1 static char help[] = "Variable-Viscosity Stokes Problem in 2d.\n\
2 Exact solutions provided by Mirko Velic.\n\n\n";
3
4 #include <petsc.h>
5
6 #include "ex75.h"
7
8 typedef struct {
9 PetscBool fem; /* Flag for FEM tests */
10 } AppCtx;
11
ProcessOptions(MPI_Comm comm,AppCtx * options)12 PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
13 {
14 PetscFunctionBeginUser;
15 options->fem = PETSC_FALSE;
16 PetscOptionsBegin(comm, "", "Stokes Problem Options", "DMPLEX");
17 PetscCall(PetscOptionsBool("-fem", "Run FEM tests", "ex75.c", options->fem, &options->fem, NULL));
18 PetscOptionsEnd();
19 PetscFunctionReturn(PETSC_SUCCESS);
20 }
21
22 /*
23 SolKxSolution - Exact Stokes solutions for exponentially varying viscosity
24
25 Input Parameters:
26 + x - The x coordinate at which to evaluate the solution
27 . z - The z coordinate at which to evaluate the solution
28 . kn - The constant defining the x-dependence of the forcing function
29 . km - The constant defining the z-dependence of the forcing function
30 - B - The viscosity coefficient
31
32 Output Parameters:
33 + vx - The x-velocity at (x,z)
34 . vz - The z-velocity at (x,z)
35 . p - The pressure at (x,z)
36 . sxx - The stress sigma_xx at (x,z)
37 . sxz - The stress sigma_xz at (x,z)
38 - szz - The stress sigma_zz at (x,z)
39
40 Note:
41 $ The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
42 $ conditions everywhere. The forcing term f is given by
43 $
44 $ fx = 0
45 $ fz = sigma*sin(km*z)*cos(kn*x)
46 $
47 $ where
48 $
49 $ km = m*Pi (m may be non-integral)
50 $ kn = n*Pi
51 $
52 $ meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). The viscosity eta is exp(2*B*x).
53 */
SolKxSolution(PetscReal x,PetscReal z,PetscReal kn,PetscReal km,PetscReal B,PetscScalar * vx,PetscScalar * vz,PetscScalar * p,PetscScalar * sxx,PetscScalar * sxz,PetscScalar * szz)54 PetscErrorCode SolKxSolution(PetscReal x, PetscReal z, PetscReal kn, PetscReal km, PetscReal B, PetscScalar *vx, PetscScalar *vz, PetscScalar *p, PetscScalar *sxx, PetscScalar *sxz, PetscScalar *szz)
55 {
56 PetscScalar sigma;
57 PetscScalar _C1, _C2, _C3, _C4;
58 PetscScalar Rp, UU, VV;
59 PetscScalar a, b, r, _aa, _bb, AA, BB, Rm;
60 PetscScalar num1, num2, num3, num4, den1;
61
62 PetscScalar t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
63 PetscScalar t11, t12, t13, t14, t15, t16, t17, t18, t19, t20, t21;
64 PetscScalar t22, t23, t24, t25, t26, t28, t29, t30, t31, t32;
65 PetscScalar t33, t34, t35, t36, t37, t38, t39, t40, t41, t42;
66 PetscScalar t44, t45, t46, t47, t48, t49, t51, t52, t53, t54;
67 PetscScalar t56, t58, t61, t62, t63, t64, t65, t66, t67, t68;
68 PetscScalar t69, t70, t71, t72, t73, t74, t75, t76, t77, t78;
69 PetscScalar t79, t80, t81, t82, t83, t84, t85, t86, t87, t88;
70 PetscScalar t89, t90, t91, t92, t93, t94, t95, t96, t97, t98;
71 PetscScalar t99, t100, t101, t103, t104, t105, t106, t107, t108, t109;
72 PetscScalar t110, t111, t112, t113, t114, t115, t116, t117, t118, t119;
73 PetscScalar t120, t121, t123, t125, t127, t128, t130, t131, t132, t133;
74 PetscScalar t135, t136, t138, t140, t141, t142, t143, t152, t160, t162;
75
76 PetscFunctionBegin;
77 /*************************************************************************/
78 /*************************************************************************/
79 /* rho = -sin(km*z)*cos(kn*x) */
80 /* viscosity Z= exp(2*B*z) */
81 /* solution valid for km not zero -- should get trivial solution if km=0 */
82 sigma = 1.0;
83 /*************************************************************************/
84 /*************************************************************************/
85 a = B * B + km * km;
86 b = 2.0 * km * B;
87 r = sqrt(a * a + b * b);
88 Rp = sqrt((r + a) / 2.0);
89 Rm = sqrt((r - a) / 2.0);
90 UU = Rp - B;
91 VV = Rp + B;
92
93 /*******************************************/
94 /* calculate the constants */
95 /*******************************************/
96 t1 = kn * kn;
97 t4 = km * km;
98 t6 = t4 * t4;
99 t7 = B * B;
100 t9 = 0.4e1 * t7 * t4;
101 t12 = 0.8e1 * t7 * kn * km;
102 t14 = 0.4e1 * t7 * t1;
103 t16 = 0.2e1 * t4 * t1;
104 t17 = t1 * t1;
105 _aa = -0.4e1 * B * t1 * sigma * (t4 + t1) / (t6 + t9 + t12 + t14 + t16 + t17) / (t6 + t9 - t12 + t14 + t16 + t17);
106
107 t2 = kn * kn;
108 t3 = t2 * t2;
109 t4 = B * B;
110 t6 = 0.4e1 * t4 * t2;
111 t7 = km * km;
112 t9 = 0.4e1 * t7 * t4;
113 t10 = t7 * t7;
114 t12 = 0.2e1 * t7 * t2;
115 t16 = 0.8e1 * t4 * kn * km;
116 _bb = sigma * kn * (t3 - t6 + t9 + t10 + t12) / (t10 + t9 + t16 + t6 + t12 + t3) / (t10 + t9 - t16 + t6 + t12 + t3);
117
118 AA = _aa;
119 BB = _bb;
120
121 t1 = Rm * Rm;
122 t2 = B - Rp;
123 t4 = Rp + B;
124 t6 = UU * x;
125 t9 = exp(t6 - 0.4e1 * Rp);
126 t13 = kn * kn;
127 t15 = B * B;
128 t18 = Rp * Rp;
129 t19 = t18 * B;
130 t20 = t15 * Rp;
131 t22 = t1 * Rp;
132 t24 = B * t1;
133 t32 = 0.8e1 * t15 * BB * kn * Rp;
134 t34 = 0.2e1 * Rm;
135 t35 = cos(t34);
136 t37 = Rm * Rp;
137 t49 = sin(t34);
138 t63 = exp(t6 - 0.2e1 * Rp);
139 t65 = Rm * t2;
140 t67 = 0.2e1 * B * kn;
141 t68 = B * Rm;
142 t69 = t67 + t68 + t37;
143 t73 = 0.3e1 * t15;
144 t75 = 0.2e1 * B * Rp;
145 t76 = t73 - t75 + t1 - t13 - t18;
146 t78 = t65 * t76 * BB;
147 t80 = Rm - kn;
148 t81 = cos(t80);
149 t83 = t68 - t67 + t37;
150 t88 = Rm + kn;
151 t89 = cos(t88);
152 t92 = t65 * t76 * AA;
153 t97 = sin(t80);
154 t103 = sin(t88);
155 t108 = exp(t6 - 0.3e1 * Rp - B);
156 t110 = Rm * t4;
157 t111 = t67 + t68 - t37;
158 t115 = t73 + t75 + t1 - t13 - t18;
159 t117 = t110 * t115 * BB;
160 t120 = -t67 + t68 - t37;
161 t127 = t110 * t115 * AA;
162 t140 = exp(t6 - Rp - B);
163 num1 = -0.4e1 * t1 * t2 * t4 * AA * t9 + ((0.2e1 * Rp * (-B * t13 + 0.3e1 * t15 * B - t19 - 0.2e1 * t20 - 0.2e1 * t22 - t24) * AA - t32) * t35 + (0.2e1 * t37 * (t1 - t13 + 0.5e1 * t15 - t18) * AA - 0.8e1 * B * BB * kn * Rm * Rp) * t49 - 0.2e1 * B * (0.3e1 * t20 - t18 * Rp - 0.2e1 * t19 - Rp * t13 - t22 - 0.2e1 * t24) * AA + t32) * t63 + ((0.2e1 * t65 * t69 * AA + t78) * t81 + (0.2e1 * t65 * t83 * AA - t78) * t89 + (t92 - 0.2e1 * t65 * t69 * BB) * t97 + (t92 + 0.2e1 * t65 * t83 * BB) * t103) * t108 + ((-0.2e1 * t110 * t111 * AA - t117) * t81 + (-0.2e1 * t110 * t120 * AA + t117) * t89 + (-t127 + 0.2e1 * t110 * t111 * BB) * t97 + (-t127 - 0.2e1 * t110 * t120 * BB) * t103) * t140;
164
165 t1 = Rp + B;
166 t2 = Rm * t1;
167 t3 = B * B;
168 t4 = 0.3e1 * t3;
169 t5 = B * Rp;
170 t7 = Rm * Rm;
171 t8 = kn * kn;
172 t9 = Rp * Rp;
173 t10 = t4 + 0.2e1 * t5 + t7 - t8 - t9;
174 t12 = t2 * t10 * AA;
175 t14 = B * Rm;
176 t20 = UU * x;
177 t23 = exp(t20 - 0.4e1 * Rp);
178 t25 = Rm * Rp;
179 t32 = Rm * kn;
180 t37 = 0.2e1 * Rm;
181 t38 = cos(t37);
182 t41 = t3 * B;
183 t44 = t3 * Rp;
184 t48 = B * t7;
185 t53 = t3 * BB;
186 t54 = kn * Rp;
187 t58 = sin(t37);
188 t69 = exp(t20 - 0.2e1 * Rp);
189 t71 = t9 * Rp;
190 t72 = Rm * t71;
191 t73 = t3 * Rm;
192 t75 = 0.5e1 * t73 * Rp;
193 t77 = 0.8e1 * t44 * kn;
194 t78 = t25 * t8;
195 t79 = t7 * Rm;
196 t80 = B * t79;
197 t81 = t14 * t8;
198 t82 = t79 * Rp;
199 t84 = 0.3e1 * t41 * Rm;
200 t85 = t14 * t9;
201 t86 = -t72 + t75 + t77 - t78 + t80 - t81 + t82 + t84 + t85;
202 t88 = t7 * t9;
203 t89 = t5 * t8;
204 t90 = t7 * t3;
205 t91 = B * t71;
206 t92 = t48 * Rp;
207 t94 = 0.2e1 * t14 * t54;
208 t96 = 0.3e1 * Rp * t41;
209 t98 = 0.2e1 * t73 * kn;
210 t100 = 0.2e1 * t9 * t3;
211 t101 = -t88 - t89 - t90 - t91 - t92 - t94 + t96 - t98 - t100;
212 t105 = Rm - kn;
213 t106 = cos(t105);
214 t108 = t75 - t77 - t78 + t85 - t72 - t81 + t80 + t84 + t82;
215 t110 = -t100 + t96 - t91 + t94 + t98 - t92 - t89 - t88 - t90;
216 t114 = Rm + kn;
217 t115 = cos(t114);
218 t121 = sin(t105);
219 t127 = sin(t114);
220 t132 = exp(t20 - 0.3e1 * Rp - B);
221 t135 = 0.2e1 * B * kn;
222 t136 = t135 + t14 - t25;
223 t142 = -t135 + t14 - t25;
224 t152 = t2 * t10 * BB;
225 t162 = exp(t20 - Rp - B);
226 num2 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t23 + ((-0.2e1 * t25 * (t7 - t8 + 0.5e1 * t3 - t9) * AA + 0.8e1 * B * BB * t32 * Rp) * t38 + (0.2e1 * Rp * (-B * t8 + 0.3e1 * t41 - t9 * B - 0.2e1 * t44 - 0.2e1 * t7 * Rp - t48) * AA - 0.8e1 * t53 * t54) * t58 - 0.2e1 * t14 * (t4 + t9 - t8 + t7) * AA + 0.8e1 * t53 * t32) * t69 + ((-t86 * AA - 0.2e1 * t101 * BB) * t106 + (-t108 * AA + 0.2e1 * t110 * BB) * t115 + (-0.2e1 * t101 * AA + t86 * BB) * t121 + (-0.2e1 * t110 * AA - t108 * BB) * t127) * t132 + ((t12 - 0.2e1 * t2 * t136 * BB) * t106 + (t12 + 0.2e1 * t2 * t142 * BB) * t115 + (-0.2e1 * t2 * t136 * AA - t152) * t121 + (-0.2e1 * t2 * t142 * AA + t152) * t127) * t162;
227
228 t1 = Rm * Rm;
229 t2 = B - Rp;
230 t4 = Rp + B;
231 t6 = VV * x;
232 t7 = exp(-t6);
233 t11 = B * t1;
234 t12 = Rp * Rp;
235 t13 = t12 * B;
236 t14 = B * B;
237 t15 = t14 * Rp;
238 t19 = kn * kn;
239 t21 = t1 * Rp;
240 t30 = 0.8e1 * t14 * BB * kn * Rp;
241 t32 = 0.2e1 * Rm;
242 t33 = cos(t32);
243 t35 = Rm * Rp;
244 t47 = sin(t32);
245 t61 = exp(-t6 - 0.2e1 * Rp);
246 t63 = Rm * t2;
247 t65 = 0.2e1 * B * kn;
248 t66 = B * Rm;
249 t67 = t65 + t66 + t35;
250 t71 = 0.3e1 * t14;
251 t73 = 0.2e1 * B * Rp;
252 t74 = t71 - t73 + t1 - t19 - t12;
253 t76 = t63 * t74 * BB;
254 t78 = Rm - kn;
255 t79 = cos(t78);
256 t81 = t66 - t65 + t35;
257 t86 = Rm + kn;
258 t87 = cos(t86);
259 t90 = t63 * t74 * AA;
260 t95 = sin(t78);
261 t101 = sin(t86);
262 t106 = exp(-t6 - 0.3e1 * Rp - B);
263 t108 = Rm * t4;
264 t109 = t65 + t66 - t35;
265 t113 = t71 + t73 + t1 - t19 - t12;
266 t115 = t108 * t113 * BB;
267 t118 = -t65 + t66 - t35;
268 t125 = t108 * t113 * AA;
269 t138 = exp(-t6 - Rp - B);
270 num3 = -0.4e1 * t1 * t2 * t4 * AA * t7 + ((-0.2e1 * Rp * (-t11 - t13 + 0.2e1 * t15 + 0.3e1 * t14 * B - B * t19 + 0.2e1 * t21) * AA + t30) * t33 + (-0.2e1 * t35 * (t1 - t19 + 0.5e1 * t14 - t12) * AA + 0.8e1 * B * BB * kn * Rm * Rp) * t47 + 0.2e1 * B * (-t12 * Rp + 0.2e1 * t11 + 0.3e1 * t15 + 0.2e1 * t13 - t21 - Rp * t19) * AA - t30) * t61 + ((-0.2e1 * t63 * t67 * AA - t76) * t79 + (-0.2e1 * t63 * t81 * AA + t76) * t87 + (-t90 + 0.2e1 * t63 * t67 * BB) * t95 + (-t90 - 0.2e1 * t63 * t81 * BB) * t101) * t106 + ((0.2e1 * t108 * t109 * AA + t115) * t79 + (0.2e1 * t108 * t118 * AA - t115) * t87 + (t125 - 0.2e1 * t108 * t109 * BB) * t95 + (t125 + 0.2e1 * t108 * t118 * BB) * t101) * t138;
271
272 t1 = B - Rp;
273 t2 = Rm * t1;
274 t3 = B * B;
275 t4 = 0.3e1 * t3;
276 t5 = B * Rp;
277 t7 = Rm * Rm;
278 t8 = kn * kn;
279 t9 = Rp * Rp;
280 t10 = t4 - 0.2e1 * t5 + t7 - t8 - t9;
281 t12 = t2 * t10 * AA;
282 t14 = B * Rm;
283 t20 = VV * x;
284 t21 = exp(-t20);
285 t23 = Rm * Rp;
286 t30 = Rm * kn;
287 t35 = 0.2e1 * Rm;
288 t36 = cos(t35);
289 t38 = B * t7;
290 t40 = t3 * Rp;
291 t42 = t3 * B;
292 t51 = t3 * BB;
293 t52 = kn * Rp;
294 t56 = sin(t35);
295 t67 = exp(-t20 - 0.2e1 * Rp);
296 t70 = 0.2e1 * B * kn;
297 t71 = t70 + t14 + t23;
298 t76 = Rm - kn;
299 t77 = cos(t76);
300 t79 = t14 - t70 + t23;
301 t84 = Rm + kn;
302 t85 = cos(t84);
303 t91 = t2 * t10 * BB;
304 t93 = sin(t76);
305 t99 = sin(t84);
306 t104 = exp(-t20 - 0.3e1 * Rp - B);
307 t106 = t9 * Rp;
308 t107 = Rm * t106;
309 t108 = t3 * Rm;
310 t110 = 0.5e1 * t108 * Rp;
311 t112 = 0.8e1 * t40 * kn;
312 t113 = t23 * t8;
313 t114 = t7 * Rm;
314 t115 = B * t114;
315 t116 = t14 * t8;
316 t117 = t114 * Rp;
317 t119 = 0.3e1 * t42 * Rm;
318 t120 = t14 * t9;
319 t121 = t107 - t110 - t112 + t113 + t115 - t116 - t117 + t119 + t120;
320 t123 = t38 * Rp;
321 t125 = 0.2e1 * t14 * t52;
322 t127 = 0.3e1 * Rp * t42;
323 t128 = t7 * t3;
324 t130 = 0.2e1 * t9 * t3;
325 t131 = t7 * t9;
326 t132 = B * t106;
327 t133 = t5 * t8;
328 t135 = 0.2e1 * t108 * kn;
329 t136 = -t123 - t125 + t127 + t128 + t130 + t131 - t132 - t133 + t135;
330 t141 = -t110 + t112 + t113 + t120 + t107 - t116 + t115 + t119 - t117;
331 t143 = t125 - t132 + t130 - t135 + t127 + t131 - t123 + t128 - t133;
332 t160 = exp(-t20 - Rp - B);
333 num4 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t21 + ((0.2e1 * t23 * (t7 - t8 + 0.5e1 * t3 - t9) * AA - 0.8e1 * B * BB * t30 * Rp) * t36 + (-0.2e1 * Rp * (-t38 - t9 * B + 0.2e1 * t40 + 0.3e1 * t42 - B * t8 + 0.2e1 * t7 * Rp) * AA + 0.8e1 * t51 * t52) * t56 - 0.2e1 * t14 * (t4 + t9 - t8 + t7) * AA + 0.8e1 * t51 * t30) * t67 + ((t12 - 0.2e1 * t2 * t71 * BB) * t77 + (t12 + 0.2e1 * t2 * t79 * BB) * t85 + (-0.2e1 * t2 * t71 * AA - t91) * t93 + (-0.2e1 * t2 * t79 * AA + t91) * t99) * t104 + ((-t121 * AA + 0.2e1 * t136 * BB) * t77 + (-t141 * AA - 0.2e1 * t143 * BB) * t85 + (0.2e1 * t136 * AA + t121 * BB) * t93 + (0.2e1 * t143 * AA - t141 * BB) * t99) * t160;
334
335 t1 = Rm * Rm;
336 t2 = Rp * Rp;
337 t3 = t1 * t2;
338 t4 = B * B;
339 t5 = t1 * t4;
340 t9 = exp(-0.4e1 * Rp);
341 t15 = cos(0.2e1 * Rm);
342 t22 = exp(-0.2e1 * Rp);
343 den1 = (-0.4e1 * t3 + 0.4e1 * t5) * t9 + ((0.8e1 * t1 + 0.8e1 * t4) * t2 * t15 - 0.8e1 * t5 - 0.8e1 * t2 * t4) * t22 - 0.4e1 * t3 + 0.4e1 * t5;
344
345 _C1 = num1 / den1;
346 _C2 = num2 / den1;
347 _C3 = num3 / den1;
348 _C4 = num4 / den1;
349
350 /*******************************************/
351 /* calculate solution */
352 /*******************************************/
353 t1 = Rm * x;
354 t2 = cos(t1);
355 t4 = sin(t1);
356 t10 = exp(-0.2e1 * x * B);
357 t12 = kn * x;
358 t13 = cos(t12);
359 t16 = sin(t12);
360 *vx = -km * (_C1 * t2 + _C2 * t4 + _C3 * t2 + _C4 * t4 + t10 * AA * t13 + t10 * BB * t16);
361
362 t2 = Rm * x;
363 t3 = cos(t2);
364 t6 = sin(t2);
365 t22 = exp(-0.2e1 * x * B);
366 t23 = B * t22;
367 t24 = kn * x;
368 t25 = cos(t24);
369 t29 = sin(t24);
370 *vz = UU * _C1 * t3 + UU * _C2 * t6 - _C1 * t6 * Rm + _C2 * t3 * Rm - VV * _C3 * t3 - VV * _C4 * t6 - _C3 * t6 * Rm + _C4 * t3 * Rm - 0.2e1 * t23 * AA * t25 - 0.2e1 * t23 * BB * t29 - t22 * AA * t29 * kn + t22 * BB * t25 * kn;
371
372 t3 = exp(0.2e1 * x * B);
373 t4 = t3 * B;
374 t8 = km * km;
375 t9 = t3 * t8;
376 t11 = 0.3e1 * t9 * Rm;
377 t12 = Rm * Rm;
378 t14 = t3 * t12 * Rm;
379 t15 = UU * UU;
380 t19 = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm;
381 t20 = Rm * x;
382 t21 = sin(t20);
383 t26 = 0.2e1 * t9 * B;
384 t33 = 0.2e1 * t4 * t12;
385 t36 = -t3 * t15 * UU - t26 + 0.3e1 * t9 * UU + 0.3e1 * t3 * UU * t12 + t33 - 0.2e1 * t4 * t15;
386 t37 = cos(t20);
387 t46 = VV * VV;
388 t53 = -t11 - t14 + 0.3e1 * t3 * t46 * Rm - 0.4e1 * t4 * VV * Rm;
389 t64 = -t26 + t33 + t3 * t46 * VV - 0.3e1 * t9 * VV - 0.2e1 * t4 * t46 - 0.3e1 * t3 * VV * t12;
390 t73 = kn * kn;
391 t74 = t73 * kn;
392 t79 = B * B;
393 t86 = B * t8;
394 t90 = kn * x;
395 t91 = sin(t90);
396 t106 = cos(t90);
397 *sxx = -((t19 * t21 + t36 * t37) * _C1 + (t36 * t21 - t19 * t37) * _C2 + (t53 * t21 + t64 * t37) * _C3 + (t64 * t21 - t53 * t37) * _C4 + (-AA * t74 - 0.4e1 * BB * t73 * B + 0.4e1 * t79 * AA * kn - 0.3e1 * t8 * AA * kn - 0.8e1 * t86 * BB) * t91 + (-0.8e1 * t86 * AA - 0.4e1 * AA * t73 * B - 0.4e1 * t79 * BB * kn + 0.3e1 * t8 * BB * kn + BB * t74) * t106) / km;
398
399 t3 = exp(0.2e1 * x * B);
400 t4 = km * km;
401 t5 = t3 * t4;
402 t6 = Rm * x;
403 t7 = cos(t6);
404 t8 = _C1 * t7;
405 t10 = sin(t6);
406 t11 = _C2 * t10;
407 t13 = _C3 * t7;
408 t15 = _C4 * t10;
409 t18 = kn * x;
410 t19 = cos(t18);
411 t22 = sin(t18);
412 t24 = UU * UU;
413 t25 = t3 * t24;
414 t28 = t3 * UU;
415 t38 = Rm * Rm;
416 t39 = t7 * t38;
417 t42 = t10 * t38;
418 t44 = t5 * t8 + t5 * t11 + t5 * t13 + t5 * t15 + t4 * AA * t19 + t4 * BB * t22 + t25 * t8 + t25 * t11 - 0.2e1 * t28 * _C1 * t10 * Rm + 0.2e1 * t28 * _C2 * t7 * Rm - t3 * _C1 * t39 - t3 * _C2 * t42;
419 t45 = VV * VV;
420 t46 = t3 * t45;
421 t49 = t3 * VV;
422 t62 = B * B;
423 t78 = kn * kn;
424 t82 = t46 * t13 + t46 * t15 + 0.2e1 * t49 * _C3 * t10 * Rm - 0.2e1 * t49 * _C4 * t7 * Rm - t3 * _C3 * t39 - t3 * _C4 * t42 + 0.4e1 * t62 * AA * t19 + 0.4e1 * t62 * BB * t22 + 0.4e1 * B * AA * t22 * kn - 0.4e1 * B * BB * t19 * kn - AA * t19 * t78 - BB * t22 * t78;
425 *sxz = t44 + t82;
426
427 t3 = exp(0.2e1 * x * B);
428 t4 = t3 * B;
429 t8 = km * km;
430 t9 = t3 * t8;
431 t10 = t9 * Rm;
432 t11 = Rm * Rm;
433 t13 = t3 * t11 * Rm;
434 t14 = UU * UU;
435 t18 = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm;
436 t19 = Rm * x;
437 t20 = sin(t19);
438 t25 = 0.2e1 * t9 * B;
439 t31 = 0.2e1 * t4 * t11;
440 t34 = -t3 * t14 * UU - t25 + t9 * UU + 0.3e1 * t3 * UU * t11 + t31 - 0.2e1 * t4 * t14;
441 t35 = cos(t19);
442 t44 = VV * VV;
443 t51 = -t10 - t13 + 0.3e1 * t3 * t44 * Rm - 0.4e1 * t4 * VV * Rm;
444 t61 = -t25 + t31 + t3 * t44 * VV - t9 * VV - 0.2e1 * t4 * t44 - 0.3e1 * t3 * VV * t11;
445 t70 = kn * kn;
446 t71 = t70 * kn;
447 t76 = B * B;
448 t82 = B * t8;
449 t86 = kn * x;
450 t87 = sin(t86);
451 t101 = cos(t86);
452 *p = ((t18 * t20 + t34 * t35) * _C1 + (t34 * t20 - t18 * t35) * _C2 + (t51 * t20 + t61 * t35) * _C3 + (t61 * t20 - t51 * t35) * _C4 + (-AA * t71 - 0.4e1 * BB * t70 * B + 0.4e1 * t76 * AA * kn - t8 * AA * kn - 0.4e1 * t82 * BB) * t87 + (-0.4e1 * t82 * AA - 0.4e1 * AA * t70 * B - 0.4e1 * t76 * BB * kn + t8 * BB * kn + BB * t71) * t101) / km;
453
454 t3 = exp(0.2e1 * x * B);
455 t4 = UU * UU;
456 t8 = km * km;
457 t9 = t3 * t8;
458 t10 = t9 * Rm;
459 t11 = Rm * Rm;
460 t13 = t3 * t11 * Rm;
461 t14 = t3 * B;
462 t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm;
463 t19 = Rm * x;
464 t20 = sin(t19);
465 t23 = 0.2e1 * t9 * B;
466 t33 = 0.2e1 * t14 * t11;
467 t34 = -t23 + 0.3e1 * t3 * UU * t11 - t9 * UU - t3 * t4 * UU - 0.2e1 * t4 * t14 + t33;
468 t35 = cos(t19);
469 t47 = VV * VV;
470 t51 = t10 - 0.4e1 * t14 * VV * Rm + 0.3e1 * t3 * t47 * Rm - t13;
471 t61 = t9 * VV - t23 + t3 * t47 * VV - 0.2e1 * t14 * t47 + t33 - 0.3e1 * t3 * VV * t11;
472 t70 = B * B;
473 t74 = kn * kn;
474 t75 = t74 * kn;
475 t83 = kn * x;
476 t84 = sin(t83);
477 t96 = cos(t83);
478 *szz = -((t18 * t20 + t34 * t35) * _C1 + (t34 * t20 - t18 * t35) * _C2 + (t51 * t20 + t61 * t35) * _C3 + (t61 * t20 - t51 * t35) * _C4 + (0.4e1 * t70 * AA * kn - AA * t75 - 0.4e1 * BB * t74 * B + t8 * AA * kn) * t84 + (-t8 * BB * kn - 0.4e1 * AA * t74 * B - 0.4e1 * t70 * BB * kn + BB * t75) * t96) / km;
479
480 /* vx = Vx, vz = Vz, sxx = xx-component of stress tensor, sxz = xz-component of stress tensor, p = pressure, szz = zz-component of stress tensor */
481 *vx *= cos(km * z); /* Vx */
482 *vz *= sin(km * z); /* Vz */
483 *p *= cos(km * z); /* p */
484 *sxx *= cos(km * z); /* sxx total stress */
485 *sxz *= sin(km * z); /* tzx stress */
486 *szz *= cos(km * z); /* szz total stress */
487
488 /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */
489 PetscFunctionReturn(PETSC_SUCCESS);
490 }
491
SolKxWrapperV(PetscInt dim,const PetscReal x[],PetscInt Nf,PetscScalar v[],PetscCtx ctx)492 PetscErrorCode SolKxWrapperV(PetscInt dim, const PetscReal x[], PetscInt Nf, PetscScalar v[], PetscCtx ctx)
493 {
494 PetscReal B = 100.0;
495 PetscReal kn = 100 * M_PI;
496 PetscReal km = 100 * M_PI;
497 PetscScalar p, sxx, sxz, szz;
498
499 PetscFunctionBeginUser;
500 SolKxSolution(x[0], x[1], kn, km, B, &v[0], &v[1], &p, &sxx, &sxz, &szz);
501 PetscFunctionReturn(PETSC_SUCCESS);
502 }
503
SolKxWrapperP(PetscInt dim,const PetscReal x[],PetscInt Nf,PetscScalar v[],PetscCtx ctx)504 PetscErrorCode SolKxWrapperP(PetscInt dim, const PetscReal x[], PetscInt Nf, PetscScalar v[], PetscCtx ctx)
505 {
506 PetscReal B = 100.0;
507 PetscReal kn = 100 * M_PI;
508 PetscReal km = 100 * M_PI;
509 PetscScalar vx, vz, sxx, sxz, szz;
510
511 PetscFunctionBeginUser;
512 SolKxSolution(x[0], x[1], kn, km, B, &vx, &vz, &v[0], &sxx, &sxz, &szz);
513 PetscFunctionReturn(PETSC_SUCCESS);
514 }
515
516 /*
517 Compare the C implementation with generated data from Maple
518 */
MapleTest(MPI_Comm comm,AppCtx * ctx)519 PetscErrorCode MapleTest(MPI_Comm comm, AppCtx *ctx)
520 {
521 const PetscInt n = 41;
522 PetscScalar vxMaple[41][41], vzMaple[41][41], pMaple[41][41], sxxMaple[41][41], sxzMaple[41][41], szzMaple[41][41];
523 PetscReal x[41], z[41];
524 PetscReal kn, km, B;
525 PetscInt i, j;
526
527 PetscFunctionBegin;
528 PetscCall(SolKxData5(x, z, &kn, &km, &B, vxMaple, vzMaple, pMaple, sxxMaple, sxzMaple, szzMaple));
529 for (i = 0; i < n; ++i) {
530 for (j = 0; j < n; ++j) {
531 PetscScalar vx, vz, p, sxx, sxz, szz;
532 PetscReal norm;
533
534 PetscCall(SolKxSolution(x[i], z[j], kn, km, B, &vx, &vz, &p, &sxx, &sxz, &szz));
535 norm = PetscSqrt(PetscSqr(PetscAbsScalar(vx - vxMaple[i][j])) + PetscSqr(PetscAbsScalar(vz - vzMaple[i][j])));
536 PetscCheck(norm > -1.0e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid solution, %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e", (double)x[i], (double)z[j], (double)PetscAbsScalar(vx - vxMaple[i][j]), (double)PetscAbsScalar(vz - vzMaple[i][j]), (double)PetscAbsScalar(p - pMaple[i][j]), (double)PetscAbsScalar(sxx - sxxMaple[i][j]), (double)PetscAbsScalar(sxz - sxzMaple[i][j]), (double)PetscAbsScalar(szz - szzMaple[i][j]), (double)norm);
537 }
538 }
539 }
540 PetscCall(PetscPrintf(comm, "Verified Maple test 5\n"));
541 PetscFunctionReturn(PETSC_SUCCESS);
542 }
543
544 PetscErrorCode FEMTest(MPI_Comm comm, AppCtx *ctx)
545 {
546 DM dm;
547 Vec u;
548 PetscErrorCode (*funcs[2])(PetscInt, const PetscReal[], PetscInt, PetscScalar *, void *) = {SolKxWrapperV, SolKxWrapperP};
549 PetscReal discError;
550
551 PetscFunctionBegin;
552 if (!ctx->fem) PetscFunctionReturn(PETSC_SUCCESS);
553 /* Create DM */
554 PetscCall(DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_FALSE, 0, PETSC_TRUE, &dm));
555 PetscCall(DMSetFromOptions(dm));
556 /* Project solution into FE space */
557 PetscCall(DMGetGlobalVector(dm, &u));
558 PetscCall(DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_VALUES, u));
559 PetscCall(DMComputeL2Diff(dm, 0.0, funcs, NULL, u, &discError));
560 PetscCall(VecViewFromOptions(u, NULL, "-vec_view"));
561 /* Cleanup */
562 PetscCall(DMRestoreGlobalVector(dm, &u));
563 PetscCall(DMDestroy(&dm));
564 PetscFunctionReturn(PETSC_SUCCESS);
565 }
566
567 int main(int argc, char **argv)
568 {
569 AppCtx user; /* user-defined work context */
570
571 PetscFunctionBeginUser;
572 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
573 PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
574 PetscCall(MapleTest(PETSC_COMM_WORLD, &user));
575 PetscCall(FEMTest(PETSC_COMM_WORLD, &user));
576 PetscCall(PetscFinalize());
577 return 0;
578 }
579