00_Basic_Problem.cpp

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//@HEADER
// *****************************************************************************
//          Tempus: Time Integration and Sensitivity Analysis Package
//
// Copyright 2017 NTESS and the Tempus contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
//@HEADER
 
#include <iomanip>
#include <iostream>
#include <stdlib.h>
#include <math.h>
#include "Teuchos_StandardCatchMacros.hpp"
 
#include "Tutorial_Regression_Tester.hpp"
 
using namespace std;
 
int main(int  /*argc*/, char * /*argv*/[])
{
  bool verbose = true;
  bool success = false;
  try {
    // Solution and its time-derivative.
    double x_n[2];      // at time index n
    double xDot_n[2];   // at time index n
 
    // Initial Conditions
    int n = 0;
    double time = 0.0;
    double epsilon = 1.0e-1;
    bool passed = true;   // ICs are considered passed.
    x_n   [0] = 2.0;
    x_n   [1] = 0.0;
    xDot_n[0] = 0.0;
    xDot_n[1] = -2.0/epsilon;
 
    // Timestep size
    double finalTime = 2.0;
    int nTimeSteps = 2000;
    const double constDT = finalTime/nTimeSteps;
 
    // Output
    cout << std::fixed;
    cout << std::setw(8)  << "index"
         << std::setw(10) << "time"
         << std::setw(12) << "x_0"
         << std::setw(12) << "x_1" << endl;
 
    cout << std::setw(8)  << n
         << std::setw(10)  << std::setprecision(3) << time
         << std::setw(12) << std::setprecision(4) << x_n[0]
         << std::setw(12) << std::setprecision(4) << x_n[1] << endl;
 
    // Advance the solution to the next timestep.
    while (passed && time < finalTime && n < nTimeSteps) {
 
      // Initialize next time step
      double x_np1[2];    // at time index n+1
      x_np1[0] = x_n[0];
      x_np1[1] = x_n[1];
 
      // Set the timestep and time.
      double dt = constDT;
      time = (n+1)*dt;
 
      // Righthand side evaluation and time-derivative at n.
      xDot_n[0] = x_n[1];
      xDot_n[1] = ((1.0 - x_n[0]*x_n[0])*x_n[1] - x_n[0])/epsilon;
 
      // Take the timestep - Forward Euler
      x_np1[0] = x_n[0] + dt*xDot_n[0];
      x_np1[1] = x_n[1] + dt*xDot_n[1];
 
      // Test if solution has passed.
      if ( std::isnan(x_n[0]) || std::isnan(x_n[1]) ) {
        passed = false;
      } else {
        // Promote to next step (n <- n+1).
        x_n[0] = x_np1[0];
        x_n[1] = x_np1[1];
        n++;
      }
 
      // Output
      if (n % 100 == 0)
        cout << std::setw(8)  << n
             << std::setw(10)  << std::setprecision(3) << time
             << std::setw(12) << std::setprecision(4) << x_n[0]
             << std::setw(12) << std::setprecision(4) << x_n[1] << endl;
    }
 
    // Test for regression.
    bool regressionPassed = tutorialRegressionTest(x_n);
 
    if (passed && regressionPassed) success = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success);
 
  if(success)
    cout << "\nEnd Result: Test Passed!" << std::endl;
 
  return ( success ? EXIT_SUCCESS : EXIT_FAILURE );
}