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Mimetic Mixed Boundary Conditions Op - MATLAB/Octave
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‎mole_MATLAB/mixedBC.m

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function BC = mixedBC(k, m, dx, left, coeffs_left, right, coeffs_right)
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% Constructs a 1D mimetic mixed boundary conditions operator
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%
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% Parameters:
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% k : Order of accuracy
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% m : Number of cells
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% dx : Step size
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% left : Type of boundary condition at the left boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_left : Coefficients for the left boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% right : Type of boundary condition at the right boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_right : Coefficients for the right boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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A = sparse(m+2, m+2);
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B = sparse(m+2, m+1);
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switch left
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case 'Dirichlet'
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A(1, 1) = coeffs_left;
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case 'Neumann'
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B(1, 1) = -coeffs_left;
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case 'Robin'
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A(1, 1) = coeffs_left(1);
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B(1, 1) = -coeffs_left(2);
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otherwise
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error('Unknown boundary condition type for left boundary');
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end
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switch right
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case 'Dirichlet'
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A(end, end) = coeffs_right;
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case 'Neumann'
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B(end, end) = coeffs_right;
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case 'Robin'
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A(end, end) = coeffs_right(1);
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B(end, end) = coeffs_right(2);
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otherwise
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error('Unknown boundary condition type for right boundary');
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end
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G = grad(k, m, dx);
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BC = A + B*G;
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end

‎mole_MATLAB/mixedBC2D.m

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function BC = mixedBC2D(k, m, dx, n, dy, left, coeffs_left, right, coeffs_right, bottom, coeffs_bottom, top, coeffs_top)
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% Constructs a 2D mimetic mixed boundary conditions operator
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%
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% Parameters:
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% k : Order of accuracy
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% m : Number of cells in x-direction
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% dx : Step size in x-direction
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% n : Number of cells in y-direction
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% dy : Step size in y-direction
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% left : Type of boundary condition at the left boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_left : Coefficients for the left boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% right : Type of boundary condition at the right boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_right : Coefficients for the right boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% bottom : Type of boundary condition at the bottom boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_bottom : Coefficients for the bottom boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% top : Type of boundary condition at the top boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_top : Coefficients for the top boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% 1-D boundary operators
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Bm = mixedBC(k, m, dx, left, coeffs_left, right, coeffs_right);
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Bn = mixedBC(k, n, dy, top, coeffs_top, bottom, coeffs_bottom);
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Im = speye(m+2);
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In = speye(n+2);
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In(1, 1) = 0;
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In(end, end) = 0;
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BC1 = kron(In, Bm);
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BC2 = kron(Bn, Im);
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BC = BC1 + BC2;
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end

‎mole_MATLAB/mixedBC3D.m

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function BC = mixedBC3D(k, m, dx, n, dy, o, dz, left, coeffs_left, right, coeffs_right, bottom, coeffs_bottom, top, coeffs_top, front, coeffs_front, back, coeffs_back)
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% Constructs a 3D mimetic mixed boundary conditions operator
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%
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% Parameters:
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% k : Order of accuracy
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% m : Number of cells in x-direction
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% dx : Step size in x-direction
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% n : Number of cells in y-direction
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% dy : Step size in y-direction
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% o : Number of cells in z-direction
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% dz : Step size in z-direction
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% left : Type of boundary condition at the left boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_left : Coefficients for the left boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% right : Type of boundary condition at the right boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_right : Coefficients for the right boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% bottom : Type of boundary condition at the bottom boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_bottom : Coefficients for the bottom boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% top : Type of boundary condition at the top boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_top : Coefficients for the top boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% front : Type of boundary condition at the front boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_front : Coefficients for the front boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% back : Type of boundary condition at the back boundary ('Dirichlet', 'Neumann', 'Robin')
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% coeffs_back : Coefficients for the back boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
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% 1-D boundary operators
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Bx = mixedBC(k, m, dx, left, coeffs_left, right, coeffs_right);
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By = mixedBC(k, n, dy, bottom, coeffs_bottom, top, coeffs_top);
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Bz = mixedBC(k, o, dz, front, coeffs_front, back, coeffs_back);
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Im = speye(m+2);
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In = speye(n+2);
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Io = speye(o+2);
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In(1, 1) = 0;
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In(end, end) = 0;
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Io(1, 1) = 0;
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Io(end, end) = 0;
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BC1 = kron(kron(Io, In), Bx);
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BC2 = kron(kron(Io, By), Im);
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BC3 = kron(kron(Bz, In), Im);
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BC = BC1 + BC2 + BC3;
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end

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