User:Tom Allen/TensorExperimentsZ28

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GTEZ2800C.jpg


NB. ... execute (ijx) ...

   gXm0All=: 1.3  1.4  _    1.6"_
   gXm1All=: 1.4  1.5  1.6  1.7"_

   nCpts=:_ _4 4 161,_ 0 0 0,_ 0 0 0,:_ _4 4 161"_

   *./^:3"3 (0=]) (]+(0|:])+0 1|:])"3 (gXM([+/"1@((<0 1)|:])"5@B2kdc nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GTEZ2801D.jpg


NB. ... script experimentalZ.ijs ...

NB. ... these verbs are valid only in Cartesian coordinates ...

FEMcvcv    =:+/"1@((<0 1)|:])"4@B2k
FEMcvcvdn  =:+/"1@((<0 1)|:])"5@B2kdc
FEMcvcvdndn=:+/"1@((<0 1)|:])"6@B2kdcdc


NB. ... execute (ijx) ...

   gXm0All=: 1.3  1.4  _    1.6"_
   gXm1All=: 1.4  1.5  1.6  1.7"_

   nCpts=:_ _4 4 161,_ 0 0 0,_ 0 0 0,:_ _4 4 161"_

NB. ... derivatives ...

   A=:(gXM([FEMcvcvdn nRef@hknQ)])                               ((0;50"_)pTRandom nCpts)''
   B=:(gXM(0|:[:(gXM([(0{])@FEMcvcv nRef@hknQ),:@])D.1])"_ 1])   ((0;50"_)pTRandom nCpts)''

   A (((2^_44);2^_15)qteq[;])"3 B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   A=:(gXM([FEMcvcvdndn nRef@hknQ)])                             ((0;50"_)pTRandom nCpts)''
   B=:(gXM(0|:[:(gXM([(0{])@FEMcvcvdn nRef@hknQ),:@])D.1])"_ 1]) ((0;50"_)pTRandom nCpts)''

   A (((2^_44);2^_12)qteq[;])"4 B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

NB. ... Maxwell's equation (2) ...

   *./^:3"3 (0=]) ((2^_44)qtsz]) (]+(0|:])+0 1|:])"3 (gXM([FEMcvcvdn nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


NB. ... script experimentalZ.ijs ...

NB. ... these verbs are valid only in Cartesian coordinates ...

NB. ... electric and magnetic fields ...

FEMcvcv01=:((<0 1){])"2@FEMcvcv
FEMcvcv02=:((<0 2){])"2@FEMcvcv
FEMcvcv03=:((<0 3){])"2@FEMcvcv
FEMcvcv10=:((<1 0){])"2@FEMcvcv
FEMcvcv12=:((<1 2){])"2@FEMcvcv
FEMcvcv13=:((<1 3){])"2@FEMcvcv
FEMcvcv20=:((<2 0){])"2@FEMcvcv
FEMcvcv21=:((<2 1){])"2@FEMcvcv
FEMcvcv23=:((<2 3){])"2@FEMcvcv
FEMcvcv30=:((<3 0){])"2@FEMcvcv
FEMcvcv31=:((<3 1){])"2@FEMcvcv
FEMcvcv32=:((<3 2){])"2@FEMcvcv

NB. ... used for Maxwell's equation (2) ...

FEMcvcvdn231=:((<2 3 1){])"3@FEMcvcvdn
FEMcvcvdn312=:((<3 1 2){])"3@FEMcvcvdn
FEMcvcvdn123=:((<1 2 3){])"3@FEMcvcvdn

FEMcvcvdn302=:((<3 0 2){])"3@FEMcvcvdn
FEMcvcvdn023=:((<0 2 3){])"3@FEMcvcvdn
FEMcvcvdn230=:((<2 3 0){])"3@FEMcvcvdn

FEMcvcvdn013=:((<0 1 3){])"3@FEMcvcvdn
FEMcvcvdn130=:((<1 3 0){])"3@FEMcvcvdn
FEMcvcvdn301=:((<3 0 1){])"3@FEMcvcvdn

FEMcvcvdn120=:((<1 2 0){])"3@FEMcvcvdn
FEMcvcvdn201=:((<2 0 1){])"3@FEMcvcvdn
FEMcvcvdn012=:((<0 1 2){])"3@FEMcvcvdn

NB. ... used for Maxwell's equation (1) ...

FEMcvcvdn011=:((<0 1 1){])"3@FEMcvcvdn
FEMcvcvdn022=:((<0 2 2){])"3@FEMcvcvdn
FEMcvcvdn033=:((<0 3 3){])"3@FEMcvcvdn

FEMcvcvdn100=:((<1 0 0){])"3@FEMcvcvdn
FEMcvcvdn122=:((<1 2 2){])"3@FEMcvcvdn
FEMcvcvdn133=:((<1 3 3){])"3@FEMcvcvdn

FEMcvcvdn200=:((<2 0 0){])"3@FEMcvcvdn
FEMcvcvdn211=:((<2 1 1){])"3@FEMcvcvdn
FEMcvcvdn233=:((<2 3 3){])"3@FEMcvcvdn

FEMcvcvdn300=:((<3 0 0){])"3@FEMcvcvdn
FEMcvcvdn311=:((<3 1 1){])"3@FEMcvcvdn
FEMcvcvdn322=:((<3 2 2){])"3@FEMcvcvdn


GTEZ2802E.jpg


NB. ... script experimentalZ.ijs ...

NB. ... these verbs are valid only in Cartesian coordinates ...

EEMcn0=:FEMcvcv30
EEMcn1=:FEMcvcv31
EEMcn2=:FEMcvcv32

EEMcn=:(0|:])@(EEMcn0,EEMcn1,:EEMcn2)

HEMcn0=:FEMcvcv12
HEMcn1=:FEMcvcv20
HEMcn2=:FEMcvcv01

HEMcn=:(0|:])@(HEMcn0,HEMcn1,:HEMcn2)


NB. ... execute (ijx) ...

   gXm0All=: 1.3  1.4  _    1.6"_
   gXm1All=: 1.4  1.5  1.6  1.7"_

   nCpts=:_ _4 4 161,_ 0 0 0,_ 0 0 0,:_ _4 4 161"_

   $ (gXM([EEMcn nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
50 3
   $ (gXM([HEMcn nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
50 3


GTEZ2803E.jpg


NB. ... execute (ijx) ...

   gXm0All=: 1.3  1.4  _    1.6"_
   gXm1All=: 1.4  1.5  1.6  1.7"_

   nCpts=:_ _4 4 161,_ 0 0 0,_ 0 0 0,:_ _4 4 161"_

NB. ... Maxwell's equation (2) ...

   (0=]) (gXM([(FEMcvcvdn231+FEMcvcvdn312+FEMcvcvdn123)nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   (0=]) (gXM([(FEMcvcvdn302+FEMcvcvdn023+FEMcvcvdn230)nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   (0=]) (gXM([(FEMcvcvdn013+FEMcvcvdn130+FEMcvcvdn301)nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   (0=]) (gXM([(FEMcvcvdn120+FEMcvcvdn201+FEMcvcvdn012)nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GTEZ2804D.jpg


NB. ... script experimentalZ.ijs ...

NB. ... these verbs are valid only in Cartesian coordinates ...

PEMcn0=:(EEMcn1*HEMcn2)+-@(EEMcn2*HEMcn1)
PEMcn1=:(EEMcn2*HEMcn0)+-@(EEMcn0*HEMcn2)
PEMcn2=:(EEMcn0*HEMcn1)+-@(EEMcn1*HEMcn0)

PEMcn=:(0|:])@(PEMcn0,PEMcn1,:PEMcn2)


NB. ... execute (ijx) ...

   gXm0All=: 1.3  1.4  _    1.6"_
   gXm1All=: 1.4  1.5  1.6  1.7"_

   nCpts=:_ _4 4 161,_ 0 0 0,_ 0 0 0,:_ _4 4 161"_

   $ (gXM([PEMcn nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
50 3


GTEZ2805F.jpg


NB. ... script experimentalZ.ijs ...

NB. ... these verbs are valid only in Cartesian coordinates ...

JEMcn  =:+/"1@((<1 2)|:])"3@FEMcvcvdn
JEMcndn=:+/"1@((<1 2)|:])"4@FEMcvcvdndn


NB. ... execute (ijx) ...

   gXm0All=: 1.3  1.4  _    1.6"_
   gXm1All=: 1.4  1.5  1.6  1.7"_

   nCpts=:_ _4 4 161,_ 0 0 0,_ 0 0 0,:_ _4 4 161"_

NB. ... derivatives ...

   A=:(gXM([JEMcndn nRef@hknQ)])                             ((0;50"_)pTRandom nCpts)''
   B=:(gXM(0|:[:(gXM([(0{])@JEMcn nRef@hknQ),:@])D.1])"_ 1]) ((0;50"_)pTRandom nCpts)''

   A (((2^_44);2^_12)qteq[;])"2 B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

NB. ... divergence is 0 ...

   (0=]) ((2^_44)qtsz]) (gXM([+/@((<0 1)|:])"2@JEMcndn nRef@hknQ)]) ((0;50"_)pTRandom nCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1



Download: File:LTEZ2800C.txt
Download: File:LTEZ2801D.txt
Download: File:LTEZ2802E.txt
Download: File:LTEZ2803E.txt
Download: File:LTEZ2804D.txt
Download: File:LTEZ2805F.txt




Download MoinMoin source: File:TensorExperimentsZ28.ijs