Finite differences grid - segmentation error

Question

I want to solve u(x,t)=7.5-sin(x) numerically over the domain [0,2pi]. The problem has periodic boundary conditions u(0)=u(2pi)=7.5

I want to create a 1-D grid consisting of N grid cells where each grid cell contains some information X and U. For each cell, I've created pointers that point to the neighbour cells to connect the grid up, and since we have periodic boundary conditions I'd like to connect the first and last cell together. A for loop is used to traverse the grid one cell at a time, and store the grid cells in a vector cells.

I have a couple of problems here:

1. interp_u and interp_x both return 0, it seems like they are using the initialised vectors with all values 0. How can I input X and U for cell[i] into the linear interpolated x and u?

2. It's giving me a segmentation fault, I'm not too sure what the problem is.

Cheers!

class Grid {
  public:
    // Pointers to neighbour cells
  Grid * LeftNeighbour;
  Grid * RightNeighbour;

  std::vector < double > X;
  std::vector < double > U;

  Grid() {
    // Initialises vectors
    std::vector < double > X(2);
    std::vector < double > U(2);
  }

  double interp_x(double t) {
    return X[0] * (1 / 2) * (1 - t) + X[1] * (1 / 2) * (1 + t);
  }

  double interp_u(double t) {
    return U[0] * (1 / 2) * (1 - t) + U[1] * (1 / 2) * (1 + t);
  }
};

int main() {
  const long double pi = 3.1415926535897932384626433832795;
  std::cout.precision(10);
  int N = 5; //number of cells
  std::vector < Grid > cells(N); //initialises vector of cells

  Grid * RightNeighbour, * LeftNeighbour;

  for (int i = 0; i < N; i++) {
    cells[i].X[0] = 0 + ((2 * pi) / N) * i;
    cells[i].X[1] = cells[i].X[0] + ((2 * pi) / N); //SEGMENTATION FAULT

    cells[i].U[0] = 7.5 - sin(cells[i].X[0]);
    cells[i].U[1] = 7.5 - sin(cells[i].X[1]);

    std::cout << "u(t=0) = " << cells[i].interp_u(0) << std::endl; //linear interpolation

    if (i == 0) { //first cell
      LeftNeighbour = & cells[N - 1];
      RightNeighbour = & cells[i + 1];
    }

    if ((i % (N - 1)) != 0) {
      LeftNeighbour = & cells[i - 1];
      RightNeighbour = & cells[i + 1];
    }

    if (i == N - 1) { //last cell
      LeftNeighbour = & cells[i - 1];
      RightNeighbour = & cells[0];
    }
  }
  return 0;
}

Answer 1

This is wrong

Grid()
{
// Initialises vectors
std::vector<double> X(2);
std::vector<double> U(2);
}

should be

Grid() : X(2), U(2) // Initialises vectors
{
}

Your version create two local variables called X and U and initialises those. The two variables have the same names as your class variables but they are different variables.

Instead use an initialiser list to initialise your class variables.

EDIT

So with the pointers, you have this in main

Grid * RightNeighbour, * LeftNeighbour;

and this

  LeftNeighbour = & cells[N - 1];
  RightNeighbour = & cells[i + 1];

etc. etc.

I'm guessing that what you really meant to do is this

  cells[i].LeftNeighbour = & cells[N - 1];
  cells[i].RightNeighbour = & cells[i + 1];

etc. etc.

Now you can delete this line in main

Grid * RightNeighbour, * LeftNeighbour;

This is basically the same error as before, you have class variables RightNeighbour and LeftNeighbour but instead of using those, you declared some different variables with exactly the same name in main.