heat equaonjupiter.ethz.ch/.../2020/docs/presentation1.pdf · 2020. 7. 10. · presentation1.pptx...

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  • Heatequa(on:

  • Heatequa(on:

    Numericalsolu(onrequiresadiscre(sa(onInbothspaceand(me

  • ?

  • Example:Fourierseries

  • Example:Fourierseries

  • Example:Fourierseries

  • Example:Fourierseries

  • Example:Fourierseries

  • Example:Fourierseries

  • Example:Fourierseries

  • Example:Fourierseries

  • Arbitraryfunc(on

    Orthogonalbasisfunc(ons

    Spectralcoefficients

    1.4 0.8 0.3

  • Finiteelements?

  • Finiteelements?

  • Finiteelements?

  • Finiteelements?

  • Finiteelements?

    T1

    T2

  • Finiteelements?

    T1

    T2

  • Finiteelements?

    N1(x) N2(x)

    T1

    T2

  • Finiteelements?

    N1(x) N2(x)

    T1

    T2

    T1.N1(x)T2.N2(x)

  • Insufficientequa(on->Risunknown!

  • Welookforthesolu(onsuchthattheprojec(onoftheresidualoverthebasisfunc(onsiszero

  • Welookforthesolu(onsuchthattheprojec(onoftheresidualoverthebasisfunc(onsiszero

  • Welookforthesolu(onsuchthattheprojec(onoftheresidualoverthebasisfunc(onsiszero

  • FEM:

    Fourier:

    Projec(ons

    Commonspace:

    ~V = Vx

    ~ex

    + Vy

    ~ey

    Vx

    = ~V · ~ex

    Vy

    = ~V · ~ey

    AAACSXicbVBLS8NAGNzUd31VPXpZLIIglKQIehEELx4VbCw0JW42X9qlmwe7m2II+XtevHnzP3jxoIgntzGIth1YmG9mPnZ3vIQzqUzzxagtLC4tr6yu1dc3Nre2Gzu7toxTQaFDYx6LrkckcBZBRzHFoZsIIKHH4c4bXU78uzEIyeLoVmUJ9EMyiFjAKFFachv3zhhobhf4HNvuAy4ncB+KY9vNqiErHKc+Mc9xFXaoH6vfaOlm892scBtNs2WWwLPEqkgTVbh2G8+OH9M0hEhRTqTsWWai+jkRilEORd1JJSSEjsgAeppGJATZz8smCnyoFR8HsdAnUrhU/27kJJQyCz2dDIkaymlvIs7zeqkKzvo5i5JUQUR/LgpSjlWMJ7VinwmgimeaECqYfiumQyIIVbr8ui7Bmv7yLLHbLctsWTcnzYt2Vccq2kcH6AhZ6BRdoCt0jTqIokf0it7Rh/FkvBmfxtdPtGZUO3voH2oL35lTs1Y=AAACSXicbVBLS8NAGNzUd31VPXpZLIIglKQIehEELx4VbCw0JW42X9qlmwe7m2II+XtevHnzP3jxoIgntzGIth1YmG9mPnZ3vIQzqUzzxagtLC4tr6yu1dc3Nre2Gzu7toxTQaFDYx6LrkckcBZBRzHFoZsIIKHH4c4bXU78uzEIyeLoVmUJ9EMyiFjAKFFachv3zhhobhf4HNvuAy4ncB+KY9vNqiErHKc+Mc9xFXaoH6vfaOlm892scBtNs2WWwLPEqkgTVbh2G8+OH9M0hEhRTqTsWWai+jkRilEORd1JJSSEjsgAeppGJATZz8smCnyoFR8HsdAnUrhU/27kJJQyCz2dDIkaymlvIs7zeqkKzvo5i5JUQUR/LgpSjlWMJ7VinwmgimeaECqYfiumQyIIVbr8ui7Bmv7yLLHbLctsWTcnzYt2Vccq2kcH6AhZ6BRdoCt0jTqIokf0it7Rh/FkvBmfxtdPtGZUO3voH2oL35lTs1Y=AAACSXicbVBLS8NAGNzUd31VPXpZLIIglKQIehEELx4VbCw0JW42X9qlmwe7m2II+XtevHnzP3jxoIgntzGIth1YmG9mPnZ3vIQzqUzzxagtLC4tr6yu1dc3Nre2Gzu7toxTQaFDYx6LrkckcBZBRzHFoZsIIKHH4c4bXU78uzEIyeLoVmUJ9EMyiFjAKFFachv3zhhobhf4HNvuAy4ncB+KY9vNqiErHKc+Mc9xFXaoH6vfaOlm892scBtNs2WWwLPEqkgTVbh2G8+OH9M0hEhRTqTsWWai+jkRilEORd1JJSSEjsgAeppGJATZz8smCnyoFR8HsdAnUrhU/27kJJQyCz2dDIkaymlvIs7zeqkKzvo5i5JUQUR/LgpSjlWMJ7VinwmgimeaECqYfiumQyIIVbr8ui7Bmv7yLLHbLctsWTcnzYt2Vccq2kcH6AhZ6BRdoCt0jTqIokf0it7Rh/FkvBmfxtdPtGZUO3voH2oL35lTs1Y=AAACSXicbVBLS8NAGNzUd31VPXpZLIIglKQIehEELx4VbCw0JW42X9qlmwe7m2II+XtevHnzP3jxoIgntzGIth1YmG9mPnZ3vIQzqUzzxagtLC4tr6yu1dc3Nre2Gzu7toxTQaFDYx6LrkckcBZBRzHFoZsIIKHH4c4bXU78uzEIyeLoVmUJ9EMyiFjAKFFachv3zhhobhf4HNvuAy4ncB+KY9vNqiErHKc+Mc9xFXaoH6vfaOlm892scBtNs2WWwLPEqkgTVbh2G8+OH9M0hEhRTqTsWWai+jkRilEORd1JJSSEjsgAeppGJATZz8smCnyoFR8HsdAnUrhU/27kJJQyCz2dDIkaymlvIs7zeqkKzvo5i5JUQUR/LgpSjlWMJ7VinwmgimeaECqYfiumQyIIVbr8ui7Bmv7yLLHbLctsWTcnzYt2Vccq2kcH6AhZ6BRdoCt0jTqIokf0it7Rh/FkvBmfxtdPtGZUO3voH2oL35lTs1Y=

    ~ex

    AAAB8HicbVBNS8NAEJ3Ur1q/qh69BIvgqSRF0GPBi8cK9kPaUDbbSbt0dxN2N8US+iu8eFDEqz/Hm//GbZuDtj4YeLw3w8y8MOFMG8/7dgobm1vbO8Xd0t7+weFR+fikpeNUUWzSmMeqExKNnElsGmY4dhKFRIQc2+H4du63J6g0i+WDmSYYCDKULGKUGCs99iZIM+w/zfrlilf1FnDXiZ+TCuRo9MtfvUFMU4HSUE607vpeYoKMKMMox1mpl2pMCB2TIXYtlUSgDrLFwTP3wioDN4qVLWnchfp7IiNC66kIbacgZqRXvbn4n9dNTXQTZEwmqUFJl4uilLsmduffuwOmkBo+tYRQxeytLh0RRaixGZVsCP7qy+ukVav6XtW/v6rUa3kcRTiDc7gEH66hDnfQgCZQEPAMr/DmKOfFeXc+lq0FJ585hT9wPn8AJjqQkg==AAAB8HicbVBNS8NAEJ3Ur1q/qh69BIvgqSRF0GPBi8cK9kPaUDbbSbt0dxN2N8US+iu8eFDEqz/Hm//GbZuDtj4YeLw3w8y8MOFMG8/7dgobm1vbO8Xd0t7+weFR+fikpeNUUWzSmMeqExKNnElsGmY4dhKFRIQc2+H4du63J6g0i+WDmSYYCDKULGKUGCs99iZIM+w/zfrlilf1FnDXiZ+TCuRo9MtfvUFMU4HSUE607vpeYoKMKMMox1mpl2pMCB2TIXYtlUSgDrLFwTP3wioDN4qVLWnchfp7IiNC66kIbacgZqRXvbn4n9dNTXQTZEwmqUFJl4uilLsmduffuwOmkBo+tYRQxeytLh0RRaixGZVsCP7qy+ukVav6XtW/v6rUa3kcRTiDc7gEH66hDnfQgCZQEPAMr/DmKOfFeXc+lq0FJ585hT9wPn8AJjqQkg==AAAB8HicbVBNS8NAEJ3Ur1q/qh69BIvgqSRF0GPBi8cK9kPaUDbbSbt0dxN2N8US+iu8eFDEqz/Hm//GbZuDtj4YeLw3w8y8MOFMG8/7dgobm1vbO8Xd0t7+weFR+fikpeNUUWzSmMeqExKNnElsGmY4dhKFRIQc2+H4du63J6g0i+WDmSYYCDKULGKUGCs99iZIM+w/zfrlilf1FnDXiZ+TCuRo9MtfvUFMU4HSUE607vpeYoKMKMMox1mpl2pMCB2TIXYtlUSgDrLFwTP3wioDN4qVLWnchfp7IiNC66kIbacgZqRXvbn4n9dNTXQTZEwmqUFJl4uilLsmduffuwOmkBo+tYRQxeytLh0RRaixGZVsCP7qy+ukVav6XtW/v6rUa3kcRTiDc7gEH66hDnfQgCZQEPAMr/DmKOfFeXc+lq0FJ585hT9wPn8AJjqQkg==AAAB8HicbVBNS8NAEJ3Ur1q/qh69BIvgqSRF0GPBi8cK9kPaUDbbSbt0dxN2N8US+iu8eFDEqz/Hm//GbZuDtj4YeLw3w8y8MOFMG8/7dgobm1vbO8Xd0t7+weFR+fikpeNUUWzSmMeqExKNnElsGmY4dhKFRIQc2+H4du63J6g0i+WDmSYYCDKULGKUGCs99iZIM+w/zfrlilf1FnDXiZ+TCuRo9MtfvUFMU4HSUE607vpeYoKMKMMox1mpl2pMCB2TIXYtlUSgDrLFwTP3wioDN4qVLWnchfp7IiNC66kIbacgZqRXvbn4n9dNTXQTZEwmqUFJl4uilLsmduffuwOmkBo+tYRQxeytLh0RRaixGZVsCP7qy+ukVav6XtW/v6rUa3kcRTiDc7gEH66hDnfQgCZQEPAMr/DmKOfFeXc+lq0FJ585hT9wPn8AJjqQkg==

    ~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

    ~VAAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeCF48V7Ae0oWy2k3bpZhN2N4US+iO8eFDEq7/Hm//GTZuDtj4YeLw3w8y8IBFcG9f9dkpb2zu7e+X9ysHh0fFJ9fSso+NUMWyzWMSqF1CNgktsG24E9hKFNAoEdoPpfe53Z6g0j+WTmSfoR3QsecgZNVbqDmbIss5iWK25dXcJskm8gtSgQGtY/RqMYpZGKA0TVOu+5ybGz6gynAlcVAapxoSyKR1j31JJI9R+tjx3Qa6sMiJhrGxJQ5bq74mMRlrPo8B2RtRM9LqXi/95/dSEd37GZZIalGy1KEwFMTHJfycjrpAZMbeEMsXtrYRNqKLM2IQqNgRv/eVN0mnUPbfuPd7Umo0ijjJcwCVcgwe30IQHaEEbGEzhGV7hzUmcF+fd+Vi1lpxi5hz+wPn8AXlpj5g=AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeCF48V7Ae0oWy2k3bpZhN2N4US+iO8eFDEq7/Hm//GTZuDtj4YeLw3w8y8IBFcG9f9dkpb2zu7e+X9ysHh0fFJ9fSso+NUMWyzWMSqF1CNgktsG24E9hKFNAoEdoPpfe53Z6g0j+WTmSfoR3QsecgZNVbqDmbIss5iWK25dXcJskm8gtSgQGtY/RqMYpZGKA0TVOu+5ybGz6gynAlcVAapxoSyKR1j31JJI9R+tjx3Qa6sMiJhrGxJQ5bq74mMRlrPo8B2RtRM9LqXi/95/dSEd37GZZIalGy1KEwFMTHJfycjrpAZMbeEMsXtrYRNqKLM2IQqNgRv/eVN0mnUPbfuPd7Umo0ijjJcwCVcgwe30IQHaEEbGEzhGV7hzUmcF+fd+Vi1lpxi5hz+wPn8AXlpj5g=AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeCF48V7Ae0oWy2k3bpZhN2N4US+iO8eFDEq7/Hm//GTZuDtj4YeLw3w8y8IBFcG9f9dkpb2zu7e+X9ysHh0fFJ9fSso+NUMWyzWMSqF1CNgktsG24E9hKFNAoEdoPpfe53Z6g0j+WTmSfoR3QsecgZNVbqDmbIss5iWK25dXcJskm8gtSgQGtY/RqMYpZGKA0TVOu+5ybGz6gynAlcVAapxoSyKR1j31JJI9R+tjx3Qa6sMiJhrGxJQ5bq74mMRlrPo8B2RtRM9LqXi/95/dSEd37GZZIalGy1KEwFMTHJfycjrpAZMbeEMsXtrYRNqKLM2IQqNgRv/eVN0mnUPbfuPd7Umo0ijjJcwCVcgwe30IQHaEEbGEzhGV7hzUmcF+fd+Vi1lpxi5hz+wPn8AXlpj5g=AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeCF48V7Ae0oWy2k3bpZhN2N4US+iO8eFDEq7/Hm//GTZuDtj4YeLw3w8y8IBFcG9f9dkpb2zu7e+X9ysHh0fFJ9fSso+NUMWyzWMSqF1CNgktsG24E9hKFNAoEdoPpfe53Z6g0j+WTmSfoR3QsecgZNVbqDmbIss5iWK25dXcJskm8gtSgQGtY/RqMYpZGKA0TVOu+5ybGz6gynAlcVAapxoSyKR1j31JJI9R+tjx3Qa6sMiJhrGxJQ5bq74mMRlrPo8B2RtRM9LqXi/95/dSEd37GZZIalGy1KEwFMTHJfycjrpAZMbeEMsXtrYRNqKLM2IQqNgRv/eVN0mnUPbfuPd7Umo0ijjJcwCVcgwe30IQHaEEbGEzhGV7hzUmcF+fd+Vi1lpxi5hz+wPn8AXlpj5g=

  • Solvingforthe(me-dependence

  • Solvingforthe(me-dependence

  • Solvingforthe(me-dependence

  • Solvingforthe(me-dependence

  • Solvingforthe(me-dependence

  • Morethanoneelement?

  • R =

    R11 R12R21 R22

    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

  • Globalmatrices

  • Globalmatrices

  • Globalmatrices

    Tn+1 = LG�1b

    AAACPnicbVC7SgNBFJ2NrxhfUUubwSAIYtgNgjZCwEILiwh5CEkMs5PZZMjs7DJzVwzLfJmN32BnaWOhiK2lk0ehMReGOZxzLvfe48eCa3DdFyezsLi0vJJdza2tb2xu5bd36jpKFGU1GolI3fpEM8ElqwEHwW5jxUjoC9bwBxcjvXHPlOaRrMIwZu2Q9CQPOCVgqU6+1vIj0dXD0H5pC9gD+EFaNeYulUeewed4nn5tOpfWceyZeapvTCdfcIvuuPB/4E1BAU2r0sk/t7oRTUImgQqiddNzY2inRAGngplcK9EsJnRAeqxpoSQh0+10fL7BB5bp4iBS9knAY/Z3R0pCPdrROkMCfT2rjch5WjOB4KydchknwCSdDAoSgSHCoyxxlytGQQwtIFRxuyumfaIIBZt4zobgzZ78H9RLRc8tejcnhXJpGkcW7aF9dIg8dIrK6ApVUA1R9Ihe0Tv6cJ6cN+fT+ZpYM860Zxf9Kef7B1q+sio=AAACPnicbVC7SgNBFJ2NrxhfUUubwSAIYtgNgjZCwEILiwh5CEkMs5PZZMjs7DJzVwzLfJmN32BnaWOhiK2lk0ehMReGOZxzLvfe48eCa3DdFyezsLi0vJJdza2tb2xu5bd36jpKFGU1GolI3fpEM8ElqwEHwW5jxUjoC9bwBxcjvXHPlOaRrMIwZu2Q9CQPOCVgqU6+1vIj0dXD0H5pC9gD+EFaNeYulUeewed4nn5tOpfWceyZeapvTCdfcIvuuPB/4E1BAU2r0sk/t7oRTUImgQqiddNzY2inRAGngplcK9EsJnRAeqxpoSQh0+10fL7BB5bp4iBS9knAY/Z3R0pCPdrROkMCfT2rjch5WjOB4KydchknwCSdDAoSgSHCoyxxlytGQQwtIFRxuyumfaIIBZt4zobgzZ78H9RLRc8tejcnhXJpGkcW7aF9dIg8dIrK6ApVUA1R9Ihe0Tv6cJ6cN+fT+ZpYM860Zxf9Kef7B1q+sio=AAACPnicbVC7SgNBFJ2NrxhfUUubwSAIYtgNgjZCwEILiwh5CEkMs5PZZMjs7DJzVwzLfJmN32BnaWOhiK2lk0ehMReGOZxzLvfe48eCa3DdFyezsLi0vJJdza2tb2xu5bd36jpKFGU1GolI3fpEM8ElqwEHwW5jxUjoC9bwBxcjvXHPlOaRrMIwZu2Q9CQPOCVgqU6+1vIj0dXD0H5pC9gD+EFaNeYulUeewed4nn5tOpfWceyZeapvTCdfcIvuuPB/4E1BAU2r0sk/t7oRTUImgQqiddNzY2inRAGngplcK9EsJnRAeqxpoSQh0+10fL7BB5bp4iBS9knAY/Z3R0pCPdrROkMCfT2rjch5WjOB4KydchknwCSdDAoSgSHCoyxxlytGQQwtIFRxuyumfaIIBZt4zobgzZ78H9RLRc8tejcnhXJpGkcW7aF9dIg8dIrK6ApVUA1R9Ihe0Tv6cJ6cN+fT+ZpYM860Zxf9Kef7B1q+sio=AAACPnicbVC7SgNBFJ2NrxhfUUubwSAIYtgNgjZCwEILiwh5CEkMs5PZZMjs7DJzVwzLfJmN32BnaWOhiK2lk0ehMReGOZxzLvfe48eCa3DdFyezsLi0vJJdza2tb2xu5bd36jpKFGU1GolI3fpEM8ElqwEHwW5jxUjoC9bwBxcjvXHPlOaRrMIwZu2Q9CQPOCVgqU6+1vIj0dXD0H5pC9gD+EFaNeYulUeewed4nn5tOpfWceyZeapvTCdfcIvuuPB/4E1BAU2r0sk/t7oRTUImgQqiddNzY2inRAGngplcK9EsJnRAeqxpoSQh0+10fL7BB5bp4iBS9knAY/Z3R0pCPdrROkMCfT2rjch5WjOB4KydchknwCSdDAoSgSHCoyxxlytGQQwtIFRxuyumfaIIBZt4zobgzZ78H9RLRc8tejcnhXJpGkcW7aF9dIg8dIrK6ApVUA1R9Ihe0Tv6cJ6cN+fT+ZpYM860Zxf9Kef7B1q+sio=