Actual source code: ex54f.F
petsc-3.5.4 2015-05-23
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: !
16: !/*T
17: ! Concepts: KSP^solving a system of linear equations
18: !T*/
19: ! -----------------------------------------------------------------------
20: program main
21: implicit none
22: #include <finclude/petscsys.h>
23: #include <finclude/petscvec.h>
24: #include <finclude/petscmat.h>
25: #include <finclude/petscksp.h>
26: #include <finclude/petscpc.h>
27: #include <finclude/petscviewer.h>
28: #include <finclude/petscviewer.h90>
29: Vec xvec,bvec,uvec
30: Mat Amat
31: KSP ksp
32: PC pc
33: PetscErrorCode ierr
34: PetscViewer viewer
35: PetscInt qj,qi,ne,M,Istart,Iend,geq,ix
36: PetscInt ki,kj,lint,nel,ll,j1,i1,ndf
37: PetscInt :: idx(4)
38: PetscBool flg,out_matlab
39: PetscMPIInt npe,mype
40: PetscScalar::ss(4,4),res(4),val
41: PetscReal::shp(3,9),sg(3,9),flux(2)
42: PetscReal::thk,a1,a2
43: PetscReal, external :: ex54_psi
44: PetscReal::norm,tol,theta,eps,h,x,y,xsj
45: PetscReal::coord(2,4),dd(2,2),ev(3),blb(2)
47: common /ex54_theta/ theta
48: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: ! Beginning of program
50: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
52: call MPI_Comm_size(PETSC_COMM_WORLD,npe,ierr)
53: call MPI_Comm_rank(PETSC_COMM_WORLD,mype,ierr)
54: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: ! set parameters
56: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: ne = 9
58: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-ne',ne,flg,ierr)
59: h = 2.d0/ne
60: M = (ne+1)*(ne+1)
61: theta = 90.d0
62: ! theta is input in degrees
63: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-theta',theta,flg,
64: $ ierr)
65: theta = theta / 57.2957795
66: eps = 1.d0
67: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-epsilon',eps,flg,
68: $ ierr)
69: ki = 2
70: call PetscOptionsGetRealArray(PETSC_NULL_CHARACTER,'-blob_center',
71: $ blb,ki,flg,ierr)
72: if ( .not. flg ) then
73: blb(1) = 0.d0
74: blb(2) = 0.d0
75: else if ( ki .ne. 2 ) then
76: print *, 'error: ', ki,
77: $ ' arguments read for -blob_center. Needs to be two.'
78: endif
79: call PetscOptionsGetBool(PETSC_NULL_CHARACTER,'-out_matlab',
80: $ out_matlab,flg,ierr)
81: if (.not.flg) out_matlab = PETSC_FALSE;
83: ev(1) = 1.d0
84: ev(2) = eps*ev(1)
85: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
86: ! Compute the matrix and right-hand-side vector that define
87: ! the linear system, Ax = b.
88: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: ! Create matrix. When using MatCreate(), the matrix format can
90: ! be specified at runtime.
91: call MatCreate(PETSC_COMM_WORLD,Amat,ierr)
92: call MatSetSizes( Amat,PETSC_DECIDE, PETSC_DECIDE, M, M, ierr )
93: if ( npe == 1 ) then
94: call MatSetType( Amat, MATAIJ, ierr )
95: else
96: call MatSetType( Amat, MATMPIAIJ, ierr )
97: endif
98: call MatMPIAIJSetPreallocation(Amat,9,PETSC_NULL_INTEGER,6,
99: $ PETSC_NULL_INTEGER, ierr)
100: call MatSetFromOptions( Amat, ierr )
101: call MatSetUp( Amat, ierr )
102: call MatGetOwnershipRange( Amat, Istart, Iend, ierr )
103: ! Create vectors. Note that we form 1 vector from scratch and
104: ! then duplicate as needed.
105: call MatGetVecs( Amat, PETSC_NULL_OBJECT, xvec, ierr )
106: call VecSetFromOptions( xvec, ierr )
107: call VecDuplicate( xvec, bvec, ierr )
108: call VecDuplicate( xvec, uvec, ierr )
109: ! Assemble matrix.
110: ! - Note that MatSetValues() uses 0-based row and column numbers
111: ! in Fortran as well as in C (as set here in the array "col").
112: thk = 1.d0 ! thickness
113: nel = 4 ! nodes per element (quad)
114: ndf = 1
115: call int2d(2,lint,sg)
116: ix = 0
117: do geq=Istart,Iend-1,1
118: qj = geq/(ne+1); qi = mod(geq,(ne+1))
119: x = h*qi - 1.d0; y = h*qj - 1.d0 ! lower left corner (-1,-1)
120: if ( qi < ne .and. qj < ne ) then
121: coord(1,1) = x; coord(2,1) = y
122: coord(1,2) = x+h; coord(2,2) = y
123: coord(1,3) = x+h; coord(2,3) = y+h
124: coord(1,4) = x; coord(2,4) = y+h
125: ! form stiff
126: ss = 0.d0
127: do ll = 1,lint
128: call shp2dquad(sg(1,ll),sg(2,ll),coord,shp,xsj,2)
129: xsj = xsj*sg(3,ll)*thk
130: call thfx2d(ev,coord,shp,dd,2,2,4,ex54_psi)
131: j1 = 1
132: do kj = 1,nel
133: a1 = (dd(1,1)*shp(1,kj) + dd(1,2)*shp(2,kj))*xsj
134: a2 = (dd(2,1)*shp(1,kj) + dd(2,2)*shp(2,kj))*xsj
135: c Compute residual
136: c p(j1) = p(j1) - a1*gradt(1) - a2*gradt(2)
137: c Compute tangent
138: i1 = 1
139: do ki = 1,nel
140: ss(i1,j1) = ss(i1,j1) + a1*shp(1,ki) + a2*shp(2,ki)
141: i1 = i1 + ndf
142: end do
143: j1 = j1 + ndf
144: end do
145: enddo
147: idx(1) = geq; idx(2) = geq+1; idx(3) = geq+(ne+1)+1
148: idx(4) = geq+(ne+1)
149: if ( qj > 0 ) then
150: call MatSetValues(Amat,4,idx,4,idx,ss,ADD_VALUES,ierr)
151: else ! a BC
152: do ki=1,4,1
153: do kj=1,4,1
154: if (ki<3 .or. kj<3 ) then
155: if ( ki==kj ) then
156: ss(ki,kj) = .1d0*ss(ki,kj)
157: else
158: ss(ki,kj) = 0.d0
159: endif
160: endif
161: enddo
162: enddo
163: call MatSetValues(Amat,4,idx,4,idx,ss,ADD_VALUES,ierr)
164: endif ! BC
165: endif ! add element
166: if ( qj > 0 ) then ! set rhs
168: val = h*h*exp(-1.d2*((x+h/2)-blb(1))**2)*
169: $ exp(-1.d2*((y+h/2)-blb(2))**2)
170: call VecSetValues(bvec,1,geq,val,INSERT_VALUES,ierr)
171: endif
172: enddo
173: call MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY,ierr)
174: call MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY,ierr)
175: call VecAssemblyBegin(bvec,ierr)
176: call VecAssemblyEnd(bvec,ierr)
178: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: ! Create the linear solver and set various options
180: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: ! Create linear solver context
184: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
186: ! Set operators. Here the matrix that defines the linear system
187: ! also serves as the preconditioning matrix.
189: call KSPSetOperators(ksp,Amat,Amat,ierr)
191: ! Set runtime options, e.g.,
192: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
193: ! These options will override those specified above as long as
194: ! KSPSetFromOptions() is called _after_ any other customization
195: ! routines.
197: call KSPSetFromOptions(ksp,ierr)
199: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200: ! Solve the linear system
201: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203: call KSPSolve(ksp,bvec,xvec,ierr)
206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: ! output
208: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: if ( out_matlab ) then
210: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Amat',
211: $ FILE_MODE_WRITE,viewer,ierr)
212: call MatView(Amat,viewer,ierr)
213: call PetscViewerDestroy(viewer,ierr)
215: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Bvec',
216: $ FILE_MODE_WRITE,viewer,ierr)
217: call VecView(bvec,viewer,ierr)
218: call PetscViewerDestroy(viewer,ierr)
220: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Xvec',
221: $ FILE_MODE_WRITE,viewer,ierr)
222: call VecView(xvec,viewer,ierr)
223: call PetscViewerDestroy(viewer,ierr)
225: call MatMult(Amat,xvec,uvec,ierr)
226: val = -1.d0
227: call VecAXPY(uvec,val,bvec,ierr)
228: call PetscViewerBinaryOpen(PETSC_COMM_WORLD,'Rvec',
229: $ FILE_MODE_WRITE,viewer,ierr)
230: call VecView(uvec,viewer,ierr)
231: call PetscViewerDestroy(viewer,ierr)
233: if ( mype == 0 ) then
234: open(1,file="ex54f.m", FORM="formatted")
235: write (1,*) "A = PetscBinaryRead('Amat');"
236: write (1,*) "[m n] = size(A);"
237: write (1,*) "mm = sqrt(m);"
238: write (1,*) "b = PetscBinaryRead('Bvec');"
239: write (1,*) "x = PetscBinaryRead('Xvec');"
240: write (1,*) "r = PetscBinaryRead('Rvec');"
241: write (1,*) "bb = reshape(b,mm,mm);"
242: write (1,*) "xx = reshape(x,mm,mm);"
243: write (1,*) "rr = reshape(r,mm,mm);"
244: c write (1,*) "imagesc(bb')"
245: c write (1,*) "title('RHS'),"
246: write (1,*) "figure,"
247: write (1,*) "imagesc(xx')"
248: write (1,2002) eps,theta*57.2957795
249: write (1,*) "figure,"
250: write (1,*) "imagesc(rr')"
251: write (1,*) "title('Residual'),"
252: close(1)
253: endif
254: endif
255: 2002 format("title('Solution: esp=",d9.3,", theta=",g8.3,"'),")
256: ! Free work space. All PETSc objects should be destroyed when they
257: ! are no longer needed.
259: call VecDestroy(xvec,ierr)
260: call VecDestroy(bvec,ierr)
261: call VecDestroy(uvec,ierr)
262: call MatDestroy(Amat,ierr)
263: call KSPDestroy(ksp,ierr)
264: call PetscFinalize(ierr)
266: end
268: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269: ! thfx2d - compute material tensor
270: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272: subroutine thfx2d(ev,xl,shp,dd,ndm,ndf,nel,dir)
274: c Compute thermal gradient and flux
276: implicit none
278: integer ndm,ndf,nel,i
279: PetscReal ev(2),xl(ndm,nel),shp(3,*),dir
280: PetscReal xx,yy,psi,cs,sn,c2,s2,dd(2,2)
282: c temp = 0.0d0
283: c gradt(1) = 0.0d0
284: c gradt(2) = 0.0d0
285: xx = 0.0d0
286: yy = 0.0d0
287: do i = 1,nel
288: c gradt(1) = gradt(1) + shp(1,i)*ul(1,i)
289: c gradt(2) = gradt(2) + shp(2,i)*ul(1,i)
290: c temp = temp + shp(3,i)*ul(1,i)
291: xx = xx + shp(3,i)*xl(1,i)
292: yy = yy + shp(3,i)*xl(2,i)
293: end do
294: psi = dir(xx,yy)
295: c Compute thermal flux
296: cs = cos(psi)
297: sn = sin(psi)
298: c2 = cs*cs
299: s2 = sn*sn
300: cs = cs*sn
302: dd(1,1) = c2*ev(1) + s2*ev(2)
303: dd(2,2) = s2*ev(1) + c2*ev(2)
304: dd(1,2) = cs*(ev(1) - ev(2))
305: dd(2,1) = dd(1,2)
307: c flux(1) = -dd(1,1)*gradt(1) - dd(1,2)*gradt(2)
308: c flux(2) = -dd(2,1)*gradt(1) - dd(2,2)*gradt(2)
310: end
312: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
313: ! shp2dquad - shape functions - compute derivatives w/r natural coords.
314: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
315: subroutine shp2dquad(s,t,xl,shp,xsj,ndm)
316: c-----[--.----+----.----+----.-----------------------------------------]
317: c Purpose: Shape function routine for 4-node isoparametric quads
318: c
319: c Inputs:
320: c s,t - Natural coordinates of point
321: c xl(ndm,*) - Nodal coordinates for element
322: c ndm - Spatial dimension of mesh
324: c Outputs:
325: c shp(3,*) - Shape functions and derivatives at point
326: c shp(1,i) = dN_i/dx or dN_i/dxi_1
327: c shp(2,i) = dN_i/dy or dN_i/dxi_2
328: c shp(3,i) = N_i
329: c xsj - Jacobian determinant at point
330: c-----[--.----+----.----+----.-----------------------------------------]
331: implicit none
332: integer ndm
333: real*8 xo,xs,xt, yo,ys,yt, xsm,xsp,xtm,xtp, ysm,ysp,ytm,ytp
334: real*8 s,t, xsj,xsj1, sh,th,sp,tp,sm,tm, xl(ndm,4),shp(3,4)
336: c Set up interpolations
338: sh = 0.5d0*s
339: th = 0.5d0*t
340: sp = 0.5d0 + sh
341: tp = 0.5d0 + th
342: sm = 0.5d0 - sh
343: tm = 0.5d0 - th
344: shp(3,1) = sm*tm
345: shp(3,2) = sp*tm
346: shp(3,3) = sp*tp
347: shp(3,4) = sm*tp
349: c Set up natural coordinate functions (times 4)
351: xo = xl(1,1)-xl(1,2)+xl(1,3)-xl(1,4)
352: xs = -xl(1,1)+xl(1,2)+xl(1,3)-xl(1,4) + xo*t
353: xt = -xl(1,1)-xl(1,2)+xl(1,3)+xl(1,4) + xo*s
354: yo = xl(2,1)-xl(2,2)+xl(2,3)-xl(2,4)
355: ys = -xl(2,1)+xl(2,2)+xl(2,3)-xl(2,4) + yo*t
356: yt = -xl(2,1)-xl(2,2)+xl(2,3)+xl(2,4) + yo*s
358: c Compute jacobian (times 16)
360: xsj1 = xs*yt - xt*ys
362: c Divide jacobian by 16 (multiply by .0625)
364: xsj = 0.0625d0*xsj1
365: if (xsj1.eq.0.0d0) then
366: xsj1 = 1.0d0
367: else
368: xsj1 = 1.0d0/xsj1
369: endif
371: c Divide functions by jacobian
373: xs = (xs+xs)*xsj1
374: xt = (xt+xt)*xsj1
375: ys = (ys+ys)*xsj1
376: yt = (yt+yt)*xsj1
378: c Multiply by interpolations
380: ytm = yt*tm
381: ysm = ys*sm
382: ytp = yt*tp
383: ysp = ys*sp
384: xtm = xt*tm
385: xsm = xs*sm
386: xtp = xt*tp
387: xsp = xs*sp
389: c Compute shape functions
391: shp(1,1) = - ytm+ysm
392: shp(1,2) = ytm+ysp
393: shp(1,3) = ytp-ysp
394: shp(1,4) = - ytp-ysm
395: shp(2,1) = xtm-xsm
396: shp(2,2) = - xtm-xsp
397: shp(2,3) = - xtp+xsp
398: shp(2,4) = xtp+xsm
400: end
402: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
403: ! int2d
404: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
405: subroutine int2d(l,lint,sg)
406: c-----[--.----+----.----+----.-----------------------------------------]
407: c Purpose: Form Gauss points and weights for two dimensions
409: c Inputs:
410: c l - Number of points/direction
412: c Outputs:
413: c lint - Total number of points
414: c sg(3,*) - Array of points and weights
415: c-----[--.----+----.----+----.-----------------------------------------]
416: implicit none
417: integer l,i,lint,lr(9),lz(9)
418: real*8 g,third,sg(3,*)
419: data lr/-1,1,1,-1,0,1,0,-1,0/,lz/-1,-1,1,1,-1,0,1,0,0/
420: data third / 0.3333333333333333d0 /
422: c Set number of total points
424: lint = l*l
426: c 2x2 integration
427: g = sqrt(third)
428: do i = 1,4
429: sg(1,i) = g*lr(i)
430: sg(2,i) = g*lz(i)
431: sg(3,i) = 1.d0
432: end do
434: end
436: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
437: ! ex54_psi - anusotropic material direction
438: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
439: PetscReal function ex54_psi(x,y)
440: implicit none
441: PetscReal x,y,theta
442: common /ex54_theta/ theta
443: ex54_psi = theta
444: if ( theta < 0. ) then ! circular
445: if (y==0) then
446: ex54_psi = 2.d0*atan(1.d0)
447: else
448: ex54_psi = atan(-x/y)
449: endif
450: endif
451: end