文档介绍：该【用julia编写的有限元程序 】是由【1781111****】上传分享，文档一共【4】页，该文档可以免费在线阅读，需要了解更多关于【用julia编写的有限元程序 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..?julia编写的有限元程序FINITEELEMENTPROGRAMMINGINJULIAPostedonApril21,2013|byAmuthanArunkumarRamabathiranFINITEELEMENTPROGRAMMINGINJULIAApril21,2013Postedon|++,:C/C++isfastandpowerfulbutverydifficulttoworkwith(forthetypicalscientificresearcherwhodoesnothaveanextensivebackgroundinprogramming),Fortranisquiteoutdatedinspiteofitsamazingspeed,-putationalhotspotsusinghighperformancelanguageslikeFortranorC/C++.,developingefficientfiniteelementcodeiscruciallydependentonfastandrobustlinearalgebralibrariesanditisanon-,whatisrequiredisalanguagethatisaseasytouseasPythonandasfastasC/C++,',xx+u,yy=-6overtheunitsquarewiththeDirichletboundaryconditionu=1+x^2+2y^-:FEniCSandFreeFem++.FEniCSisacollectionofsoftwareforhighlevelfiniteelementcodedevelopmentwritteninPythonandC++.FreeFem++isapartialdifferentialequationssolverwritteninC++andusesitsownDSL(DomainSpecificLanguage)withaC++:..ThankstoJulia'selegantsyntaxthecodeislargelyself-:,,,,,,dbcandf_extPoissonequationisobtainedfromthevariationalformulationasgrad(u).grad(v).Thisisspecifiedinthefunctionpoisson_stiffness,asshownbelow,intermsoftheshapefunctionvectorNandthematrixcontainingthepartialderivativesoftheshapefunctionsdNwheredN[i,j]=dN_i/dx_j.#Stiffnessmatrixfunctionpoisson_stiffness(N,dN,i,j)dN[i,1]*dN[j,1]+dN[i,2]*dN[j,2]endAtriangularmeshovertheunitsquareisgeneratedusingmesh=UnitSquare(100)=fe_space_C0(mesh,dbc)Finally,thesolutionofthefiniteelementproblemisobtainedas:solve_fe(mesh,u,poisson_stiffness,f_ext)-,referredhenceforthasmethods1,2and3,areexploredinthefunctionsolve_fe:#Method1#K=zeros(n_size,n_size)#fe_matrices(mesh,u,stiffness,fext,K,F)#Method2#K=spzeros(n_size,n_size)#fe_matrices(mesh,u,stiffness,fext,K,F)#Method3iu,ju,vu=fe_matrices(mesh,u,stiffness,fext,F)K=sparse(iu,ju,vu,n_size,n_size)-zeroelementsofthesparsematrixisunknown,,-zeroentriesinasparsematrixKtoinitializedthreevectorsI,JandVsuchthatK[I[n],J[n]]=V[n],(inseconds),asafunctionofthetotalnumberofnodes(N),forthethreeparedwithPoissonsolversimplementedinFEniCSandFreeFem++++:..++----(method1).Initializingthesparsestiffnessmatrixasinmethod2worksfineforsmallN,(guessed)numberofnon-++codesformuchlargervaluesofNisshownbelow:ItcanbeseenthattheperformanceoftheJuliacodeisasgoodasFEniCS'andclosetothatofFreeFem++forNrangingfrom10^2to10^,,-orientation,butitstypesystem,++:thesurfaceplotatthebeginningofthearticleisthesolutionofthePoissonequationovertheunitsquarewithzeroDirichletboundaryconditiononallitsedgesandanexternalloadf(x,y)=2sin(2pi*x)sin(2pi*y).,alongwithanyassociatedsourcecodeandfiles,islicensedunderTheCodeProjectOpenLicense(CPOL)AbouttheAuthor:..AmuthanArunkumarRamabathiranFranceAmuthanArunkumarRamabathiranisapost-doctoralresearcheratGeM,,IndianInstituteofScience(IISc),,IndianInstituteofTechnology(IIT)-academicfront,heactivelylearnsandplayssouthIndianclassicalmusiconthefretlesselectricguitar.