Chaste  Release::3.4
BackwardEulerIvpOdeSolver.cpp
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36 
37 #include "BackwardEulerIvpOdeSolver.hpp"
38 #include <cmath>
39 
41  double timeStep,
42  double time,
43  std::vector<double>& rCurrentYValues,
44  std::vector<double>& rCurrentGuess)
45 {
46  std::vector<double> dy(mSizeOfOdeSystem); //For JC to optimize
47  pAbstractOdeSystem->EvaluateYDerivatives(time+timeStep, rCurrentGuess, dy);
48  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
49  {
50  mResidual[i] = rCurrentGuess[i] - timeStep * dy[i] - rCurrentYValues[i];
51  }
52 }
53 
55  double timeStep,
56  double time,
57  std::vector<double>& rCurrentYValues,
58  std::vector<double>& rCurrentGuess)
59 {
60  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
61  {
62  for (unsigned j=0; j<mSizeOfOdeSystem; j++)
63  {
64  mJacobian[i][j] = 0.0;
65  }
66  }
67 
68  if (pAbstractOdeSystem->GetUseAnalyticJacobian() && !mForceUseOfNumericalJacobian)
69  {
70  // The ODE system has an analytic jacobian, so use that
72  = static_cast<AbstractOdeSystemWithAnalyticJacobian*>(pAbstractOdeSystem);
73  p_ode_system->AnalyticJacobian(rCurrentGuess, mJacobian, time, timeStep);
74  }
75  else
76  {
77  ComputeNumericalJacobian(pAbstractOdeSystem,
78  timeStep,
79  time,
80  rCurrentYValues,
81  rCurrentGuess);
82  }
83 }
84 
86 {
87  double fact;
88  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
89  {
90  for (unsigned ii=i+1; ii<mSizeOfOdeSystem; ii++)
91  {
92  fact = mJacobian[ii][i]/mJacobian[i][i];
93  for (unsigned j=i; j<mSizeOfOdeSystem; j++)
94  {
95  mJacobian[ii][j] -= fact*mJacobian[i][j];
96  }
97  mResidual[ii] -= fact*mResidual[i];
98  }
99  }
100  // This needs to int, since a downloop in unsigned won't terminate properly
101  for (int i=mSizeOfOdeSystem-1; i>=0; i--)
102  {
103  mUpdate[i] = mResidual[i];
104  for (unsigned j=i+1; j<mSizeOfOdeSystem; j++)
105  {
106  mUpdate[i] -= mJacobian[i][j]*mUpdate[j];
107  }
108  mUpdate[i] /= mJacobian[i][i];
109  }
110 }
111 
113 {
114  double norm = 0.0;
115  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
116  {
117  if (fabs(pVector[i]) > norm)
118  {
119  norm = fabs(pVector[i]);
120  }
121  }
122  return norm;
123 }
124 
126  double timeStep,
127  double time,
128  std::vector<double>& rCurrentYValues,
129  std::vector<double>& rCurrentGuess)
130 {
131  std::vector<double> residual(mSizeOfOdeSystem);
132  std::vector<double> residual_perturbed(mSizeOfOdeSystem);
133  std::vector<double> guess_perturbed(mSizeOfOdeSystem);
134 
135  double epsilon = mNumericalJacobianEpsilon;
136 
137  ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, rCurrentGuess);
138  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
139  {
140  residual[i] = mResidual[i];
141  }
142 
143  for (unsigned global_column=0; global_column<mSizeOfOdeSystem; global_column++)
144  {
145  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
146  {
147  guess_perturbed[i] = rCurrentGuess[i];
148  }
149 
150  guess_perturbed[global_column] += epsilon;
151 
152  ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, guess_perturbed);
153  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
154  {
155  residual_perturbed[i] = mResidual[i];
156  }
157 
158  // Compute residual_perturbed - residual
159  double one_over_eps = 1.0/epsilon;
160  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
161  {
162  mJacobian[i][global_column] = one_over_eps*(residual_perturbed[i] - residual[i]);
163  }
164  }
165 }
166 
168  double timeStep,
169  double time,
170  std::vector<double>& rCurrentYValues,
171  std::vector<double>& rNextYValues)
172 {
173  // Check the size of the ODE system matches the solvers expected
174  assert(mSizeOfOdeSystem == pAbstractOdeSystem->GetNumberOfStateVariables());
175 
176  unsigned counter = 0;
177 // const double eps = 1e-6 * rCurrentGuess[0]; // Our tolerance (should use min(guess) perhaps?)
178  const double eps = 1e-6; // JonW tolerance
179  double norm = 2*eps;
180 
181  std::vector<double> current_guess(mSizeOfOdeSystem);
182  current_guess.assign(rCurrentYValues.begin(), rCurrentYValues.end());
183 
184  while (norm > eps)
185  {
186  // Calculate Jacobian and mResidual for current guess
187  ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, current_guess);
188  ComputeJacobian(pAbstractOdeSystem, timeStep, time, rCurrentYValues, current_guess);
189 // // Update norm (our style)
190 // norm = ComputeNorm(mResidual);
191 
192  // Solve Newton linear system
194 
195  // Update norm (JonW style)
196  norm = ComputeNorm(mUpdate);
197 
198  // Update current guess
199  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
200  {
201  current_guess[i] -= mUpdate[i];
202  }
203 
204  counter++;
205  assert(counter < 20); // avoid infinite loops
206  }
207  rNextYValues.assign(current_guess.begin(), current_guess.end());
208 }
209 
211 {
212  mSizeOfOdeSystem = sizeOfOdeSystem;
213 
214  // default epsilon
217 
218  // allocate memory
219  mResidual = new double[mSizeOfOdeSystem];
220  mUpdate = new double[mSizeOfOdeSystem];
221 
222  mJacobian = new double*[mSizeOfOdeSystem];
223  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
224  {
225  mJacobian[i] = new double[mSizeOfOdeSystem];
226  }
227 }
228 
230 {
231  // Delete pointers
232  delete[] mResidual;
233  delete[] mUpdate;
234 
235  for (unsigned i=0; i<mSizeOfOdeSystem; i++)
236  {
237  delete[] mJacobian[i];
238  }
239  delete[] mJacobian;
240 }
241 
243 {
244  assert(epsilon > 0);
245  mNumericalJacobianEpsilon = epsilon;
246 }
247 
249 {
251 }
252 
253 
254 // Serialization for Boost >= 1.36
void SetEpsilonForNumericalJacobian(double epsilon)
BackwardEulerIvpOdeSolver(unsigned sizeOfOdeSystem)
virtual void EvaluateYDerivatives(double time, const std::vector< double > &rY, std::vector< double > &rDY)=0
void ComputeJacobian(AbstractOdeSystem *pAbstractOdeSystem, double timeStep, double time, std::vector< double > &rCurrentYValues, std::vector< double > &rCurrentGuess)
virtual void AnalyticJacobian(const std::vector< double > &rSolutionGuess, double **jacobian, double time, double timeStep)=0
void ComputeNumericalJacobian(AbstractOdeSystem *pAbstractOdeSystem, double timeStep, double time, std::vector< double > &rCurrentYValues, std::vector< double > &rCurrentGuess)
#define CHASTE_CLASS_EXPORT(T)
void ComputeResidual(AbstractOdeSystem *pAbstractOdeSystem, double timeStep, double time, std::vector< double > &rCurrentYValues, std::vector< double > &rCurrentGuess)
void CalculateNextYValue(AbstractOdeSystem *pAbstractOdeSystem, double timeStep, double time, std::vector< double > &rCurrentYValues, std::vector< double > &rNextYValues)