194 {
196 phase->m_order = order;
197 phase->m_name =
198 std::string("DIRKOrder" + std::to_string(phase->m_order) + variant);
199
200 phase->m_numsteps = 1;
201 char const &stage = variant.back();
202 phase->m_numstages = std::atoi(&stage);
203
204 phase->m_A = Array<OneD, Array<TwoD, NekDouble>>(1);
205 phase->m_B = Array<OneD, Array<TwoD, NekDouble>>(1);
206
207 phase->m_A[0] =
208 Array<TwoD, NekDouble>(phase->m_numstages, phase->m_numstages, 0.0);
209 phase->m_B[0] =
210 Array<TwoD, NekDouble>(phase->m_numsteps, phase->m_numstages, 0.0);
211 phase->m_U =
212 Array<TwoD, NekDouble>(phase->m_numstages, phase->m_numsteps, 1.0);
213 phase->m_V =
214 Array<TwoD, NekDouble>(phase->m_numsteps, phase->m_numsteps, 1.0);
215
217 switch (phase->m_order)
218 {
219 case 3:
220 {
221
222
223
225 std::string("DIRKOrder3_ES" +
226 std::to_string(phase->m_numstages) +
227 " not defined"));
228
230 (freeParams.size()) ? freeParams[0] : 9.0 / 40.0;
231
232 phase->m_A[0][0][0] = 0.0;
233 phase->m_A[0][1][0] = lambda;
234 phase->m_A[0][2][0] = 9.0 * (1.0 + ConstSqrt2) / 80.0;
235 phase->m_A[0][3][0] =
236 (22.0 + 15.0 * ConstSqrt2) / (80.0 * (1.0 + ConstSqrt2));
237 phase->m_A[0][4][0] = (2398.0 + 1205.0 * ConstSqrt2) /
238 (2835.0 * (4.0 + 3.0 * ConstSqrt2));
239
240 phase->m_A[0][1][1] = phase->m_A[0][1][0];
241 phase->m_A[0][2][1] = phase->m_A[0][2][0];
242 phase->m_A[0][3][1] = phase->m_A[0][3][0];
243 phase->m_A[0][4][1] = phase->m_A[0][4][0];
244
245 phase->m_A[0][2][2] = lambda;
246 phase->m_A[0][3][2] = -7.0 / (40.0 * (1.0 + ConstSqrt2));
247 phase->m_A[0][4][2] = -2374.0 * (1.0 + 2.0 * ConstSqrt2) /
248 (2835.0 * (5.0 + 3.0 * ConstSqrt2));
249
250 phase->m_A[0][3][3] = lambda;
251 phase->m_A[0][4][3] = 5827.0 / 7560.0;
252
253 phase->m_A[0][4][4] = lambda;
254
255 phase->m_B[0][0][0] = phase->m_A[0][4][0];
256 phase->m_B[0][0][1] = phase->m_A[0][4][1];
257 phase->m_B[0][0][2] = phase->m_A[0][4][2];
258 phase->m_B[0][0][3] = phase->m_A[0][4][3];
259 phase->m_B[0][0][4] = phase->m_A[0][4][4];
260 }
261 break;
262
263 case 4:
264 {
265
266
267
269 std::string("DIRKOrder4_ES" +
270 std::to_string(phase->m_numstages) +
271 " not defined"));
272
274 (freeParams.size()) ? freeParams[0] : 1.0 / 4.0;
275
276 phase->m_A[0][0][0] = 0.0;
277 phase->m_A[0][1][0] = lambda;
278 phase->m_A[0][2][0] = (1.0 - ConstSqrt2) / 8.0;
279 phase->m_A[0][3][0] = (5.0 - 7.0 * ConstSqrt2) / 64.0;
280 phase->m_A[0][4][0] =
281 (-13796.0 - 54539.0 * ConstSqrt2) / 125000.0;
282 phase->m_A[0][5][0] = (1181.0 - 987.0 * ConstSqrt2) / 13782.0;
283
284 phase->m_A[0][1][1] = phase->m_A[0][1][0];
285 phase->m_A[0][2][1] = phase->m_A[0][2][0];
286 phase->m_A[0][3][1] = phase->m_A[0][3][0];
287 phase->m_A[0][4][1] = phase->m_A[0][4][0];
288 phase->m_A[0][5][1] = phase->m_A[0][5][0];
289
290 phase->m_A[0][2][2] = lambda;
291 phase->m_A[0][3][2] = 7.0 * (1.0 + ConstSqrt2) / 32.0;
292 phase->m_A[0][4][2] =
293 (506605.0 + 132109.0 * ConstSqrt2) / 437500.0;
294 phase->m_A[0][5][2] =
295 47.0 * (-267.0 + 1783.0 * ConstSqrt2) / 273343.0;
296
297 phase->m_A[0][3][3] = lambda;
298 phase->m_A[0][4][3] =
299 166.0 * (-97.0 + 376.0 * ConstSqrt2) / 109375.0;
300 phase->m_A[0][5][3] =
301 -16.0 * (-22922.0 + 3525.0 * ConstSqrt2) / 571953.0;
302
303 phase->m_A[0][4][4] = lambda;
304 phase->m_A[0][5][4] =
305 -15625.0 * (97.0 + 376.0 * ConstSqrt2) / 90749876.0;
306
307 phase->m_A[0][5][5] = lambda;
308
309 phase->m_B[0][0][0] = phase->m_A[0][5][0];
310 phase->m_B[0][0][1] = phase->m_A[0][5][1];
311 phase->m_B[0][0][2] = phase->m_A[0][5][2];
312 phase->m_B[0][0][3] = phase->m_A[0][5][3];
313 phase->m_B[0][0][4] = phase->m_A[0][5][4];
314 phase->m_B[0][0][5] = phase->m_A[0][5][5];
315 }
316 break;
317 default:
318 {
319 ASSERTL0(
false, std::string(
"ESDIRK of order" +
320 std::to_string(phase->m_order) +
321 " not defined"));
322 break;
323 }
324 }
325
326 phase->m_numMultiStepValues = 1;
327 phase->m_numMultiStepImplicitDerivs = 0;
328 phase->m_numMultiStepExplicitDerivs = 0;
329 phase->m_timeLevelOffset = Array<OneD, size_t>(phase->m_numsteps);
330 phase->m_timeLevelOffset[0] = 0;
331
332 phase->CheckAndVerify();
333 }