Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 1 Numerical Methods of Electromagnetic Field Theory I (NFT I) Numerische Methoden der Elektromagnetischen.

Präsentation zum Thema: "Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 1 Numerical Methods of Electromagnetic Field Theory I (NFT I) Numerische Methoden der Elektromagnetischen."—  Präsentation transkript:

1 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 1 Numerical Methods of Electromagnetic Field Theory I (NFT I) Numerische Methoden der Elektromagnetischen Feldtheorie I (NFT I) / 9th Lecture / 9. Vorlesung Universität Kassel Fachbereich Elektrotechnik / Informatik (FB 16) Fachgebiet Theoretische Elektrotechnik (FG TET) Wilhelmshöher Allee 71 Büro: Raum 2113 / 2115 D-34121 Kassel Dr.-Ing. René Marklein marklein@uni-kassel.de http://www.tet.e-technik.uni-kassel.de http://www.uni-kassel.de/fb16/tet/marklein/index.html University of Kassel Dept. Electrical Engineering / Computer Science (FB 16) Electromagnetic Field Theory (FG TET) Wilhelmshöher Allee 71 Office: Room 2113 / 2115 D-34121 Kassel

2 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 2 FDTD and FIT / FDTD und FIT FDTD : Finite Difference Time Domain / Finite Differenzen im Zeitbereich FIT : Finite Integration Technique / Finite Integrationstechnik FDTD Maxwells equations in differential form / Maxwellsche Gleichungen in Differentialform FIT Maxwells equations in integral form / Maxwellsche Gleichungen in Integralform FD approximation of spatial and temporal derivatives / FD-Approximation von räumlichen und zeitlichen Ableitungen FIT approximation of spatial and temporal integrals / FIT-Approximation von räumlichen und zeitlichen Integralen Central difference approximation / Zentrale Differenzen Approximation Mid point rule approximation of a 1-D integral / Mittelpunktsregel-Approximation eines 1D-Integrals

3 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 3 Definition of Material Cells / Definition der Materialzellen Material cell / Materialzelle

4 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 4 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle Field component in the middle / Feldkomponente in der Mitte Approximation error / Approximationsfehler

5 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 5 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

6 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 6 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen Field component in the middle / Feldkomponente in der Mitte Approximation error / Approximationsfehler

7 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 7 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

8 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 8 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

9 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 9 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

10 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 10 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

11 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 11 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen

12 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 12 Dual-Orthogonal Grid System in Space / Dual-orthogonales Gittersystem im Raum 3-D / 3D Global node numbering / Globale Gitternummerierung

13 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 13 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen Local grid equations in local notation / Lokale Gittergleichungen in lokaler Notation Local grid equations in global grid node notation / Lokale Gittergleichungen in globaler Gitterknotennotation

14 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 14 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen Local spatial shift operators / Lokale räumliche Schiebeoperatoren Local grid equations in global grid node notation / Lokale Gittergleichungen in globaler Gitterknotennotation Local grid equations with local spatial shift operators in global grid node notation / Lokale Gittergleichungen mit lokalen räumlichen Schiebeoperatoren in globaler Gitterknotennotation

15 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 15 3-D FIT – Local Spatial Shift Operators / 3D-FIT – Lokale räumliche Schiebeoperatoren 1. Simple spatial shift operation / Einfache räumliche Schiebeoperation 2. Identity operation / Identitätsoperation 3. Multiple shift operations / Zusammengesetzte Schiebeoperationen Special case for / Speziell folgt für 4. Local difference operator / Lokaler Differenzoperator 5. Local averaging operator / Lokaler Mittelungsoperator

16 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 16 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen … in local matrix form / … in lokaler Matrixform Local grid equations with local spatial shift operators in global grid node notation / Lokale Gittergleichungen mit lokalen räumlichen Schiebeoperatoren in globaler Gitterknotennotation

17 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 17 3-D FIT – … Discrete Grid Equations in Local Matrix Form / 3D-FIT –... diskreten Gittergleichungen in lokaler Matrixform

18 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 18 3-D FIT – … Discrete Grid Equations in Local Matrix Form / 3D-FIT –... diskreten Gittergleichungen in lokaler Matrixform Faradays induction law in local matrix form / Faradaysches Induktionsgesetz in lokaler Matrixform

19 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 19 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

20 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 20 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

21 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 21 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

22 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 22 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen

23 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 23 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

24 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 24 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

25 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 25 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

26 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 26 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen integration cell / -Integrationszelle

27 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 27 3-D FIT – Derivation of the Discrete Grid Equations / 3D-FIT – Ableitung der diskreten Gittergleichungen

28 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 28 3-D FIT – … Discrete Grid Equations in Local Matrix Form / 3D-FIT –... diskreten Gittergleichungen in lokaler Matrixform

29 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 29 3-D FIT – … Discrete Grid Equations in Local Matrix Form / 3D-FIT –... diskreten Gittergleichungen in lokaler Matrixform

30 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 30 3-D FIT – … Discrete Grid Equations in Local and Global Matrix Form / 3D-FIT –... diskreten Gittergleichungen in lokaler und globaler Matrixform Discrete grid equations in local matrix form / Diskrete Gittergleichungen in lokaler Matrixform Discrete grid equations in global matrix form / Diskrete Gittergleichungen in globaler Matrixform Maxwells equations in integral form / Maxwellsche Gleichungen in Integralform

31 Dr.-Ing. René Marklein - NFT I - L 9 / V 9 - WS 2006 / 2007 31 End of Lecture 9 / Ende der 9. Vorlesung