Chaste  Release::2018.1
SimpleNewtonNonlinearSolver.cpp
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35 
36 #include "SimpleNewtonNonlinearSolver.hpp"
37 #include <iostream>
38 #include <cassert>
39 #include "Exception.hpp"
40 
42  : mTolerance(1e-5),
43  mWriteStats(false)
44 {
45  mTestDampingValues.push_back(-0.1);
46  mTestDampingValues.push_back(0.05);
47  for (unsigned i=1; i<=12; i++)
48  {
49  double val = double(i)/10;
50  mTestDampingValues.push_back(val);
51  }
52 }
53 
55 {}
56 
57 Vec SimpleNewtonNonlinearSolver::Solve(PetscErrorCode (*pComputeResidual)(SNES,Vec,Vec,void*),
58 #if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>=5)
59  PetscErrorCode (*pComputeJacobian)(SNES,Vec,Mat,Mat,void*),
60 #else
61  PetscErrorCode (*pComputeJacobian)(SNES,Vec,Mat*,Mat*,MatStructure*,void*),
62 #endif
63  Vec initialGuess,
64  unsigned fill,
65  void* pContext)
66 {
67  PetscInt size;
68  VecGetSize(initialGuess, &size);
69 
70  Vec current_solution;
71  VecDuplicate(initialGuess, &current_solution);
72  VecCopy(initialGuess, current_solution);
73 
74  // The "false" says that we are allowed to do new mallocs without PETSc 3.3 causing an error
75  LinearSystem linear_system(current_solution, fill, false);
76 
77  (*pComputeResidual)(nullptr, current_solution, linear_system.rGetRhsVector(), pContext);
78 
79 
80  double residual_norm;
81  VecNorm(linear_system.rGetRhsVector(), NORM_2, &residual_norm);
82  double scaled_residual_norm = residual_norm/size;
83 
84  if (mWriteStats)
85  {
86  std::cout << "Newton's method:\n Initial ||residual||/N = " << scaled_residual_norm
87  << "\n Attempting to solve to tolerance " << mTolerance << "..\n";
88  }
89 
90  double old_scaled_residual_norm;
91  unsigned counter = 0;
92  while (scaled_residual_norm > mTolerance)
93  {
94  counter++;
95 
96  // Store the old norm to check with the new later
97  old_scaled_residual_norm = scaled_residual_norm;
98 
99  // Compute Jacobian and solve J dx = f for the (negative) update dx, (J the jacobian, f the residual)
100 #if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>=5)
101  (*pComputeJacobian)(nullptr, current_solution, (linear_system.rGetLhsMatrix()), nullptr, pContext);
102 #else
103  (*pComputeJacobian)(nullptr, current_solution, &(linear_system.rGetLhsMatrix()), nullptr, nullptr, pContext);
104 #endif
105 
106  Vec negative_update = linear_system.Solve();
107 
108 
109  Vec test_vec;
110  VecDuplicate(initialGuess, &test_vec);
111 
112  double best_damping_factor = 1.0;
113  double best_scaled_residual = 1e20; // large
114 
115  // Loop over all the possible damping value and determine which gives smallest residual
116  for (unsigned i=0; i<mTestDampingValues.size(); i++)
117  {
118  // Note: WAXPY calls VecWAXPY(w,a,x,y) which computes w = ax+y
119  PetscVecTools::WAXPY(test_vec,-mTestDampingValues[i],negative_update,current_solution);
120 
121  // Compute new residual
122  linear_system.ZeroLinearSystem();
123  (*pComputeResidual)(nullptr, test_vec, linear_system.rGetRhsVector(), pContext);
124  VecNorm(linear_system.rGetRhsVector(), NORM_2, &residual_norm);
125  scaled_residual_norm = residual_norm/size;
126 
127  if (scaled_residual_norm < best_scaled_residual)
128  {
129  best_scaled_residual = scaled_residual_norm;
130  best_damping_factor = mTestDampingValues[i];
131  }
132  }
133  PetscTools::Destroy(test_vec);
134 
135  // Check the smallest residual was actually smaller than the previous; if not, quit
136  if (best_scaled_residual > old_scaled_residual_norm)
137  {
138  // Free memory
139  PetscTools::Destroy(current_solution);
140  PetscTools::Destroy(negative_update);
141 
142  // Raise error
143  EXCEPTION("Iteration " << counter << ", unable to find damping factor such that residual decreases in update direction");
144  }
145 
146  if (mWriteStats)
147  {
148  std::cout << " Best damping factor = " << best_damping_factor << "\n";
149  }
150 
151  // Update solution: current_guess = current_solution - best_damping_factor*negative_update
152  PetscVecTools::AddScaledVector(current_solution, negative_update, -best_damping_factor);
153  scaled_residual_norm = best_scaled_residual;
154  PetscTools::Destroy(negative_update);
155 
156  // Compute best residual vector again and store in linear_system for next Solve()
157  linear_system.ZeroLinearSystem();
158  (*pComputeResidual)(nullptr, current_solution, linear_system.rGetRhsVector(), pContext);
159 
160  if (mWriteStats)
161  {
162  std::cout << " Iteration " << counter << ": ||residual||/N = " << scaled_residual_norm << "\n";
163  }
164  }
165 
166  if (mWriteStats)
167  {
168  std::cout << " ..solved!\n\n";
169  }
170 
171  return current_solution;
172 }
173 
175 {
176  assert(tolerance > 0);
177  mTolerance = tolerance;
178 }
void ZeroLinearSystem()
Vec Solve(Vec lhsGuess=nullptr)
#define EXCEPTION(message)
Definition: Exception.hpp:143
virtual Vec Solve(PetscErrorCode(*pComputeResidual)(SNES, Vec, Vec, void *), PetscErrorCode(*pComputeJacobian)(SNES, Vec, Mat *, Mat *, MatStructure *, void *), Vec initialGuess, unsigned fill, void *pContext)
Mat & rGetLhsMatrix()
Vec & rGetRhsVector()
static void AddScaledVector(Vec y, Vec x, double scaleFactor)
static void Destroy(Vec &rVec)
Definition: PetscTools.hpp:352
static void WAXPY(Vec w, double a, Vec x, Vec y)