Table of Contents

Five Point Stencil

Routine Name: fivePointStencil

Author: Philip Nelson

Language: C++

Description

fivePointStencil returns an \(N^2\)x\(N^2\) matrix for the five point stencil for the 2D finite difference method

Input

Matrix<T, N * N, N * N> fivePointStencil() takes no input but requires the size and template parameters \(N\) and \(T\)

Output

A \(N^2\)x\(N^2\) matrix with the stencil

Code

template <typename T, std::size_t N>
Matrix<T, N * N, N * N> fivePointStencil()
{
  return Matrix<T, N * N, N * N>([](int i, int j) {
    if (i == j) return -4;
    if (i + 1 == j) return i % 3 != 2 ? 1 : 0;
    if (i == j + 1) return i % 3 != 0 ? 1 : 0;
    if (i + 3 == j) return 1;
    if (i == j + 3) return 1;
    return 0;

  });
}

Example

int main()
{
  std::cout << fivePointStencil<double, 3>() << std::endl;
}

Result

|         -4         1         0         1         0         0         0         0         0 |
|          1        -4         1         0         1         0         0         0         0 |
|          0         1        -4         0         0         1         0         0         0 |
|          1         0         0        -4         1         0         1         0         0 |
|          0         1         0         1        -4         1         0         1         0 |
|          0         0         1         0         1        -4         0         0         1 |
|          0         0         0         1         0         0        -4         1         0 |
|          0         0         0         0         1         0         1        -4         1 |
|          0         0         0         0         0         1         0         1        -4 |

Last Modification date: 27 February 2018