Line data Source code
1 : //* This file is part of the MOOSE framework
2 : //* https://mooseframework.inl.gov
3 : //*
4 : //* All rights reserved, see COPYRIGHT for full restrictions
5 : //* https://github.com/idaholab/moose/blob/master/COPYRIGHT
6 : //*
7 : //* Licensed under LGPL 2.1, please see LICENSE for details
8 : //* https://www.gnu.org/licenses/lgpl-2.1.html
9 :
10 : // * This file is part of the MOOSE framework
11 : // * https://mooseframework.inl.gov
12 : // *
13 : // * All rights reserved, see COPYRIGHT for full restrictions
14 : // * https://github.com/idaholab/moose/blob/master/COPYRIGHT
15 : // *
16 : // * Licensed under LGPL 2.1, please see LICENSE for details
17 : // * https://www.gnu.org/licenses/lgpl-2.1.html
18 :
19 : #pragma once
20 :
21 : #include "Moose.h"
22 : #include "MooseUtils.h"
23 : #include "libmesh/dense_matrix.h"
24 :
25 : namespace FluidPropertiesUtils
26 : {
27 : /**
28 : * NewtonSolve does a 1D Newton Solve to solve the equation y = f(x, z) for variable z.
29 : * @param[in] x constant first argument of the f(x, z) term
30 : * @param[in] y constant which should be equal to f(x, z) with a converged z
31 : * @param[in] z_initial_guess initial guess for return variables
32 : * @param[in] tolerance criterion for relative or absolute (if y is sufficiently close to zero)
33 : * convergence checking
34 : * @param[in] y_from_x_z two-variable function returning both values and derivatives as references
35 : * @param[in] caller_name name of the fluid properties appended to name of the routine calling the
36 : * method
37 : * @param[in] max_its the maximum number of iterations for Newton's method
38 : * @param[in] verbose whether to output Newton iteration data
39 : * @return a pair in which the first member is the value z such that f(x, z) = y and the second
40 : * member is dy/dz
41 : */
42 : template <typename T, typename Functor>
43 : std::pair<T, T>
44 379 : NewtonSolve(const T & x,
45 : const T & y,
46 : const Real z_initial_guess,
47 : const Real tolerance,
48 : const Functor & y_from_x_z,
49 : const std::string & caller_name,
50 : const unsigned int max_its = 100,
51 : const bool verbose = false)
52 : {
53 : // R represents residual
54 :
55 : std::function<bool(const T &, const T &)> abs_tol_check =
56 : [tolerance](const T & R, const T & /*y*/)
57 9 : { return std::abs(MetaPhysicL::raw_value(R)) < tolerance; };
58 235 : std::function<bool(const T &, const T &)> rel_tol_check = [tolerance](const T & R, const T & y)
59 905 : { return std::abs(MetaPhysicL::raw_value(R / y)) < tolerance; };
60 757 : auto convergence_check = MooseUtils::absoluteFuzzyEqual(MetaPhysicL::raw_value(y), 0, tolerance)
61 : ? abs_tol_check
62 : : rel_tol_check;
63 :
64 78 : T z = z_initial_guess, R, new_y, dy_dx, dy_dz;
65 : unsigned int iteration = 0;
66 :
67 : using std::isnan;
68 379 : if (verbose)
69 : Moose::out << "Target value for 1D Newton inversion:\n" << y << std::endl;
70 :
71 : do
72 : {
73 582 : y_from_x_z(x, z, new_y, dy_dx, dy_dz);
74 914 : R = new_y - y;
75 :
76 : // We always want to perform at least one update in order to get derivatives on z correct (z
77 : // corresponding to the initial guess will have no derivative information), so we don't
78 : // immediately return if we are converged
79 914 : const bool converged = convergence_check(R, y);
80 :
81 : #ifndef NDEBUG
82 : static constexpr Real perturbation_factor = 1 + 1e-8;
83 : T perturbed_y, dummy, dummy2;
84 : y_from_x_z(x, perturbation_factor * z, perturbed_y, dummy, dummy2);
85 : // Check the accuracy of the Jacobian
86 : auto J_differenced = (perturbed_y - new_y) / (1e-8 * z);
87 : if (!MooseUtils::relativeFuzzyEqual(J_differenced, dy_dz, 1e-2))
88 : mooseDoOnce(mooseWarning(caller_name + ": Bad Jacobian in NewtonSolve"));
89 : #endif
90 :
91 914 : z += -(R / dy_dz);
92 :
93 914 : if (verbose)
94 : {
95 : Moose::out << "Iteration " << iteration << std::endl;
96 : Moose::out << "Current solution vector: " << z << std::endl;
97 0 : Moose::out << "Current (minus) residual: " << -R << std::endl;
98 : Moose::out << "Current Jacobian: " << dy_dz << std::endl;
99 : }
100 :
101 : // Check for NaNs
102 914 : if (isnan(z))
103 0 : mooseException(caller_name + ": NaN detected in Newton solve");
104 :
105 914 : if (converged)
106 : break;
107 535 : } while (++iteration < max_its);
108 :
109 : // Check for divergence or slow convergence of Newton's method
110 379 : if (iteration >= max_its)
111 0 : mooseException(caller_name +
112 : ": Newton solve convergence failed: maximum number of iterations, ",
113 : max_its,
114 : ", exceeded");
115 :
116 675 : return {z, dy_dz};
117 : }
118 :
119 : /**
120 : * NewtonSolve2D does a 2D Newton Solve to solve for the x and y such that:
121 : * f = f_from_x_y(x, y) and g = g_from_x_y(x, y). This is done for example in the constant of (v, e)
122 : * to (p, T) variable set conversion.
123 : * @param[in] f target value for f_from_x_y
124 : * @param[in] g target value for g_from_x_y
125 : * @param[in] x0 initial guess for first output variable
126 : * @param[in] y0 initial guess for second output variable
127 : * @param[out] x_final output for first variable
128 : * @param[out] y_final output for second variable
129 : * @param[in] f_tol criterion for relative or absolute (if f is sufficently close to zero)
130 : * convergence checking
131 : * @param[in] g_tol criterion for relative or absolute (if g is sufficently close to zero)
132 : * convergence checking
133 : * @param[in] f_from_x_y two-variable function returning both values and derivatives as references
134 : * @param[in] g_from_x_y two-variable function returning both values and derivatives as references
135 : * @param[in] caller_name routine calling this solve
136 : * @param[in] max_its the maximum number of iterations for Newton's method
137 : * @param[in] debug whether to output the solution, residual and Jacobian on every iteration
138 : */
139 : template <typename T, typename Functor1, typename Functor2>
140 : void
141 520314 : NewtonSolve2D(const T & f,
142 : const T & g,
143 : const Real x0,
144 : const Real y0,
145 : T & x_final,
146 : T & y_final,
147 : const Real f_tol,
148 : const Real g_tol,
149 : const Functor1 & f_from_x_y,
150 : const Functor2 & g_from_x_y,
151 : const std::string & caller_name = "",
152 : const unsigned int max_its = 100,
153 : bool debug = false)
154 : {
155 :
156 : constexpr unsigned int system_size = 2;
157 520314 : DenseVector<T> targets = {{f, g}};
158 639989 : DenseVector<Real> tolerances = {{f_tol, g_tol}};
159 : // R represents a residual equal to y - y_in
160 14137628 : auto convergence_check = [&targets, &tolerances](const auto & minus_R)
161 : {
162 : using std::abs;
163 :
164 14665250 : for (const auto i : index_range(minus_R))
165 : {
166 14264642 : const auto error = abs(MooseUtils::absoluteFuzzyEqual(targets(i), 0, tolerances(i))
167 32 : ? minus_R(i)
168 14264578 : : minus_R(i) / targets(i));
169 14264610 : if (error >= tolerances(i))
170 : return false;
171 : }
172 : return true;
173 : };
174 :
175 639989 : DenseVector<T> u = {{x0, y0}};
176 520314 : DenseVector<T> minus_R(system_size), func_evals(system_size), u_update(system_size);
177 520314 : DenseMatrix<T> J(system_size, system_size);
178 : unsigned int iteration = 0;
179 : #ifndef NDEBUG
180 : DenseVector<Real> svs(system_size), evs_real(system_size), evs_imag(system_size);
181 : DenseMatrix<Real> raw_J(system_size, system_size), raw_J2(system_size, system_size);
182 : #endif
183 :
184 : typedef std::function<void(const T &, const T &, T &, T &, T &)> FuncType;
185 : std::array<FuncType, 2> func = {{f_from_x_y, g_from_x_y}};
186 :
187 18 : auto assign_solution = [&u, &x_final, &y_final]()
188 : {
189 520314 : x_final = u(0);
190 520314 : y_final = u(1);
191 : };
192 759630 : auto status_string = [&u, &func_evals, &targets, &minus_R](unsigned int comp) -> std::stringstream
193 : {
194 239316 : std::stringstream ss;
195 478632 : ss << "Current solution for component " << comp << ": " << u(comp)
196 239316 : << " (current ordinate: " << func_evals(comp) << " -> target: " << targets(comp)
197 239316 : << ", scaled residual: " << minus_R(comp) << ")";
198 239316 : return ss;
199 0 : };
200 520314 : if (debug)
201 : Moose::out << "Target values for 2D Newton inversion:\n" << targets << std::endl;
202 :
203 : using std::isnan, std::max, std::abs;
204 :
205 : do
206 : {
207 40851942 : for (const auto i : make_range(system_size))
208 27234628 : func[i](u(0), u(1), func_evals(i), J(i, 0), J(i, 1));
209 :
210 40851942 : for (const auto i : make_range(system_size))
211 27234628 : minus_R(i) = targets(i) - func_evals(i);
212 :
213 : // We always want to perform at least one update in order to get derivatives on z correct (z
214 : // corresponding to the initial guess will have no derivative information), so we don't
215 : // immediately return if we are converged
216 13617314 : const bool converged = convergence_check(minus_R);
217 :
218 : // Check for NaNs before proceeding to system solve. We may simultaneously not have NaNs in z
219 : // but have NaNs in the function evaluation
220 40851909 : for (const auto i : make_range(system_size))
221 27234612 : if (isnan(minus_R(i)))
222 : {
223 0 : assign_solution();
224 34 : mooseException(caller_name + ": NaN detected in Newton solve");
225 : }
226 :
227 13617297 : if (debug)
228 : {
229 : Moose::out << "Iteration " << iteration << std::endl;
230 : Moose::out << "Current solution vector:\n" << u << std::endl;
231 : Moose::out << "Current (minus) residual:\n" << minus_R << std::endl;
232 : Moose::out << "Current Jacobian:\n" << J << std::endl;
233 : }
234 :
235 : // Do some Jacobi (rowmax) preconditioning and check for an empty row
236 : int degenerate_row = -1;
237 40851891 : for (const auto i : make_range(system_size))
238 : {
239 27234594 : const auto rowmax = max(abs(J(i, 0)), abs(J(i, 1)));
240 27234594 : if (rowmax > 0)
241 : {
242 81687576 : for (const auto j : make_range(system_size))
243 54458384 : J(i, j) /= rowmax;
244 27229192 : minus_R(i) /= rowmax;
245 : }
246 : else
247 : {
248 5402 : if (degenerate_row != -1)
249 0 : mooseException(caller_name + ": Jacobian is all zeros in NewtonSolve2D");
250 5402 : degenerate_row = i;
251 : }
252 : }
253 :
254 : #ifndef NDEBUG
255 : //
256 : // Check nature of linearized system
257 : //
258 : for (const auto i : make_range(system_size))
259 : for (const auto j : make_range(system_size))
260 : {
261 : raw_J(i, j) = MetaPhysicL::raw_value(J(i, j));
262 : raw_J2(i, j) = MetaPhysicL::raw_value(J(i, j));
263 : }
264 : raw_J.svd(svs);
265 : raw_J2.evd(evs_real, evs_imag);
266 : if (debug)
267 : Moose::out << "Jacobian singular values:\n" << svs << std::endl;
268 : #endif
269 :
270 13617297 : if (degenerate_row == -1)
271 13611895 : J.lu_solve(minus_R, u_update);
272 : else
273 : {
274 : // use a 1D newton when the Jacobian has an empty row
275 5402 : const auto other_row = system_size - 1 - degenerate_row;
276 5402 : u_update(other_row) = minus_R(other_row) / J(other_row, other_row);
277 5402 : u_update(degenerate_row) = 0;
278 : }
279 : // reset the decomposition
280 23 : J.zero();
281 13617297 : u += u_update;
282 :
283 : // Check for NaNs
284 40851891 : for (const auto i : make_range(system_size))
285 27234594 : if (isnan(u(i)))
286 : {
287 0 : assign_solution();
288 0 : mooseException(caller_name + ": NaN detected in NewtonSolve2D\n" + status_string(0).str() +
289 : "\n" + status_string(1).str());
290 : }
291 :
292 13617297 : if (converged)
293 : break;
294 13216658 : } while (++iteration < max_its);
295 :
296 6 : assign_solution();
297 :
298 : // Check for divergence or slow convergence of Newton's method
299 520297 : if (iteration >= max_its)
300 717948 : mooseException(caller_name +
301 : ": Newton solve convergence failed: maximum number of iterations, ",
302 : max_its,
303 : ", exceeded.\n" + status_string(0).str() + "\n" + status_string(1).str());
304 920959 : }
305 : } // namespace FluidPropertiesUtils
|
