program main use SparseClass use IOClass use FEMDomainClass implicit none type(COO_) :: coo, Kmatrix_COO,Mmatrix_COO type(CRS_) :: crs, Kmatrix,Mmatrix real(real64),allocatable :: x(:) complex(real64),allocatable :: u(:),u_p(:),u_m(:) real(real64),allocatable :: Force(:),K_inv_F(:) complex(real64) :: alpha real(real64) :: K,dt,h,b_c_spring,damping_coeff integer(int32) :: timestep type(Math_) :: math type(IO_) :: f integer(int32) :: DOF complex(real64) :: fix_disp type(FEMDomain_),allocatable :: point(:) integer(int32) :: i ! Motion Equation and Exponential integrator ! [M]{d^2 u/dt^2} + [C]{du/dt} + [K]{u} = {f} ! {d^2 u/dt^2} + [M]^{-1}[C]{du/dt} + [M]^{-1}[K]{u} = [M]^{-1}{f} ! [M]^{-1}[C] = 2*h*([M]^{-1}[K])^{1/2}であるとする． ! [w] = [M]^{-1}[K]とおくと ! u(t) = exp( -h + sqrt(h^2 - 1) )t[w]) a + exp( -h - sqrt(h^2 - 1) )t[w]) b ! u(t+dt) = exp( -h + sqrt(h^2 - 1) )(t+dt)[w]) a ! + exp( -h - sqrt(h^2 - 1) )(t+dt)[w]) b ! u(t+dt) = exp(( -h + sqrt(h^2 - 1) )(dt)[w])exp( -h + sqrt(h^2 - 1) )(t)[w]) a ! + exp(( -h - sqrt(h^2 - 1) )(dt)[w])exp( -h - sqrt(h^2 - 1) )(t)[w]) b ! u(t)^{+} := exp( -h + sqrt(h^2 - 1) )(t)[w]) a ! u(t)^{-} := exp( -h - sqrt(h^2 - 1) )(t)[w]) a ! u(t+dt) = exp( -h + sqrt(h^2 - 1)(dt) ) exp([w])u(t)^{+} ! + exp( -h - sqrt(h^2 - 1)(dt) ) exp([w])u(t)^{-} DOF = 2 call coo%init(DOF) call Kmatrix_COO%init(DOF) call Mmatrix_COO%init(DOF) ! create mass-matrix do i=1,DOF-1 call Mmatrix_COO%add(i , i , 0.50d0) call Mmatrix_COO%add(i , i+1, 0.50d0) call Mmatrix_COO%add(i+1, i , 0.50d0) call Mmatrix_COO%add(i+1, i+1, 0.50d0) enddo ! create stiffness-matrix do i=1,DOF-1 K = 9.0d0 call Kmatrix_COO%add(i , i , K) call Kmatrix_COO%add(i , i+1, - K) call Kmatrix_COO%add(i+1, i , - K) call Kmatrix_COO%add(i+1, i+1, K) enddo Mmatrix = Mmatrix_COO%to_CRS() Kmatrix = Kmatrix_COO%to_CRS() crs = Kmatrix%divide_by(diag_vector=Mmatrix%diag(cell_centered=.true.)) !do i=1,DOF ! if(i<DOF/2)then ! K = 100.0d0 ! else ! K = 10.0d0 ! endif ! call coo%add(i , i , K) ! call coo%add(i , i+1, - K) ! call coo%add(i+1, i , - K) ! call coo%add(i+1, i+1, K) !enddo !crs = coo%to_crs() ! u(+) u_p = zeros(DOF) u_p(DOF) = 0.50d0 !u_p(DOF) = 20.d0 ! u(-) u_m = zeros(DOF) u_m(DOF) = 0.50d0 !u_m(DOF) = 20.d0 ! f force = zeros(DOF) force(DOF) = 1.0d0 b_c_spring = 100000.0d0 damping_coeff = 100.0d0 u = zeros(DOF) u(DOF)=1.0d0 ! parameters dt = 1.0d0/10.0d0 h = 0.010d0 if(h<1.0d0)then alpha = sqrt(sqrt(abs(1.0d0-h*h)))*math%i else alpha = sqrt(h*h-1.0d0) endif call f%open("result.txt","w") allocate(point(DOF)) do i=1,DOF call point(i)%create("Cube3D",x_num=2,y_num=2,z_num=2) call point(i)%resize(x=0.80d0,y=0.80d0,z=0.80d0) call point(i)%move(z=(i-1)*2.0d0) enddo !call Kmatrix%fix(idx=[1],RHS=Force,val=[0.0d0]) K_inv_F = 0.0d0*Force/K !call Kmatrix%BiCGSTAB(x=K_inv_F,b=Force) !print *, dt*(timestep-1), abs(u) write(f%fh,*) dt*(0), dble(u),imag(u) do timestep=1,1000 !u(t) = exp(dt*(sqrt(h*h-1)-h ) )exp([w])u(+) + exp(dt*(-sqrt(h*h-1)-h ) )exp([w])u(-) !print *, dt*timestep, exp(dt*sqrt(dcmplx(h*h-1)) - dt*h ) print *, timestep !Force(1) = -b_c_spring*dble(u_p(1)+u_m(1) ) - damping_coeff*dble(- u(1) + u_p(1) + u_m(1))/dt if(timestep>=100) then K_inv_F=0.0d0 endif fix_disp = 0.0d0 u_p = crs%tensor_exp_sqrt(v=u_p,& tol = dble(1.0e-10),coeff= dt*alpha - dt*h,& itrmax=100,fix_idx=[1],fix_val=[0.0d0*math%i])+K_inv_F/2.0d0 u_m = crs%tensor_exp_sqrt(v=u_m,& tol = dble(1.0e-10),coeff=-dt*alpha - dt*h,& itrmax=100,fix_idx=[1],fix_val=[0.0d0*math%i])+K_inv_F/2.0d0 ! post processing do i=1,DOF call point(i)%move(x=dble(- u(i) + u_p(i) + u_m(i)) ) enddo u = u_p + u_m do i=1,DOF call point(i)%vtk("result_p"+str(i)+"_"+zfill(timestep,6) ) enddo !print *, dt*(timestep-1), abs(u) write(f%fh,*) dt*(timestep), dble(u),imag(u) enddo call f%close() ! eigen frequency is ! 1/2*pi*(k/m)^0.5 = 1/2*pi*(9)^0.5 = 1.5/3.1415... = 0.47746... (Hz) ! T = 2.09439... sec end program main