program main !*****************************************************************************80 ! !! FEM1D_PACK_TEST tests the FEM1D_PACK library. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 19 March 2011 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM1D_PACK_TEST' write ( *, '(a)' ) ' FORTRAN90 version' write ( *, '(a)' ) ' Test the FEM1D_PACK library.' call test01 ( ) call test02 ( ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM1D_PACK_TEST' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop 0 end subroutine test01 ( ) !*****************************************************************************80 ! !! TEST01 verifies LOCAL_BASIS_1D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 March 2011 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: node_num = 4 integer i integer j real ( kind = rk ) node_x(node_num) real ( kind = rk ) phi(node_num) real ( kind = rk ) phi_matrix(node_num,node_num) real ( kind = rk ) r8_uniform integer seed real ( kind = rk ) x write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TEST01:' write ( *, '(a)' ) ' LOCAL_BASIS_1D evaluates the local basis functions' write ( *, '(a)' ) ' for a 1D element.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Test that the basis functions, evaluated at the nodes,' write ( *, '(a)' ) ' form the identity matrix.' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Number of nodes = ', node_num node_x(1:node_num) = (/ 1.0D+00, 2.0D+00, 4.0D+00, 4.5D+00 /); write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Node coordinates:' write ( *, '(a)' ) ' ' do j = 1, node_num write ( *, '(2x,i8,2x,f7.3,2x,f7.3)' ) j, node_x(j) end do do j = 1, node_num x = node_x(j) call local_basis_1d ( node_num, node_x, x, phi_matrix(1,j) ) end do write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' A(I,J) = PHI(I) at node (J):' write ( *, '(a)' ) ' ' do i = 1, node_num write ( *, '(2x,10f7.3)' ) phi_matrix(i,1:node_num) end do seed = 123456789 write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The PHI functions should sum to 1 at random X values:' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' X Sum ( PHI(:)(X) )' write ( *, '(a)' ) ' ' do j = 1, 5 x = r8_uniform ( 1.0D+00, 4.5D+00, seed ) call local_basis_1d ( node_num, node_x, x, phi ) write ( *, '(2x,g14.6,2x,g14.6)' ) x, sum ( phi(1:node_num) ) end do return end subroutine test02 ( ) !*****************************************************************************80 ! !! TEST02 verifies LOCAL_BASIS_PRIME_1D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 19 March 2011 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: node_num = 4 real ( kind = rk ) dphidx(node_num) real ( kind = rk ) dphidx_matrix(node_num,node_num) integer i integer j real ( kind = rk ) node_x(node_num) real ( kind = rk ) r8_uniform integer seed real ( kind = rk ) x write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TEST02:' write ( *, '(a)' ) ' LOCAL_BASIS_PRIME_1D evaluates the local basis function' write ( *, '(a)' ) ' derivatives for a 1D element.' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Number of nodes = ', node_num node_x(1:node_num) = (/ 1.0D+00, 2.0D+00, 4.0D+00, 4.5D+00 /); write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Node coordinates:' write ( *, '(a)' ) ' ' do j = 1, node_num write ( *, '(2x,i8,2x,f7.3,2x,f7.3)' ) j, node_x(j) end do do j = 1, node_num x = node_x(j) call local_basis_prime_1d ( node_num, node_x, x, dphidx_matrix(1,j) ) end do write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' A(I,J) = dPHIdx(I) at node(J):' write ( *, '(a)' ) ' The diagonal should be 0.' write ( *, '(a)' ) ' Columns should sum to 0.' write ( *, '(a)' ) ' ' do i = 1, node_num write ( *, '(2x,10f7.3)' ) dphidx_matrix(i,1:node_num) end do seed = 123456789 write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The dPHIdx functions should sum to 0 at random X values:' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' X Sum ( dPHIdx(:)(X) )' write ( *, '(a)' ) ' ' do j = 1, 5 x = r8_uniform ( 1.0D+00, 4.5D+00, seed ) call local_basis_prime_1d ( node_num, node_x, x, dphidx ) write ( *, '(2x,g14.6,2x,g14.6)' ) x, sum ( dphidx(1:node_num) ) end do return end