Chaste  Release::2018.1
CardiacNewtonSolver.hpp
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35 #ifndef CARDIACNEWTONSOLVER_HPP_
36 #define CARDIACNEWTONSOLVER_HPP_
37 
38 #include <cmath>
39 #include "IsNan.hpp"
40 #include "UblasCustomFunctions.hpp"
41 #include "AbstractBackwardEulerCardiacCell.hpp"
42 #include "Warnings.hpp"
43 
56 template<unsigned SIZE, typename CELLTYPE>
58 {
59 public:
66  {
68  return &inst;
69  }
70 
78  void Solve(CELLTYPE &rCell,
79  double time,
80  double rCurrentGuess[SIZE])
81  {
82  unsigned counter = 0;
83  const double eps = 1e-6; // JonW tolerance
84 
85  // check that the initial guess that was given gives a valid residual
86  rCell.ComputeResidual(time, rCurrentGuess, mResidual.data());
87  double norm_of_residual = norm_inf(mResidual);
88  assert(!std::isnan(norm_of_residual));
89  double norm_of_update = 0.0; //Properly initialised in the loop
90  do
91  {
92  // Calculate Jacobian for current guess
93  rCell.ComputeJacobian(time, rCurrentGuess, mJacobian);
94 
95  // Solve Newton linear system for mUpdate, given mJacobian and mResidual
97 
98  // Update norm (JonW style)
99  norm_of_update = norm_inf(mUpdate);
100 
101  // Update current guess and recalculate residual
102  for (unsigned i=0; i<SIZE; i++)
103  {
104  rCurrentGuess[i] -= mUpdate[i];
105  }
106  double norm_of_previous_residual = norm_of_residual;
107  rCell.ComputeResidual(time, rCurrentGuess, mResidual.data());
108  norm_of_residual = norm_inf(mResidual);
109  if (norm_of_residual > norm_of_previous_residual && norm_of_update > eps)
110  {
111  //Second part of guard:
112  //Note that if norm_of_update < eps (converged) then it's
113  //likely that both the residual and the previous residual were
114  //close to the root.
115 
116  //Work out where the biggest change in the guess has happened.
117  double relative_change_max = 0.0;
118  unsigned relative_change_direction = 0;
119  for (unsigned i=0; i<SIZE; i++)
120  {
121  double relative_change = fabs(mUpdate[i]/rCurrentGuess[i]);
122  if (relative_change > relative_change_max)
123  {
124  relative_change_max = relative_change;
125  relative_change_direction = i;
126  }
127  }
128 
129  if (relative_change_max > 1.0)
130  {
131  //Only walk 0.2 of the way in that direction (put back 0.8)
132  rCurrentGuess[relative_change_direction] += 0.8*mUpdate[relative_change_direction];
133  rCell.ComputeResidual(time, rCurrentGuess, mResidual.data());
134  norm_of_residual = norm_inf(mResidual);
135  WARNING("Residual increasing and one direction changing radically - back tracking in that direction");
136  }
137  }
138  counter++;
139 
140  // avoid infinite loops
141  if (counter > 15)
142  {
143 // LCOV_EXCL_START
144  EXCEPTION("Newton method diverged in CardiacNewtonSolver::Solve()");
145 // LCOV_EXCL_STOP
146  }
147  }
148  while (norm_of_update > eps);
149 
150 // LCOV_EXCL_START
151 #ifndef NDEBUG
152  if (norm_of_residual > 2e-10)
153  { //This line is for correlation - in case we use norm_of_residual as convergence criterion
154  WARN_ONCE_ONLY("Newton iteration terminated because update vector norm is small, but residual norm is not small.");
155  }
156 #endif // NDEBUG
157 // LCOV_EXCL_STOP
158  }
159 
160 protected:
163  {}
168 
179  {
180  for (unsigned i=0; i<SIZE; i++)
181  {
182  for (unsigned ii=i+1; ii<SIZE; ii++)
183  {
184  double fact = mJacobian[ii][i]/mJacobian[i][i];
185  for (unsigned j=i; j<SIZE; j++)
186  {
187  mJacobian[ii][j] -= fact*mJacobian[i][j];
188  }
189  mResidual[ii] -= fact*mResidual[i];
190  }
191  }
192  for (unsigned i=SIZE; i-- > 0; )
193  {
194  mUpdate[i] = mResidual[i];
195  for (unsigned j=i+1; j<SIZE; j++)
196  {
197  mUpdate[i] -= mJacobian[i][j]*mUpdate[j];
198  }
199  mUpdate[i] /= mJacobian[i][i];
200  }
201  }
202 
203 private:
205  c_vector<double, SIZE> mResidual;
207  double mJacobian[SIZE][SIZE];
209  c_vector<double, SIZE> mUpdate;
210 };
211 
212 #endif /*CARDIACNEWTONSOLVER_HPP_*/
CardiacNewtonSolver< SIZE, CELLTYPE > & operator=(const CardiacNewtonSolver< SIZE, CELLTYPE > &)
c_vector< double, SIZE > mResidual
void Solve(CELLTYPE &rCell, double time, double rCurrentGuess[SIZE])
#define EXCEPTION(message)
Definition: Exception.hpp:143
c_vector< double, SIZE > mUpdate
static CardiacNewtonSolver< SIZE, CELLTYPE > * Instance()
double mJacobian[SIZE][SIZE]