method are best understood wth an example. dmensonal transent heat conducton equaton T
More informationA new integrated-rbf-based domain-embedding scheme for solving fluid-flow problems
Home Search Collectons Journals About Contact us My IOPscence A new ntegrated-rbf-based doman-embeddng scheme for solvng flud-flow problems Ths artcle has been downloaded from IOPscence. Please scroll
More informationwhere the sums are over the partcle labels. In general H = p2 2m + V s(r ) V j = V nt (jr, r j j) (5) where V s s the sngle-partcle potental and V nt
Physcs 543 Quantum Mechancs II Fall 998 Hartree-Fock and the Self-consstent Feld Varatonal Methods In the dscusson of statonary perturbaton theory, I mentoned brey the dea of varatonal approxmaton schemes.
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationApplication of B-Spline to Numerical Solution of a System of Singularly Perturbed Problems
Mathematca Aeterna, Vol. 1, 011, no. 06, 405 415 Applcaton of B-Splne to Numercal Soluton of a System of Sngularly Perturbed Problems Yogesh Gupta Department of Mathematcs Unted College of Engneerng &
More informationModeling acoustic transducer surface waves by Transmission Line Matrix method
Modelng acoustc transducer surface waves by Transmsson Lne Matrx method Andreas Wlde Fraunhofer Insttut für Integrerte Schaltungen, Außenstelle EAS Peter-Chrstan Eccardt Semens AG, CT MS, München Wllam
More informationResearch Article Green s Theorem for Sign Data
Internatonal Scholarly Research Network ISRN Appled Mathematcs Volume 2012, Artcle ID 539359, 10 pages do:10.5402/2012/539359 Research Artcle Green s Theorem for Sgn Data Lous M. Houston The Unversty of
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationLecture 21: Numerical methods for pricing American type derivatives
Lecture 21: Numercal methods for prcng Amercan type dervatves Xaoguang Wang STAT 598W Aprl 10th, 2014 (STAT 598W) Lecture 21 1 / 26 Outlne 1 Fnte Dfference Method Explct Method Penalty Method (STAT 598W)
More informationA PROCEDURE FOR SIMULATING THE NONLINEAR CONDUCTION HEAT TRANSFER IN A BODY WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY.
Proceedngs of the th Brazlan Congress of Thermal Scences and Engneerng -- ENCIT 006 Braz. Soc. of Mechancal Scences and Engneerng -- ABCM, Curtba, Brazl,- Dec. 5-8, 006 A PROCEDURE FOR SIMULATING THE NONLINEAR
More informationPART 8. Partial Differential Equations PDEs
he Islamc Unverst of Gaza Facult of Engneerng Cvl Engneerng Department Numercal Analss ECIV 3306 PAR 8 Partal Dfferental Equatons PDEs Chapter 9; Fnte Dfference: Ellptc Equatons Assocate Prof. Mazen Abualtaef
More informationNew Method for Solving Poisson Equation. on Irregular Domains
Appled Mathematcal Scences Vol. 6 01 no. 8 369 380 New Method for Solvng Posson Equaton on Irregular Domans J. Izadan and N. Karamooz Department of Mathematcs Facult of Scences Mashhad BranchIslamc Azad
More informationCME 302: NUMERICAL LINEAR ALGEBRA FALL 2005/06 LECTURE 13
CME 30: NUMERICAL LINEAR ALGEBRA FALL 005/06 LECTURE 13 GENE H GOLUB 1 Iteratve Methods Very large problems (naturally sparse, from applcatons): teratve methods Structured matrces (even sometmes dense,
More informationThe Finite Element Method: A Short Introduction
Te Fnte Element Metod: A Sort ntroducton Wat s FEM? Te Fnte Element Metod (FEM) ntroduced by engneers n late 50 s and 60 s s a numercal tecnque for solvng problems wc are descrbed by Ordnary Dfferental
More informationAdjoint Methods of Sensitivity Analysis for Lyapunov Equation. Boping Wang 1, Kun Yan 2. University of Technology, Dalian , P. R.
th World Congress on Structural and Multdscplnary Optmsaton 7 th - th, June 5, Sydney Australa Adjont Methods of Senstvty Analyss for Lyapunov Equaton Bopng Wang, Kun Yan Department of Mechancal and Aerospace
More informationNumerical Solutions of a Generalized Nth Order Boundary Value Problems Using Power Series Approximation Method
Appled Mathematcs, 6, 7, 5-4 Publshed Onlne Jul 6 n ScRes. http://www.scrp.org/journal/am http://.do.org/.436/am.6.77 umercal Solutons of a Generalzed th Order Boundar Value Problems Usng Power Seres Approxmaton
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationCIE4801 Transportation and spatial modelling Trip distribution
CIE4801 ransportaton and spatal modellng rp dstrbuton Rob van Nes, ransport & Plannng 17/4/13 Delft Unversty of echnology Challenge the future Content What s t about hree methods Wth specal attenton for
More informationIntegrals and Invariants of
Lecture 16 Integrals and Invarants of Euler Lagrange Equatons NPTEL Course Varatonal Methods and Structural Optmzaton G. K. Ananthasuresh Professor, Mechancal Engneerng, Indan Insttute of Scence, Banagalore
More informationLecture 7: Boltzmann distribution & Thermodynamics of mixing
Prof. Tbbtt Lecture 7 etworks & Gels Lecture 7: Boltzmann dstrbuton & Thermodynamcs of mxng 1 Suggested readng Prof. Mark W. Tbbtt ETH Zürch 13 März 018 Molecular Drvng Forces Dll and Bromberg: Chapters
More informationMarkov Chain Monte Carlo (MCMC), Gibbs Sampling, Metropolis Algorithms, and Simulated Annealing Bioinformatics Course Supplement
Markov Chan Monte Carlo MCMC, Gbbs Samplng, Metropols Algorthms, and Smulated Annealng 2001 Bonformatcs Course Supplement SNU Bontellgence Lab http://bsnuackr/ Outlne! Markov Chan Monte Carlo MCMC! Metropols-Hastngs
More informationProfessor Terje Haukaas University of British Columbia, Vancouver The Q4 Element
Professor Terje Haukaas Unversty of Brtsh Columba, ancouver www.nrsk.ubc.ca The Q Element Ths document consders fnte elements that carry load only n ther plane. These elements are sometmes referred to
More informationThree-dimensional eddy current analysis by the boundary element method using vector potential
Physcs Electrcty & Magnetsm felds Okayama Unversty Year 1990 Three-dmensonal eddy current analyss by the boundary element method usng vector potental H. Tsubo M. Tanaka Okayama Unversty Okayama Unversty
More informationField computation with finite element method applied for diagnosis eccentricity fault in induction machine
Proceedngs of the Internatonal Conference on Recent Advances n Electrcal Systems, Tunsa, 216 Feld computaton wth fnte element method appled for dagnoss eccentrcty fault n nducton machne Moufd Mohammed,
More informationAPPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS
6th ICPT, Sapporo, Japan, July 008 APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS James MAINA Prncpal Researcher, Transport and Infrastructure Engneerng, CSIR Bult Envronment
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More information4DVAR, according to the name, is a four-dimensional variational method.
4D-Varatonal Data Assmlaton (4D-Var) 4DVAR, accordng to the name, s a four-dmensonal varatonal method. 4D-Var s actually a drect generalzaton of 3D-Var to handle observatons that are dstrbuted n tme. The
More information2.29 Numerical Fluid Mechanics Fall 2011 Lecture 12
REVIEW Lecture 11: 2.29 Numercal Flud Mechancs Fall 2011 Lecture 12 End of (Lnear) Algebrac Systems Gradent Methods Krylov Subspace Methods Precondtonng of Ax=b FINITE DIFFERENCES Classfcaton of Partal
More informationOptimal Control of Temperature in Fluid Flow
Kawahara Lab. 5 March. 27 Optmal Control of Temperature n Flud Flow Dasuke YAMAZAKI Department of Cvl Engneerng, Chuo Unversty Kasuga -3-27, Bunkyou-ku, Tokyo 2-855, Japan E-mal : d33422@educ.kc.chuo-u.ac.jp
More informationCOMPUTATIONAL METHODS AND ALGORITHMS Vol. II - Finite Element Method - Jacques-Hervé SAIAC
COMPUTATIONAL METHODS AND ALGORITHMS Vol. II - Fnte Element Method - Jacques-Hervé SAIAC FINITE ELEMENT METHOD Jacques-Hervé SAIAC Départment de Mathématques, Conservatore Natonal des Arts et Méters, Pars,
More informationON MECHANICS WITH VARIABLE NONCOMMUTATIVITY
ON MECHANICS WITH VARIABLE NONCOMMUTATIVITY CIPRIAN ACATRINEI Natonal Insttute of Nuclear Physcs and Engneerng P.O. Box MG-6, 07725-Bucharest, Romana E-mal: acatrne@theory.npne.ro. Receved March 6, 2008
More informationPolynomial Regression Models
LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance
More informationInternational Journal of Pure and Applied Sciences and Technology
Int. J. Pure Appl. Sc. Technol., 4() (03), pp. 5-30 Internatonal Journal of Pure and Appled Scences and Technology ISSN 9-607 Avalable onlne at www.jopaasat.n Research Paper Schrödnger State Space Matrx
More informationHomework 4. 1 Electromagnetic surface waves (55 pts.) Nano Optics, Fall Semester 2015 Photonics Laboratory, ETH Zürich
Homework 4 Contact: frmmerm@ethz.ch Due date: December 04, 015 Nano Optcs, Fall Semester 015 Photoncs Laboratory, ETH Zürch www.photoncs.ethz.ch The goal of ths problem set s to understand how surface
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationChapter 3 Differentiation and Integration
MEE07 Computer Modelng Technques n Engneerng Chapter Derentaton and Integraton Reerence: An Introducton to Numercal Computatons, nd edton, S. yakowtz and F. zdarovsky, Mawell/Macmllan, 990. Derentaton
More informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
More informationTensor Smooth Length for SPH Modelling of High Speed Impact
Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru
More informationTHE STURM-LIOUVILLE EIGENVALUE PROBLEM - A NUMERICAL SOLUTION USING THE CONTROL VOLUME METHOD
Journal of Appled Mathematcs and Computatonal Mechancs 06, 5(), 7-36 www.amcm.pcz.pl p-iss 99-9965 DOI: 0.75/jamcm.06..4 e-iss 353-0588 THE STURM-LIOUVILLE EIGEVALUE PROBLEM - A UMERICAL SOLUTIO USIG THE
More informationMonte Carlo Integration Technique for Method of Moments Solution of EFIE in Scattering Problems
J. Electromagnetc Analyss & Applcatons, 2009, 1: 254-258 do:10.4236/jemaa.2009.14039 Publshed Onlne December 2009 (http://www.scrp.org/journal/jemaa) Monte Carlo Integraton Technque for Method of Moments
More informationImposition of the essential boundary conditions in transient heat conduction problem based on Isogeometric analysis
Imposton of the essental boundary condtons n transent heat conducton problem based on Isogeometrc analyss S. Shojaee, E. Izadpanah, S. Nazar Department of Cvl Engneerng, Shahd Bahonar Unversty, Kerman,
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationFrequency dependence of the permittivity
Frequency dependence of the permttvty February 7, 016 In materals, the delectrc constant and permeablty are actually frequency dependent. Ths does not affect our results for sngle frequency modes, but
More informationVQ widely used in coding speech, image, and video
at Scalar quantzers are specal cases of vector quantzers (VQ): they are constraned to look at one sample at a tme (memoryless) VQ does not have such constrant better RD perfomance expected Source codng
More information18.1 Introduction and Recap
CS787: Advanced Algorthms Scrbe: Pryananda Shenoy and Shjn Kong Lecturer: Shuch Chawla Topc: Streamng Algorthmscontnued) Date: 0/26/2007 We contnue talng about streamng algorthms n ths lecture, ncludng
More informationGeneralized Linear Methods
Generalzed Lnear Methods 1 Introducton In the Ensemble Methods the general dea s that usng a combnaton of several weak learner one could make a better learner. More formally, assume that we have a set
More informationAging model for a 40 V Nch MOS, based on an innovative approach F. Alagi, R. Stella, E. Viganò
Agng model for a 4 V Nch MOS, based on an nnovatve approach F. Alag, R. Stella, E. Vganò ST Mcroelectroncs Cornaredo (Mlan) - Italy Agng modelng WHAT IS AGING MODELING: Agng modelng s a tool to smulate
More informationMAE140 - Linear Circuits - Winter 16 Final, March 16, 2016
ME140 - Lnear rcuts - Wnter 16 Fnal, March 16, 2016 Instructons () The exam s open book. You may use your class notes and textbook. You may use a hand calculator wth no communcaton capabltes. () You have
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationWaveguides and resonant cavities
Wavegudes and resonant cavtes February 8, 014 Essentally, a wavegude s a conductng tube of unform cross-secton and a cavty s a wavegude wth end caps. The dmensons of the gude or cavty are chosen to transmt,
More information2.29 Numerical Fluid Mechanics
REVIEW Lecture 10: Sprng 2015 Lecture 11 Classfcaton of Partal Dfferental Equatons PDEs) and eamples wth fnte dfference dscretzatons Parabolc PDEs Ellptc PDEs Hyperbolc PDEs Error Types and Dscretzaton
More informationNumerical Transient Heat Conduction Experiment
Numercal ransent Heat Conducton Experment OBJECIVE 1. o demonstrate the basc prncples of conducton heat transfer.. o show how the thermal conductvty of a sold can be measured. 3. o demonstrate the use
More informationA boundary element method with analytical integration for deformation of inhomogeneous elastic materials
Journal of Physcs: Conference Seres PAPER OPEN ACCESS A boundary element method wth analytcal ntegraton for deformaton of nhomogeneous elastc materals To cte ths artcle: Moh. Ivan Azs et al 2018 J. Phys.:
More informationGrid Generation around a Cylinder by Complex Potential Functions
Research Journal of Appled Scences, Engneerng and Technolog 4(): 53-535, 0 ISSN: 040-7467 Mawell Scentfc Organzaton, 0 Submtted: December 0, 0 Accepted: Januar, 0 Publshed: June 0, 0 Grd Generaton around
More informationDFT with Planewaves pseudopotential accuracy (LDA, PBE) Fast time to solution 1 step in minutes (not hours!!!) to be useful for MD
LLNL-PRES-673679 Ths work was performed under the auspces of the U.S. Department of Energy by under contract DE-AC52-07NA27344. Lawrence Lvermore Natonal Securty, LLC Sequoa, IBM BGQ, 1,572,864 cores O(N)
More informationThe Discretization Process
FMIA F Moukalled L Mangan M Darwsh An Advanced Introducton wth OpenFOAM and Matlab Ths textbook explores both the theoretcal foundaton of the Fnte Volume Method (FVM) and ts applcatons n Computatonal Flud
More informationSingle-Facility Scheduling over Long Time Horizons by Logic-based Benders Decomposition
Sngle-Faclty Schedulng over Long Tme Horzons by Logc-based Benders Decomposton Elvn Coban and J. N. Hooker Tepper School of Busness, Carnege Mellon Unversty ecoban@andrew.cmu.edu, john@hooker.tepper.cmu.edu
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationCIS526: Machine Learning Lecture 3 (Sept 16, 2003) Linear Regression. Preparation help: Xiaoying Huang. x 1 θ 1 output... θ M x M
CIS56: achne Learnng Lecture 3 (Sept 6, 003) Preparaton help: Xaoyng Huang Lnear Regresson Lnear regresson can be represented by a functonal form: f(; θ) = θ 0 0 +θ + + θ = θ = 0 ote: 0 s a dummy attrbute
More informationSTUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS
Blucher Mechancal Engneerng Proceedngs May 0, vol., num. www.proceedngs.blucher.com.br/evento/0wccm STUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS Takahko Kurahash,
More informationChapter 4 The Wave Equation
Chapter 4 The Wave Equaton Another classcal example of a hyperbolc PDE s a wave equaton. The wave equaton s a second-order lnear hyperbolc PDE that descrbes the propagaton of a varety of waves, such as
More information9 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations
Physcs 171/271 - Chapter 9R -Davd Klenfeld - Fall 2005 9 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys a set
More informationThermal-Fluids I. Chapter 18 Transient heat conduction. Dr. Primal Fernando Ph: (850)
hermal-fluds I Chapter 18 ransent heat conducton Dr. Prmal Fernando prmal@eng.fsu.edu Ph: (850) 410-6323 1 ransent heat conducton In general, he temperature of a body vares wth tme as well as poston. In
More informationModule 1 : The equation of continuity. Lecture 1: Equation of Continuity
1 Module 1 : The equaton of contnuty Lecture 1: Equaton of Contnuty 2 Advanced Heat and Mass Transfer: Modules 1. THE EQUATION OF CONTINUITY : Lectures 1-6 () () () (v) (v) Overall Mass Balance Momentum
More informationNumerical Solution of Ordinary Differential Equations
Numercal Methods (CENG 00) CHAPTER-VI Numercal Soluton of Ordnar Dfferental Equatons 6 Introducton Dfferental equatons are equatons composed of an unknown functon and ts dervatves The followng are examples
More informationSolution for singularly perturbed problems via cubic spline in tension
ISSN 76-769 England UK Journal of Informaton and Computng Scence Vol. No. 06 pp.6-69 Soluton for sngularly perturbed problems va cubc splne n tenson K. Aruna A. S. V. Rav Kant Flud Dynamcs Dvson Scool
More informationNUMERICAL MODELING OF ACTIVE DEVICES CHARACTERIZED BY MEASURED S-PARAMETERS IN FDTD
Progress In Electromagnetcs Research, PIER 80, 381 392, 2008 NUMERICAL MODELING OF ACTIVE DEVICES CHARACTERIZED BY MEASURED S-PARAMETERS IN FDTD D. Y. Su, D. M. Fu, and Z. H. Chen Natonal Key Lab of Antennas
More informationModule 3: Element Properties Lecture 1: Natural Coordinates
Module 3: Element Propertes Lecture : Natural Coordnates Natural coordnate system s bascally a local coordnate system whch allows the specfcaton of a pont wthn the element by a set of dmensonless numbers
More informationConstitutive Modelling of Superplastic AA-5083
TECHNISCHE MECHANIK, 3, -5, (01, 1-6 submtted: September 19, 011 Consttutve Modellng of Superplastc AA-5083 G. Gulano In ths study a fast procedure for determnng the constants of superplastc 5083 Al alloy
More informationFeb 14: Spatial analysis of data fields
Feb 4: Spatal analyss of data felds Mappng rregularly sampled data onto a regular grd Many analyss technques for geophyscal data requre the data be located at regular ntervals n space and/or tme. hs s
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationRelaxation Methods for Iterative Solution to Linear Systems of Equations
Relaxaton Methods for Iteratve Soluton to Lnear Systems of Equatons Gerald Recktenwald Portland State Unversty Mechancal Engneerng Department gerry@pdx.edu Overvew Techncal topcs Basc Concepts Statonary
More informationNote: Please use the actual date you accessed this material in your citation.
MIT OpenCourseWare http://ocw.mt.edu 6.13/ESD.13J Electromagnetcs and Applcatons, Fall 5 Please use the followng ctaton format: Markus Zahn, Erch Ippen, and Davd Staeln, 6.13/ESD.13J Electromagnetcs and
More informationWorkshop: Approximating energies and wave functions Quantum aspects of physical chemistry
Workshop: Approxmatng energes and wave functons Quantum aspects of physcal chemstry http://quantum.bu.edu/pltl/6/6.pdf Last updated Thursday, November 7, 25 7:9:5-5: Copyrght 25 Dan Dll (dan@bu.edu) Department
More informationAdvanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017)
Advanced rcuts Topcs - Part by Dr. olton (Fall 07) Part : Some thngs you should already know from Physcs 0 and 45 These are all thngs that you should have learned n Physcs 0 and/or 45. Ths secton s organzed
More informationChapter 12. Ordinary Differential Equation Boundary Value (BV) Problems
Chapter. Ordnar Dfferental Equaton Boundar Value (BV) Problems In ths chapter we wll learn how to solve ODE boundar value problem. BV ODE s usuall gven wth x beng the ndependent space varable. p( x) q(
More informationSuppose that there s a measured wndow of data fff k () ; :::; ff k g of a sze w, measured dscretely wth varable dscretzaton step. It s convenent to pl
RECURSIVE SPLINE INTERPOLATION METHOD FOR REAL TIME ENGINE CONTROL APPLICATIONS A. Stotsky Volvo Car Corporaton Engne Desgn and Development Dept. 97542, HA1N, SE- 405 31 Gothenburg Sweden. Emal: astotsky@volvocars.com
More informationStatistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA
14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton
More information16 Reflection and transmission, TE mode
16 Reflecton transmsson TE mode Last lecture we learned how to represent plane-tem waves propagatng n a drecton ˆ n terms of feld phasors such that η = Ẽ = E o e j r H = ˆ Ẽ η µ ɛ = ˆ = ω µɛ E o =0. Such
More information