Neko  0.8.99
A portable framework for high-order spectral element flow simulations
gmres.f90
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34 module gmres
35  use krylov, only : ksp_t, ksp_monitor_t
36  use precon, only : pc_t
37  use ax_product, only : ax_t
38  use num_types, only: rp, xp
39  use field, only : field_t
40  use coefs, only : coef_t
41  use gather_scatter, only : gs_t, gs_op_add
42  use bc, only : bc_list_t, bc_list_apply
43  use math, only : glsc3, rzero, rone, copy, sub2, cmult2, abscmp
44  use comm
45  implicit none
46  private
47 
49  type, public, extends(ksp_t) :: gmres_t
50  integer :: lgmres
51  real(kind=rp), allocatable :: w(:)
52  real(kind=rp), allocatable :: r(:)
53  real(kind=rp), allocatable :: z(:,:)
54  real(kind=rp), allocatable :: v(:,:)
56  real(kind=xp), allocatable :: h(:,:)
57  real(kind=xp), allocatable :: s(:)
58  real(kind=xp), allocatable :: gam(:)
59  real(kind=xp), allocatable :: c(:)
60  contains
61  procedure, pass(this) :: init => gmres_init
62  procedure, pass(this) :: free => gmres_free
63  procedure, pass(this) :: solve => gmres_solve
64  procedure, pass(this) :: solve_coupled => gmres_solve_coupled
65  end type gmres_t
66 
67 contains
68 
70  subroutine gmres_init(this, n, max_iter, M, lgmres, &
71  rel_tol, abs_tol, monitor)
72  class(gmres_t), intent(inout) :: this
73  integer, intent(in) :: n
74  integer, intent(in) :: max_iter
75  class(pc_t), optional, intent(in), target :: M
76  integer, optional, intent(in) :: lgmres
77  real(kind=rp), optional, intent(in) :: rel_tol
78  real(kind=rp), optional, intent(in) :: abs_tol
79  logical, optional, intent(in) :: monitor
80 
81  if (present(lgmres)) then
82  this%lgmres = lgmres
83  else
84  this%lgmres = 30
85  end if
86 
87 
88  call this%free()
89 
90  if (present(m)) then
91  this%M => m
92  end if
93 
94  allocate(this%w(n))
95  allocate(this%r(n))
96 
97  allocate(this%c(this%lgmres))
98  allocate(this%s(this%lgmres))
99  allocate(this%gam(this%lgmres + 1))
100 
101  allocate(this%z(n, this%lgmres))
102  allocate(this%v(n, this%lgmres))
103 
104  allocate(this%h(this%lgmres, this%lgmres))
105 
106  if (present(rel_tol) .and. present(abs_tol) .and. present(monitor)) then
107  call this%ksp_init(max_iter, rel_tol, abs_tol, monitor = monitor)
108  else if (present(rel_tol) .and. present(abs_tol)) then
109  call this%ksp_init(max_iter, rel_tol, abs_tol)
110  else if (present(monitor) .and. present(abs_tol)) then
111  call this%ksp_init(max_iter, abs_tol = abs_tol, monitor = monitor)
112  else if (present(rel_tol) .and. present(monitor)) then
113  call this%ksp_init(max_iter, rel_tol, monitor = monitor)
114  else if (present(rel_tol)) then
115  call this%ksp_init(max_iter, rel_tol = rel_tol)
116  else if (present(abs_tol)) then
117  call this%ksp_init(max_iter, abs_tol = abs_tol)
118  else if (present(monitor)) then
119  call this%ksp_init(max_iter, monitor = monitor)
120  else
121  call this%ksp_init(max_iter)
122  end if
123 
124  end subroutine gmres_init
125 
127  subroutine gmres_free(this)
128  class(gmres_t), intent(inout) :: this
129 
130  call this%ksp_free()
131 
132  if (allocated(this%w)) then
133  deallocate(this%w)
134  end if
135 
136  if (allocated(this%c)) then
137  deallocate(this%c)
138  end if
139 
140  if (allocated(this%r)) then
141  deallocate(this%r)
142  end if
143 
144  if (allocated(this%z)) then
145  deallocate(this%z)
146  end if
147 
148  if (allocated(this%h)) then
149  deallocate(this%h)
150  end if
151 
152  if (allocated(this%v)) then
153  deallocate(this%v)
154  end if
155 
156  if (allocated(this%s)) then
157  deallocate(this%s)
158  end if
159 
160 
161  if (allocated(this%gam)) then
162  deallocate(this%gam)
163  end if
164 
165  nullify(this%M)
166 
167  end subroutine gmres_free
168 
170  function gmres_solve(this, Ax, x, f, n, coef, blst, gs_h, niter) &
171  result(ksp_results)
172  class(gmres_t), intent(inout) :: this
173  class(ax_t), intent(in) :: ax
174  type(field_t), intent(inout) :: x
175  integer, intent(in) :: n
176  real(kind=rp), dimension(n), intent(in) :: f
177  type(coef_t), intent(inout) :: coef
178  type(bc_list_t), intent(in) :: blst
179  type(gs_t), intent(inout) :: gs_h
180  type(ksp_monitor_t) :: ksp_results
181  integer, optional, intent(in) :: niter
182  integer :: iter, max_iter
183  integer :: i, j, k, l, ierr
184  real(kind=xp) :: w_plus(neko_blk_size), x_plus(neko_blk_size)
185  real(kind=xp) :: alpha, lr, alpha2, norm_fac
186  real(kind=rp) :: temp, rnorm
187  logical :: conv
188 
189  conv = .false.
190  iter = 0
191 
192  if (present(niter)) then
193  max_iter = niter
194  else
195  max_iter = this%max_iter
196  end if
197 
198  associate(w => this%w, c => this%c, r => this%r, z => this%z, h => this%h, &
199  v => this%v, s => this%s, gam => this%gam)
200 
201  norm_fac = 1.0_rp / sqrt(coef%volume)
202  call rzero(x%x, n)
203  gam = 0.0_xp
204  s = 1.0_xp
205  c = 1.0_xp
206  h = 0.0_xp
207  call this%monitor_start('GMRES')
208  do while (.not. conv .and. iter .lt. max_iter)
209 
210  if (iter .eq. 0) then
211  call copy(r, f, n)
212  else
213  call copy(r, f, n)
214  call ax%compute(w, x%x, coef, x%msh, x%Xh)
215  call gs_h%op(w, n, gs_op_add)
216  call bc_list_apply(blst, w, n)
217  call sub2(r, w, n)
218  end if
219 
220  gam(1) = sqrt(glsc3(r, r, coef%mult, n))
221  if (iter .eq. 0) then
222  ksp_results%res_start = gam(1) * norm_fac
223  end if
224 
225  if (abscmp(gam(1), 0.0_xp)) return
226 
227  rnorm = 0.0_rp
228  temp = 1.0_rp / gam(1)
229  call cmult2(v(1,1), r, temp, n)
230  do j = 1, this%lgmres
231  iter = iter+1
232 
233  call this%M%solve(z(1,j), v(1,j), n)
234 
235  call ax%compute(w, z(1,j), coef, x%msh, x%Xh)
236  call gs_h%op(w, n, gs_op_add)
237  call bc_list_apply(blst, w, n)
238 
239  do l = 1, j
240  h(l,j) = 0.0_rp
241  end do
242 
243  do i = 0, n, neko_blk_size
244  if (i + neko_blk_size .le. n) then
245  do l = 1, j
246  do k = 1, neko_blk_size
247  h(l,j) = h(l,j) + &
248  w(i+k) * v(i+k,l) * coef%mult(i+k,1,1,1)
249  end do
250  end do
251  else
252  do k = 1, n-i
253  do l = 1, j
254  h(l,j) = h(l,j) + &
255  w(i+k) * v(i+k,l) * coef%mult(i+k,1,1,1)
256  end do
257  end do
258  end if
259  end do
260 
261  call mpi_allreduce(mpi_in_place, h(1,j), j, &
262  mpi_extra_precision, mpi_sum, neko_comm, ierr)
263 
264  alpha2 = 0.0_rp
265  do i = 0, n, neko_blk_size
266  if (i + neko_blk_size .le. n) then
267  do k = 1, neko_blk_size
268  w_plus(k) = 0.0_rp
269  end do
270  do l = 1,j
271  do k = 1, neko_blk_size
272  w_plus(k) = w_plus(k) - h(l,j) * v(i+k,l)
273  end do
274  end do
275  do k = 1, neko_blk_size
276  w(i+k) = w(i+k) + w_plus(k)
277  alpha2 = alpha2 + w(i+k)**2 * coef%mult(i+k,1,1,1)
278  end do
279  else
280  do k = 1, n-i
281  w_plus(1) = 0.0_rp
282  do l = 1, j
283  w_plus(1) = w_plus(1) - h(l,j) * v(i+k,l)
284  end do
285  w(i+k) = w(i+k) + w_plus(1)
286  alpha2 = alpha2 + (w(i+k)**2) * coef%mult(i+k,1,1,1)
287  end do
288  end if
289  end do
290 
291  call mpi_allreduce(mpi_in_place,alpha2, 1, &
292  mpi_extra_precision, mpi_sum, neko_comm, ierr)
293  alpha = sqrt(alpha2)
294  do i = 1, j-1
295  temp = h(i,j)
296  h(i,j) = c(i)*temp + s(i) * h(i+1,j)
297  h(i+1,j) = -s(i)*temp + c(i) * h(i+1,j)
298  end do
299 
300  rnorm = 0.0_rp
301  if (abscmp(alpha, 0.0_xp)) then
302  conv = .true.
303  exit
304  end if
305 
306  lr = sqrt(h(j,j) * h(j,j) + alpha2)
307  temp = 1.0_rp / lr
308  c(j) = h(j,j) * temp
309  s(j) = alpha * temp
310  h(j,j) = lr
311  gam(j+1) = -s(j) * gam(j)
312  gam(j) = c(j) * gam(j)
313  rnorm = abs(gam(j+1)) * norm_fac
314  call this%monitor_iter(iter, rnorm)
315  if (rnorm .lt. this%abs_tol) then
316  conv = .true.
317  exit
318  end if
319 
320  if (iter + 1 .gt. max_iter) exit
321 
322  if (j .lt. this%lgmres) then
323  temp = 1.0_rp / alpha
324  call cmult2(v(1,j+1), w, temp, n)
325  end if
326 
327  end do
328 
329  j = min(j, this%lgmres)
330  do k = j, 1, -1
331  temp = gam(k)
332  do i = j, k+1, -1
333  temp = temp - h(k,i) * c(i)
334  end do
335  c(k) = temp / h(k,k)
336  end do
337 
338  do i = 0, n, neko_blk_size
339  if (i + neko_blk_size .le. n) then
340  do k = 1, neko_blk_size
341  x_plus(k) = 0.0_rp
342  end do
343  do l = 1,j
344  do k = 1, neko_blk_size
345  x_plus(k) = x_plus(k) + c(l) * z(i+k,l)
346  end do
347  end do
348  do k = 1, neko_blk_size
349  x%x(i+k,1,1,1) = x%x(i+k,1,1,1) + x_plus(k)
350  end do
351  else
352  do k = 1, n-i
353  x_plus(1) = 0.0_rp
354  do l = 1, j
355  x_plus(1) = x_plus(1) + c(l) * z(i+k,l)
356  end do
357  x%x(i+k,1,1,1) = x%x(i+k,1,1,1) + x_plus(1)
358  end do
359  end if
360  end do
361  end do
362 
363  end associate
364  call this%monitor_stop()
365  ksp_results%res_final = rnorm
366  ksp_results%iter = iter
367 
368  end function gmres_solve
369 
371  function gmres_solve_coupled(this, Ax, x, y, z, fx, fy, fz, &
372  n, coef, blstx, blsty, blstz, gs_h, niter) result(ksp_results)
373  class(gmres_t), intent(inout) :: this
374  class(ax_t), intent(in) :: ax
375  type(field_t), intent(inout) :: x
376  type(field_t), intent(inout) :: y
377  type(field_t), intent(inout) :: z
378  integer, intent(in) :: n
379  real(kind=rp), dimension(n), intent(in) :: fx
380  real(kind=rp), dimension(n), intent(in) :: fy
381  real(kind=rp), dimension(n), intent(in) :: fz
382  type(coef_t), intent(inout) :: coef
383  type(bc_list_t), intent(in) :: blstx
384  type(bc_list_t), intent(in) :: blsty
385  type(bc_list_t), intent(in) :: blstz
386  type(gs_t), intent(inout) :: gs_h
387  type(ksp_monitor_t), dimension(3) :: ksp_results
388  integer, optional, intent(in) :: niter
389 
390  ksp_results(1) = this%solve(ax, x, fx, n, coef, blstx, gs_h, niter)
391  ksp_results(2) = this%solve(ax, y, fy, n, coef, blsty, gs_h, niter)
392  ksp_results(3) = this%solve(ax, z, fz, n, coef, blstz, gs_h, niter)
393 
394  end function gmres_solve_coupled
395 
396 end module gmres
397 
398 
Defines a Matrix-vector product.
Definition: ax.f90:34
Defines a boundary condition.
Definition: bc.f90:34
Coefficients.
Definition: coef.f90:34
Definition: comm.F90:1
type(mpi_comm) neko_comm
MPI communicator.
Definition: comm.F90:16
type(mpi_datatype) mpi_extra_precision
Definition: comm.F90:24
Defines a field.
Definition: field.f90:34
Gather-scatter.
Defines various GMRES methods.
Definition: gmres.f90:34
type(ksp_monitor_t) function, dimension(3) gmres_solve_coupled(this, Ax, x, y, z, fx, fy, fz, n, coef, blstx, blsty, blstz, gs_h, niter)
Standard GMRES coupled solve.
Definition: gmres.f90:373
subroutine gmres_free(this)
Deallocate a standard GMRES solver.
Definition: gmres.f90:128
subroutine gmres_init(this, n, max_iter, M, lgmres, rel_tol, abs_tol, monitor)
Initialise a standard GMRES solver.
Definition: gmres.f90:72
type(ksp_monitor_t) function gmres_solve(this, Ax, x, f, n, coef, blst, gs_h, niter)
Standard GMRES solve.
Definition: gmres.f90:172
Implements the base abstract type for Krylov solvers plus helper types.
Definition: krylov.f90:34
Definition: math.f90:60
subroutine, public cmult2(a, b, c, n)
Multiplication by constant c .
Definition: math.f90:701
real(kind=rp) function, public glsc3(a, b, c, n)
Weighted inner product .
Definition: math.f90:895
subroutine, public rone(a, n)
Set all elements to one.
Definition: math.f90:228
subroutine, public copy(a, b, n)
Copy a vector .
Definition: math.f90:239
subroutine, public rzero(a, n)
Zero a real vector.
Definition: math.f90:195
subroutine, public sub2(a, b, n)
Vector substraction .
Definition: math.f90:629
integer, parameter, public xp
Definition: num_types.f90:14
integer, parameter, public rp
Global precision used in computations.
Definition: num_types.f90:12
Krylov preconditioner.
Definition: precon.f90:34
Base type for a matrix-vector product providing .
Definition: ax.f90:43
A list of boundary conditions.
Definition: bc.f90:104
Coefficients defined on a given (mesh, ) tuple. Arrays use indices (i,j,k,e): element e,...
Definition: coef.f90:55
Standard preconditioned generalized minimal residual method.
Definition: gmres.f90:49
Type for storing initial and final residuals in a Krylov solver.
Definition: krylov.f90:56
Base abstract type for a canonical Krylov method, solving .
Definition: krylov.f90:66
Defines a canonical Krylov preconditioner.
Definition: precon.f90:40