Table of Contents

Nine Point Stencil

Routine Name: ninePointStencil

Author: Philip Nelson

Language: C++

Description

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

Input

Matrix<T, N * N, N * N> ninePointStencil() 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> ninePointStencil()
{
  return Matrix<T, N * N, N * N>([](int i, int j) {
    if (i == j) return -20;
    if (i + 1 == j) return i % 3 != 2 ? 4 : 0;
    if (i == j + 1) return i % 3 != 0 ? 4 : 0;
    if (i + 2 == j) return i % 3 != 0 ? 1 : 0;
    if (i == j + 2) return i % 3 != 2 ? 1 : 0;
    ;
    if (i + 3 == j) return 4;
    if (i == j + 3) return 4;
    if (i + 4 == j) return i % 3 != 2 ? 1 : 0;
    if (i == j + 4) return i % 3 != 0 ? 1 : 0;
    ;
  });
}

Example

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

Result

|        -20         4         0         4         1         0         0         0         0 |
|          4       -20         4         1         4         1         0         0         0 |
|          0         4       -20         0         1         4         0         0         0 |
|          4         1         0       -20         4         0         4         1         0 |
|          1         4         1         4       -20         4         1         4         1 |
|          0         1         4         0         4       -20         0         1         4 |
|          0         0         0         4         1         0       -20         4         0 |
|          0         0         0         1         4         1         4       -20         4 |
|          0         0         0         0         1         4         0         4       -20 |

Last Modification date: 27 February 2018