PETSc----Solves a tridiagonal linear system with KSP

! ! Description: Solves a tridiagonal linear system with KSP. ! !/*T ! Concepts: KSP^solving a system of linear equations ! Processors: 1 !T*/ ! ----------------------------------------------------------------------- program main implicit none ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Include files ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! ! This program uses CPP for preprocessing, as indicated by the use of ! PETSc include files in the directory petsc/include/finclude. This ! convention enables use of the CPP preprocessor, which allows the use ! of the #include statements that define PETSc objects and variables. ! ! Use of the conventional Fortran include statements is also supported ! In this case, the PETsc include files are located in the directory ! petsc/include/foldinclude. ! ! Since one must be very careful to include each file no more than once ! in a Fortran routine, application programmers must exlicitly list ! each file needed for the various PETSc components within their ! program (unlike the C/C++ interface). ! ! See the Fortran section of the PETSc users manual for details. ! ! The following include statements are required for KSP Fortran programs: ! petscsys.h - base PETSc routines ! petscvec.h - vectors ! petscmat.h - matrices ! petscksp.h - Krylov subspace methods ! petscpc.h - preconditioners ! Other include statements may be needed if using additional PETSc ! routines in a Fortran program, e.g., ! petscviewer.h - viewers 阅读器 ! petscis.h - index sets 索引集 ! #include "finclude/petscsys.h" !系统程序 #include "finclude/petscvec.h" ! 向量 #include "finclude/petscmat.h" ! 矩阵 #include "finclude/petscksp.h" !Krylov子空间方法 #include "finclude/petscpc.h" !预条件子 ! ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Variable declarations ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! ! Variables: ! ksp - linear solver context ! ksp - Krylov subspace method context ! pc - preconditioner context ! x, b, u - approx solution, right-hand-side, exact solution vectors ! A - matrix that defines linear system // 线性方程组系数矩阵 ! its - iterations for convergence // 收敛的迭代次数 ! norm - norm of error in solution // 解误差的范数 ! Vec x,b,u !近似解、右端项、精确解 Mat A !线性方程组系数矩阵 KSP ksp !Krylov子空间方法环境 PC pc !预条件子环境 PetscReal norm,tol PetscErrorCode ierr PetscInt i,n,col(3),its,i1,i2,i3 PetscTruth flg PetscMPIInt size,rank PetscScalar none,one,value(3) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Beginning of program ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - call PetscInitialize(PETSC_NULL_CHARACTER,ierr) !初始化工作 call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr) !获取进程数量size if (size .ne. 1) then call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr) !当前的进程号 if (rank .eq. 0) then write(6,*) 'This is a uniprocessor example only!' endif SETERRQ(1,' ',ierr) endif none = -1.0 one = 1.0 n = 10 i1 = 1 i2 = 2 i3 = 3 call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr) !Gets the integer value for a particular option in the database ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! 计算定义线性方程组Ax = b的矩阵和右端向量 ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! 创建矩阵. When using MatCreate(), the matrix format can ! be specified at runtime. call MatCreate(PETSC_COMM_WORLD,A,ierr) call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n,ierr) !local: PETSC_DECIDE x PETSC_DECIDE, global: n x n call MatSetFromOptions(A,ierr) !Creates a matrix where the type is determined from the options database. ! Generates a parallel MPI matrix if the communicator has more than one processor. !The default matrix type is AIJ, using the routines MatCreateSeqAIJ() and MatCreateMPIAIJ() , !if you do not select a type in the options database. ! 聚集矩阵 ! - Note that MatSetValues() uses 0-based row and column numbers ! in Fortran as well as in C (as set here in the array "col"). value(1) = -1.0 value(2) = 2.0 value(3) = -1.0 do 50 i=1,n-2 col(1) = i-1 col(2) = i col(3) = i+1 call MatSetValues(A,i1,i,i3,col,value,INSERT_VALUES,ierr) 50 continue i = n - 1 col(1) = n - 2 col(2) = n - 1 call MatSetValues(A,i1,i,i2,col,value,INSERT_VALUES,ierr) i = 0 col(1) = 0 col(2) = 1 value(1) = 2.0 value(2) = -1.0 call MatSetValues(A,i1,i,i2,col,value,INSERT_VALUES,ierr) !矩阵元素赋值后，在它们使用之前必须进行如下处理 call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr) call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr) ! 创建向量并复制它. Note that we form 1 vector from scratch and ! then duplicate as needed. call VecCreate(PETSC_COMM_WORLD,x,ierr) call VecSetSizes(x,PETSC_DECIDE,n,ierr) call VecSetFromOptions(x,ierr) call VecDuplicate(x,b,ierr) call VecDuplicate(x,u,ierr) ! Set exact solution; then compute right-hand-side vector. call VecSet(u,one,ierr) ! 设置向量为一个单一的值 call MatMult(A,u,b,ierr) ! 计算b = Au. ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Create the linear solver and set various options ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Create linear solver context ! Creates the default KSP context call KSPCreate(PETSC_COMM_WORLD,ksp,ierr) ! Set operators. Here the matrix that defines the linear system ! also serves as the preconditioning matrix. call KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN,ierr) ! Set linear solver defaults for this problem (optional). ! - By extracting the KSP and PC contexts from the KSP context, ! we can then directly directly call any KSP and PC routines ! to set various options. ! - The following four statements are optional; all of these ! parameters could alternatively be specified at runtime via ! KSPSetFromOptions(); call KSPGetPC(ksp,pc,ierr) call PCSetType(pc,PCJACOBI,ierr) tol = 1.d-7 !Sets the relative, absolute, divergence, and maximum iteration tolerances used by the default KSP convergence testers. call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_DOUBLE_PRECISION, & & PETSC_DEFAULT_DOUBLE_PRECISION,PETSC_DEFAULT_INTEGER,ierr) ! Set runtime options, e.g., ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol> ! These options will override those specified above as long as ! KSPSetFromOptions() is called _after_ any other customization ! routines. call KSPSetFromOptions(ksp,ierr) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Solve the linear system ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - call KSPSolve(ksp,b,x,ierr) ! View solver info; we could instead use the option -ksp_view call KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD,ierr) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Check solution and clean up ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Check the error call VecAXPY(x,none,u,ierr) !Computes u = x * none + y. call VecNorm(x,NORM_2,norm,ierr) !Computes the vector norm. call KSPGetIterationNumber(ksp,its,ierr) !Gets the current iteration number if (norm .gt. 1.e-12) then write(6,100) norm,its else write(6,200) its endif 100 format('Norm of error = ',e10.4,', Iterations = ',i5) 200 format('Norm of error < 1.e-12,Iterations = ',i5) ! Free work space. All PETSc objects should be destroyed when they ! are no longer needed. call VecDestroy(x,ierr) call VecDestroy(u,ierr) call VecDestroy(b,ierr) call MatDestroy(A,ierr) call KSPDestroy(ksp,ierr) call PetscFinalize(ierr) end  

 

函数请参考：http://www.caspur.it/risorse/softappl/doc/petsc_docs/manualpages/singleindex.html