Actual source code: ex54f.F90
1: !
2: ! Description: Solve Ax=b. A comes from an anisotropic 2D thermal problem with Q1 FEM on domain (-1,1)^2.
3: ! Material conductivity given by tensor:
4: !
5: ! D = | 1 0 |
6: ! | 0 epsilon |
7: !
8: ! rotated by angle 'theta' (-theta <90> in degrees) with anisotropic parameter 'epsilon' (-epsilon <0.0>).
9: ! Blob right hand side centered at C (-blob_center C(1),C(2) <0,0>)
10: ! Dirichlet BCs on y=-1 face.
11: !
12: ! -out_matlab will generate binary files for A,x,b and a ex54f.m file that reads them and plots them in matlab.
13: !
14: ! User can change anisotropic shape with function ex54_psi(). Negative theta will switch to a circular anisotropy.
15: !
17: ! -----------------------------------------------------------------------
18: program main
19: #include <petsc/finclude/petscksp.h>
20: use petscksp
21: implicit none
23: Vec xvec,bvec,uvec
24: Mat Amat
25: KSP ksp
26: PetscErrorCode ierr
27: PetscViewer viewer
28: PetscInt qj,qi,ne,M,Istart,Iend,geq
29: PetscInt ki,kj,nel,ll,j1,i1,ndf,f4
30: PetscInt f2,f9,f6,one
31: PetscInt :: idx(4)
32: PetscBool flg,out_matlab
33: PetscMPIInt size,rank
34: PetscScalar::ss(4,4),val
35: PetscReal::shp(3,9),sg(3,9)
36: PetscReal::thk,a1,a2
37: PetscReal, external :: ex54_psi
38: PetscReal::theta,eps,h,x,y,xsj
39: PetscReal::coord(2,4),dd(2,2),ev(3),blb(2)
41: common /ex54_theta/ theta
42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43: ! Beginning of program
44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
46: if (ierr .ne. 0) then
47: print*,'Unable to initialize PETSc'
48: stop
49: endif
50: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
51: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
52: one = 1
53: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
54: ! set parameters
55: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
56: f4 = 4
57: f2 = 2
58: f9 = 9
59: f6 = 6
60: ne = 9
61: call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-ne',ne,flg,ierr)
62: h = 2.0/real(ne)
63: M = (ne+1)*(ne+1)
64: theta = 90.0
65: ! theta is input in degrees
66: call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-theta',theta,flg,ierr)
67: theta = theta / 57.2957795
68: eps = 1.0
69: call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-epsilon',eps,flg,ierr)
70: ki = 2
71: call PetscOptionsGetRealArray(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-blob_center',blb,ki,flg,ierr)
72: if (.not. flg) then
73: blb(1) = 0.0
74: blb(2) = 0.0
75: else if (ki .ne. 2) then
76: print *, 'error: ', ki,' arguments read for -blob_center. Needs to be two.'
77: endif
78: call PetscOptionsGetBool(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-out_matlab',out_matlab,flg,ierr)
79: if (.not.flg) out_matlab = PETSC_FALSE;
81: ev(1) = 1.0
82: ev(2) = eps*ev(1)
83: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: ! Compute the matrix and right-hand-side vector that define
85: ! the linear system, Ax = b.
86: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: ! Create matrix. When using MatCreate(), the matrix format can
88: ! be specified at runtime.
89: call MatCreate(PETSC_COMM_WORLD,Amat,ierr)
90: call MatSetSizes( Amat,PETSC_DECIDE, PETSC_DECIDE, M, M, ierr)
91: call MatSetType( Amat, MATAIJ, ierr)
92: call MatSetOption(Amat,MAT_SPD,PETSC_TRUE,ierr)
93: if (size == 1) then
94: call MatSetType( Amat, MATAIJ, ierr)
95: else
96: call MatSetType( Amat, MATMPIAIJ, ierr)
97: endif
98: call MatMPIAIJSetPreallocation(Amat,f9,PETSC_NULL_INTEGER,f6,PETSC_NULL_INTEGER, ierr)
99: call MatSetFromOptions( Amat, ierr)
100: call MatSetUp( Amat, ierr)
101: call MatGetOwnershipRange( Amat, Istart, Iend, ierr)
102: ! Create vectors. Note that we form 1 vector from scratch and
103: ! then duplicate as needed.
104: call MatCreateVecs( Amat, PETSC_NULL_VEC, xvec, ierr)
105: call VecSetFromOptions( xvec, ierr)
106: call VecDuplicate( xvec, bvec, ierr)
107: call VecDuplicate( xvec, uvec, ierr)
108: ! Assemble matrix.
109: ! - Note that MatSetValues() uses 0-based row and column numbers
110: ! in Fortran as well as in C (as set here in the array "col").
111: thk = 1.0 ! thickness
112: nel = 4 ! nodes per element (quad)
113: ndf = 1
114: call int2d(f2,sg)
115: do geq=Istart,Iend-1,1
116: qj = geq/(ne+1); qi = mod(geq,(ne+1))
117: x = h*qi - 1.0; y = h*qj - 1.0 ! lower left corner (-1,-1)
118: if (qi < ne .and. qj < ne) then
119: coord(1,1) = x; coord(2,1) = y
120: coord(1,2) = x+h; coord(2,2) = y
121: coord(1,3) = x+h; coord(2,3) = y+h
122: coord(1,4) = x; coord(2,4) = y+h
123: ! form stiff
124: ss = 0.0
125: do ll = 1,4
126: call shp2dquad(sg(1,ll),sg(2,ll),coord,shp,xsj,f2)
127: xsj = xsj*sg(3,ll)*thk
128: call thfx2d(ev,coord,shp,dd,f2,f2,f4,ex54_psi)
129: j1 = 1
130: do kj = 1,nel
131: a1 = (dd(1,1)*shp(1,kj) + dd(1,2)*shp(2,kj))*xsj
132: a2 = (dd(2,1)*shp(1,kj) + dd(2,2)*shp(2,kj))*xsj
133: ! Compute residual
134: ! p(j1) = p(j1) - a1*gradt(1) - a2*gradt(2)
135: ! Compute tangent
136: i1 = 1
137: do ki = 1,nel
138: ss(i1,j1) = ss(i1,j1) + a1*shp(1,ki) + a2*shp(2,ki)
139: i1 = i1 + ndf
140: end do
141: j1 = j1 + ndf
142: end do
143: enddo
145: idx(1) = geq; idx(2) = geq+1; idx(3) = geq+(ne+1)+1
146: idx(4) = geq+(ne+1)
147: if (qj > 0) then
148: call MatSetValues(Amat,f4,idx,f4,idx,ss,ADD_VALUES,ierr)
149: else ! a BC
150: do ki=1,4,1
151: do kj=1,4,1
152: if (ki<3 .or. kj<3) then
153: if (ki==kj) then
154: ss(ki,kj) = .1*ss(ki,kj)
155: else
156: ss(ki,kj) = 0.0
157: endif
158: endif
159: enddo
160: enddo
161: call MatSetValues(Amat,f4,idx,f4,idx,ss,ADD_VALUES,ierr)
162: endif ! BC
163: endif ! add element
164: if (qj > 0) then ! set rhs
165: val = h*h*exp(-100*((x+h/2)-blb(1))**2)*exp(-100*((y+h/2)-blb(2))**2)
166: call VecSetValues(bvec,one,geq,val,INSERT_VALUES,ierr)
167: endif
168: enddo
169: call MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY,ierr)
170: call MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY,ierr)
171: call VecAssemblyBegin(bvec,ierr)
172: call VecAssemblyEnd(bvec,ierr)
174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: ! Create the linear solver and set various options
176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: ! Create linear solver context
180: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
182: ! Set operators. Here the matrix that defines the linear system
183: ! also serves as the preconditioning matrix.
185: call KSPSetOperators(ksp,Amat,Amat,ierr)
187: ! Set runtime options, e.g.,
188: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
189: ! These options will override those specified above as long as
190: ! KSPSetFromOptions() is called _after_ any other customization
191: ! routines.
193: call KSPSetFromOptions(ksp,ierr)
195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: ! Solve the linear system
197: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: call KSPSolve(ksp,bvec,xvec,ierr)
200: CHKERRA(ierr)
202: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203: ! output
204: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: if (out_matlab) then
206: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Amat',FILE_MODE_WRITE,viewer,ierr)
207: call MatView(Amat,viewer,ierr)
208: call PetscViewerDestroy(viewer,ierr)
210: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Bvec',FILE_MODE_WRITE,viewer,ierr)
211: call VecView(bvec,viewer,ierr)
212: call PetscViewerDestroy(viewer,ierr)
214: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Xvec',FILE_MODE_WRITE,viewer,ierr)
215: call VecView(xvec,viewer,ierr)
216: call PetscViewerDestroy(viewer,ierr)
218: call MatMult(Amat,xvec,uvec,ierr)
219: val = -1.0
220: call VecAXPY(uvec,val,bvec,ierr)
221: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Rvec',FILE_MODE_WRITE,viewer,ierr)
222: call VecView(uvec,viewer,ierr)
223: call PetscViewerDestroy(viewer,ierr)
225: if (rank == 0) then
226: open(1,file='ex54f.m', FORM='formatted')
227: write (1,*) 'A = PetscBinaryRead(''Amat'');'
228: write (1,*) '[m n] = size(A);'
229: write (1,*) 'mm = sqrt(m);'
230: write (1,*) 'b = PetscBinaryRead(''Bvec'');'
231: write (1,*) 'x = PetscBinaryRead(''Xvec'');'
232: write (1,*) 'r = PetscBinaryRead(''Rvec'');'
233: write (1,*) 'bb = reshape(b,mm,mm);'
234: write (1,*) 'xx = reshape(x,mm,mm);'
235: write (1,*) 'rr = reshape(r,mm,mm);'
236: ! write (1,*) 'imagesc(bb')'
237: ! write (1,*) 'title('RHS'),'
238: write (1,*) 'figure,'
239: write (1,*) 'imagesc(xx'')'
240: write (1,2002) eps,theta*57.2957795
241: write (1,*) 'figure,'
242: write (1,*) 'imagesc(rr'')'
243: write (1,*) 'title(''Residual''),'
244: close(1)
245: endif
246: endif
247: 2002 format('title(''Solution: esp='',d9.3,'', theta='',g8.3,''),')
248: ! Free work space. All PETSc objects should be destroyed when they
249: ! are no longer needed.
251: call VecDestroy(xvec,ierr)
252: call VecDestroy(bvec,ierr)
253: call VecDestroy(uvec,ierr)
254: call MatDestroy(Amat,ierr)
255: call KSPDestroy(ksp,ierr)
256: call PetscFinalize(ierr)
258: end
260: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
261: ! thfx2d - compute material tensor
262: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
263: ! Compute thermal gradient and flux
265: subroutine thfx2d(ev,xl,shp,dd,ndm,ndf,nel,dir)
266: implicit none
268: PetscInt ndm,ndf,nel,i
269: PetscReal ev(2),xl(ndm,nel),shp(3,*),dir
270: PetscReal xx,yy,psi,cs,sn,c2,s2,dd(2,2)
272: xx = 0.0
273: yy = 0.0
274: do i = 1,nel
275: xx = xx + shp(3,i)*xl(1,i)
276: yy = yy + shp(3,i)*xl(2,i)
277: end do
278: psi = dir(xx,yy)
279: ! Compute thermal flux
280: cs = cos(psi)
281: sn = sin(psi)
282: c2 = cs*cs
283: s2 = sn*sn
284: cs = cs*sn
286: dd(1,1) = c2*ev(1) + s2*ev(2)
287: dd(2,2) = s2*ev(1) + c2*ev(2)
288: dd(1,2) = cs*(ev(1) - ev(2))
289: dd(2,1) = dd(1,2)
291: ! flux(1) = -dd(1,1)*gradt(1) - dd(1,2)*gradt(2)
292: ! flux(2) = -dd(2,1)*gradt(1) - dd(2,2)*gradt(2)
294: end
296: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297: ! shp2dquad - shape functions - compute derivatives w/r natural coords.
298: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
299: subroutine shp2dquad(s,t,xl,shp,xsj,ndm)
300: !-----[--.----+----.----+----.-----------------------------------------]
301: ! Purpose: Shape function routine for 4-node isoparametric quads
302: !
303: ! Inputs:
304: ! s,t - Natural coordinates of point
305: ! xl(ndm,*) - Nodal coordinates for element
306: ! ndm - Spatial dimension of mesh
308: ! Outputs:
309: ! shp(3,*) - Shape functions and derivatives at point
310: ! shp(1,i) = dN_i/dx or dN_i/dxi_1
311: ! shp(2,i) = dN_i/dy or dN_i/dxi_2
312: ! shp(3,i) = N_i
313: ! xsj - Jacobian determinant at point
314: !-----[--.----+----.----+----.-----------------------------------------]
315: implicit none
316: PetscInt ndm
317: PetscReal xo,xs,xt, yo,ys,yt, xsm,xsp,xtm
318: PetscReal xtp, ysm,ysp,ytm,ytp
319: PetscReal s,t, xsj,xsj1, sh,th,sp,tp,sm
320: PetscReal tm, xl(ndm,4),shp(3,4)
322: ! Set up interpolations
324: sh = 0.5*s
325: th = 0.5*t
326: sp = 0.5 + sh
327: tp = 0.5 + th
328: sm = 0.5 - sh
329: tm = 0.5 - th
330: shp(3,1) = sm*tm
331: shp(3,2) = sp*tm
332: shp(3,3) = sp*tp
333: shp(3,4) = sm*tp
335: ! Set up natural coordinate functions (times 4)
337: xo = xl(1,1)-xl(1,2)+xl(1,3)-xl(1,4)
338: xs = -xl(1,1)+xl(1,2)+xl(1,3)-xl(1,4) + xo*t
339: xt = -xl(1,1)-xl(1,2)+xl(1,3)+xl(1,4) + xo*s
340: yo = xl(2,1)-xl(2,2)+xl(2,3)-xl(2,4)
341: ys = -xl(2,1)+xl(2,2)+xl(2,3)-xl(2,4) + yo*t
342: yt = -xl(2,1)-xl(2,2)+xl(2,3)+xl(2,4) + yo*s
344: ! Compute jacobian (times 16)
346: xsj1 = xs*yt - xt*ys
348: ! Divide jacobian by 16 (multiply by .0625)
350: xsj = 0.0625*xsj1
351: if (xsj1.eq.0.0) then
352: xsj1 = 1.0
353: else
354: xsj1 = 1.0/xsj1
355: endif
357: ! Divide functions by jacobian
359: xs = (xs+xs)*xsj1
360: xt = (xt+xt)*xsj1
361: ys = (ys+ys)*xsj1
362: yt = (yt+yt)*xsj1
364: ! Multiply by interpolations
366: ytm = yt*tm
367: ysm = ys*sm
368: ytp = yt*tp
369: ysp = ys*sp
370: xtm = xt*tm
371: xsm = xs*sm
372: xtp = xt*tp
373: xsp = xs*sp
375: ! Compute shape functions
377: shp(1,1) = - ytm+ysm
378: shp(1,2) = ytm+ysp
379: shp(1,3) = ytp-ysp
380: shp(1,4) = - ytp-ysm
381: shp(2,1) = xtm-xsm
382: shp(2,2) = - xtm-xsp
383: shp(2,3) = - xtp+xsp
384: shp(2,4) = xtp+xsm
386: end
388: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
389: ! int2d
390: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
391: subroutine int2d(l,sg)
392: !-----[--.----+----.----+----.-----------------------------------------]
393: ! Purpose: Form Gauss points and weights for two dimensions
395: ! Inputs:
396: ! l - Number of points/direction
398: ! Outputs:
399: ! sg(3,*) - Array of points and weights
400: !-----[--.----+----.----+----.-----------------------------------------]
401: implicit none
402: PetscInt l,i,lr(9),lz(9)
403: PetscReal g,third,sg(3,*)
404: data lr/-1,1,1,-1,0,1,0,-1,0/,lz/-1,-1,1,1,-1,0,1,0,0/
405: data third / 0.3333333333333333 /
407: ! 2x2 integration
408: g = sqrt(third)
409: do i = 1,4
410: sg(1,i) = g*lr(i)
411: sg(2,i) = g*lz(i)
412: sg(3,i) = 1.0
413: end do
415: end
417: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
418: ! ex54_psi - anusotropic material direction
419: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
420: PetscReal function ex54_psi(x,y)
421: implicit none
422: PetscReal x,y,theta
423: common /ex54_theta/ theta
424: ex54_psi = theta
425: if (theta < 0.) then ! circular
426: if (y==0) then
427: ex54_psi = 2.0*atan(1.0)
428: else
429: ex54_psi = atan(-x/y)
430: endif
431: endif
432: end
434: !
435: !/*TEST
436: !
437: ! build:
438: !
439: ! test:
440: ! nsize: 4
441: ! args: -ne 39 -theta 30.0 -epsilon 1.e-1 -blob_center 0.,0. -ksp_type cg -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mat_coarsen_type hem -pc_gamg_square_graph 0 -ksp_monitor_short -pc_gamg_esteig_ksp_max_it 5
442: ! requires: !single
443: !
444: !TEST*/