PDE工具箱教程2

o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Ko!˜„ý†Ô¯Kû¤S3ŒÆêÆÆE:[e-mail]!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯K8¹1ý¯K2Ô¯Ko!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯K^PDEó䇦)n‡ý¯Kü þPoisson§Ñ¯K­¡¯Ko!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§Äü þPoisson§Š¯K−Δu=1,Ω=(x,y)|x2+y21.u|∂Ω=0.Ù°()u(x,y)=1−x2−y24k|^pdetool·-‹mPDEóä‡GUI.¡,üÂOptionsèüeGridÀ‘.e¡©Ú?1öŠ.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§Äü þPoisson§Š¯K−Δu=1,Ω=(x,y)|x2+y21.u|∂Ω=0.Ù°()u(x,y)=1−x2−y24k|^pdetool·-‹mPDEóä‡GUI.¡,üÂOptionsèüeGridÀ‘.e¡©Ú?1öŠ.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§Äü þPoisson§Š¯K−Δu=1,Ω=(x,y)|x2+y21.u|∂Ω=0.Ù°()u(x,y)=1−x2−y24k|^pdetool·-‹mPDEóä‡GUI.¡,üÂOptionsèüeGridÀ‘.e¡©Ú?1öŠ.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§1x˜‡%(0,0),Œ»1ü ;2˜.^‡:Â∂ΩUÜ,éuoã.,ÅãVÂ.½ö|^Shift…ÓžÀJoã.,2V½|^BoundaryèüSpecifyBoundaryConditions...À‘‹mBoundaryConditioné{µ,Ñ\.^‡.KDirichlet^‡,æ^%@Š=Œ.3˜§:ÂPDEUܽüÂPDEèü¥PDESpecification...À‘‹mPDESpecificationé{µ,ÀJ§a..KElliptic,ëêc=1,a=0,f=1.4‚¿©|^n/UܽMeshèü¥InitializeMeshÀ‘,Щz‚¿©.XI‚\—,üÂõ‡n/UܽMeshèü¥RefineMeshÀ‘,Xd„Œ±UY\—.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§5)§üÂÒUܽöSolveèü¥SolvePDEÀ‘,¬w«§çÚ).üÂMatlabãIUܽPlotèü¥Parameters...À‘,‹mPlotSelectioné{µ,À‘kColor,Contour,Arrows,Deformedmesh,Height(3-Dplot),„Œ±˜Š‚ê8.~ÀJColor,Contour,Height(3-Dplot)ÚShowmesho‘,,üÂPlotUÜ,‰Ñ)ã/.؊½)¯K)uã/ ,Œ±Š|gradu|,|cgradu|ã/.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§5)§üÂÒUܽöSolveèü¥SolvePDEÀ‘,¬w«§çÚ).üÂMatlabãIUܽPlotèü¥Parameters...À‘,‹mPlotSelectioné{µ,À‘kColor,Contour,Arrows,Deformedmesh,Height(3-Dplot),„Œ±˜Š‚ê8.~ÀJColor,Contour,Height(3-Dplot)ÚShowmesho‘,,üÂPlotUÜ,‰Ñ)ã/.؊½)¯K)uã/ ,Œ±Š|gradu|,|cgradu|ã/.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§5)§üÂÒUܽöSolveèü¥SolvePDEÀ‘,¬w«§çÚ).üÂMatlabãIUܽPlotèü¥Parameters...À‘,‹mPlotSelectioné{µ,À‘kColor,Contour,Arrows,Deformedmesh,Height(3-Dplot),„Œ±˜Š‚ê8.~ÀJColor,Contour,Height(3-Dplot)ÚShowmesho‘,,üÂPlotUÜ,‰Ñ)ã/.؊½)¯K)uã/ ,Œ±Š|gradu|,|cgradu|ã/.o!˜„ý†Ô¯Kû¤S8¹ý¯KÔ¯Kü þPoisson§5)§üÂÒUܽöSolveèü¥SolvePDEÀ‘,¬w«§çÚ).üÂMatlabãIUܽPlotèü¥Parameters...À‘,‹mPlotSelectioné{µ,À‘kColor,Contour,Arrows,Deformedmesh,Height(3-Dplot),„Œ±˜Š‚ê8.~ÀJColor,Contour,Height(3-Dplot)ÚShowmesho‘,,üÂPlotUÜ