MATLAB/Octave API

MATLAB/Octave API#

This page documents the API of the MOLE MATLAB/Octave module. Functions are organized by category.

Differential Operators#

Gradient Operators#

grad(k, m, dx, dc, nc)#

PURPOSE#

Returns a one-dimensional mimetic gradient operator depending on whether

SYNOPSIS#

function grad

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (2x1 vector for left and right vertices, resp.)
(optional) nc : b0 (2x1 vector for left and right vertices, resp.)

               k : Order of accuracy
               m : Number of cells
              dx : Step size

CROSS-REFERENCE INFORMATION#

This function calls:

gradPeriodic() Returns a m by m+2 one-dimensional mimetic gradient operator

gradNonPeriodic() Returns a m+1 by m+2 one-dimensional mimetic gradient operator

This function is called by:

grad3DCurv() Returns a 3D curvilinear mimetic gradient

robinBC() Returns a m+2 by m+2 one-dimensional mimetic boundary operator that

mixedBC() Constructs a 1D mimetic mixed boundary conditions operator

lap() Returns a one-dimensional mimetic Laplacian operator depending on whether

gradNonUniform() Returns a m+1 by m+2 one-dimensional non-uniform mimetic gradient

mimeticB() Returns a m+2 by m+1 one-dimensional mimetic boundary operator

weightsP() Returns the m+1 weights of P

addScalarBC1Dlhs() This functions uses geometry and boundary type conditions to create

grad2D(k, m, dx, n, dy, dc, nc)#

PURPOSE#

Returns a two-dimensional mimetic gradient operator depending on whether

SYNOPSIS#

function grad2D

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (4x1 vector for left, right, bottom, top boundaries, resp.)
(optional) nc : b0 (4x1 vector for left, right, bottom, top boundaries, resp.)

               k : Order of accuracy
               m : Number of cells
              dx : Step size
               n : Number of cells along y-axis
              dy : Step size along y-axis

CROSS-REFERENCE INFORMATION#

This function calls:

gradNonPeriodic2D() Returns a two-dimensional mimetic gradient operator

gradPeriodic() Returns a m by m+2 one-dimensional mimetic gradient operator

gradNonPeriodic() Returns a m+1 by m+2 one-dimensional mimetic gradient operator

This function is called by:

grad2DCurv() Returns a 2D curvilinear mimetic gradient

lap2D() Returns a two-dimensional mimetic Laplacian operator depending on whether

grad2DCurv(k, X, Y)#

PURPOSE#

Returns a 2D curvilinear mimetic gradient

SYNOPSIS#

function grad2DCurv

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

This function calls:

grad2D() Returns a two-dimensional mimetic gradient operator depending on whether

jacobian2D() Returns:

GI2()

grad2DNonUniform(k, xticks, yticks)#

PURPOSE#

Returns a two-dimensional non-uniform mimetic gradient operator

SYNOPSIS#

function grad2DNonUniform

DESCRIPTION#

(including the boundaries!)

               k : Order of accuracy
          xticks : Centers' ticks (x-axis)
          yticks : Centers' ticks (y-axis)

CROSS-REFERENCE INFORMATION#

This function calls:

gradNonUniform() Returns a m+1 by m+2 one-dimensional non-uniform mimetic gradient

grad3D(k, m, dx, n, dy, o, dz, dc, nc)#

PURPOSE#

Returns a three-dimensional mimetic gradient operator depending on whether

SYNOPSIS#

function grad3D

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
(optional) nc : b0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)

               k : Order of accuracy
               m : Number of cells
              dx : Step size
               n : Number of cells along y-axis
              dy : Step size along y-axis
               o : Number of cells along z-axis
              dz : Step size along z-axis

CROSS-REFERENCE INFORMATION#

This function calls:

gradNonPeriodic3D() Returns a three-dimensional mimetic gradient operator

gradPeriodic() Returns a m by m+2 one-dimensional mimetic gradient operator

gradNonPeriodic() Returns a m+1 by m+2 one-dimensional mimetic gradient operator

This function is called by:

lap3D() Returns a three-dimensional mimetic Laplacian operator depending on whether

grad3DCurv() Returns a 3D curvilinear mimetic gradient

grad3DCurv(k, X, Y, Z)#

PURPOSE#

Returns a 3D curvilinear mimetic gradient

SYNOPSIS#

function grad3DCurv

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

This function calls:

grad() Returns a one-dimensional mimetic gradient operator depending on whether

grad3D() Returns a three-dimensional mimetic gradient operator depending on whether

jacobian3D() Returns:

GI13()

grad3DNonUniform(k, xticks, yticks, zticks)#

PURPOSE#

Returns a three-dimensional non-uniform mimetic gradient operator

SYNOPSIS#

function grad3DNonUniform

DESCRIPTION#

(including the boundaries!)

               k : Order of accuracy
          xticks : Centers' ticks (x-axis)
          yticks : Centers' ticks (y-axis)
          zticks : Centers' ticks (z-axis)

CROSS-REFERENCE INFORMATION#

This function calls:

gradNonUniform() Returns a m+1 by m+2 one-dimensional non-uniform mimetic gradient

gradNonUniform(k, ticks)#

PURPOSE#

Returns a m+1 by m+2 one-dimensional non-uniform mimetic gradient

SYNOPSIS#

function gradNonUniform

DESCRIPTION#

operator
(including the boundaries!)

               k : Order of accuracy
           ticks : Centers' ticks e.g. [0 0.5 1 3 5 7 8 9 9.5 10]

CROSS-REFERENCE INFORMATION#

This function calls:

grad() Returns a one-dimensional mimetic gradient operator depending on whether

This function is called by:

grad2DNonUniform() Returns a two-dimensional non-uniform mimetic gradient operator

grad3DNonUniform() Returns a three-dimensional non-uniform mimetic gradient operator

Divergence Operators#

div(k, m, dx, dc, nc)#

PURPOSE#

Returns a one-dimensional mimetic divergence operator depending on whether

SYNOPSIS#

function div

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (2x1 vector for left and right vertices, resp.)
(optional) nc : b0 (2x1 vector for left and right vertices, resp.)

               k : Order of accuracy
               m : Number of cells
              dx : Step size

CROSS-REFERENCE INFORMATION#

This function calls:

divNonPeriodic() Returns a m+2 by m+1 one-dimensional mimetic divergence operator

divPeriodic() Returns a m+2 by m one-dimensional mimetic divergence operator

This function is called by:

div3DCurv()

divNonUniform() Returns a m+2 by m+1 one-dimensional non-uniform mimetic divergence

lap() Returns a one-dimensional mimetic Laplacian operator depending on whether

mimeticB() Returns a m+2 by m+1 one-dimensional mimetic boundary operator

weightsQ() Returns the m+2 weights of Q

div2D(k, m, dx, n, dy, dc, nc)#

PURPOSE#

Returns a two-dimensional mimetic divergence operator depending on whether

SYNOPSIS#

function div2D

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (4x1 vector for left, right, bottom, top boundaries, resp.)
(optional) nc : b0 (4x1 vector for left, right, bottom, top boundaries, resp.)

               k : Order of accuracy
               m : Number of cells
              dx : Step size
               n : Number of cells along y-axis
              dy : Step size along y-axis

CROSS-REFERENCE INFORMATION#

This function calls:

divNonPeriodic() Returns a m+2 by m+1 one-dimensional mimetic divergence operator

divPeriodic() Returns a m+2 by m one-dimensional mimetic divergence operator

divNonPeriodic2D() Returns a two-dimensional mimetic divergence operator

This function is called by:

div2DCurv()

curl2D() Returns a two-dimensional mimetic curl operator

lap2D() Returns a two-dimensional mimetic Laplacian operator depending on whether

div2DCurv(k, X, Y)#

div2DNonUniform(k, xticks, yticks)#

PURPOSE#

Returns a two-dimensional non-uniform mimetic divergence operator

SYNOPSIS#

function div2DNonUniform

DESCRIPTION#

     k : Order of accuracy
xticks : Edges' ticks (x-axis)
yticks : Edges' ticks (y-axis)

CROSS-REFERENCE INFORMATION#

This function calls:

divNonUniform() Returns a m+2 by m+1 one-dimensional non-uniform mimetic divergence

div3D(k, m, dx, n, dy, o, dz, dc, nc)#

PURPOSE#

Returns a three-dimensional mimetic divergence operator depending on whether

SYNOPSIS#

function div3D

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
(optional) nc : b0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)

               k : Order of accuracy
               m : Number of cells
              dx : Step size
               n : Number of cells along y-axis
              dy : Step size along y-axis
               o : Number of cells along z-axis
              dz : Step size along z-axis

CROSS-REFERENCE INFORMATION#

This function calls:

divNonPeriodic() Returns a m+2 by m+1 one-dimensional mimetic divergence operator

divNonPeriodic3D() Returns a three-dimensional mimetic divergence operator

divPeriodic() Returns a m+2 by m one-dimensional mimetic divergence operator

This function is called by:

lap3D() Returns a three-dimensional mimetic Laplacian operator depending on whether

div3DCurv()

div3DCurv(k, X, Y, Z)#

div3DNonUniform(k, xticks, yticks, zticks)#

PURPOSE#

Returns a three-dimensional non-uniform mimetic divergence operator

SYNOPSIS#

function div3DNonUniform

DESCRIPTION#

     k : Order of accuracy
xticks : Edges' ticks (x-axis)
yticks : Edges' ticks (y-axis)
zticks : Edges' ticks (z-axis)

CROSS-REFERENCE INFORMATION#

This function calls:

divNonUniform() Returns a m+2 by m+1 one-dimensional non-uniform mimetic divergence

divNonUniform(k, ticks)#

PURPOSE#

Returns a m+2 by m+1 one-dimensional non-uniform mimetic divergence

SYNOPSIS#

function divNonUniform

DESCRIPTION#

operator

               k : Order of accuracy
           ticks : Edges' ticks e.g. [0 0.1 0.15 0.2 0.3 0.4 0.45]

CROSS-REFERENCE INFORMATION#

This function calls:

div() Returns a one-dimensional mimetic divergence operator depending on whether

This function is called by:

div2DNonUniform() Returns a two-dimensional non-uniform mimetic divergence operator

div3DNonUniform() Returns a three-dimensional non-uniform mimetic divergence operator

Curl Operators#

curl2D(k, m, dx, n, dy, west, east, south, north, U, V)#

PURPOSE#

Returns a two-dimensional mimetic curl operator

SYNOPSIS#

function curl2D

DESCRIPTION#

west, east,
south, north : west, east, south, north limits
U(X,Y) must be defined as function handle
V(X,Y) must be defined as function handle

               k : Order of accuracy
               m : Number of cells along x-axis
              dx : Step size along x-axis
               n : Number of cells along y-axis
              dy : Step size along y-axis
               U : Vector space function acting on x-direction
               V : Vector space function acting on y-direction

CROSS-REFERENCE INFORMATION#

This function calls:

div2D() Returns a two-dimensional mimetic divergence operator depending on whether

Laplacian Operators#

lap(k, m, dx, dc, nc)#

PURPOSE#

Returns a one-dimensional mimetic Laplacian operator depending on whether

SYNOPSIS#

function lap

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (2x1 vector for left and right vertices, resp.)
(optional) nc : b0 (2x1 vector for left and right vertices, resp.)

               k : Order of accuracy
               m : Number of cells
              dx : Step size

CROSS-REFERENCE INFORMATION#

This function calls:

div() Returns a one-dimensional mimetic divergence operator depending on whether

grad() Returns a one-dimensional mimetic gradient operator depending on whether

lapNonPeriodic() Returns a m+2 by m+2 one-dimensional mimetic laplacian operator

lap2D(k, m, dx, n, dy, dc, nc)#

PURPOSE#

Returns a two-dimensional mimetic Laplacian operator depending on whether

SYNOPSIS#

function lap2D

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (4x1 vector for left, right, bottom, top boundaries, resp.)
(optional) nc : b0 (4x1 vector for left, right, bottom, top boundaries, resp.)

               k : Order of accuracy
               m : Number of cells along x-axis
              dx : Step size along x-axis
               n : Number of cells along y-axis
              dy : Step size along y-axis

CROSS-REFERENCE INFORMATION#

This function calls:

div2D() Returns a two-dimensional mimetic divergence operator depending on whether

grad2D() Returns a two-dimensional mimetic gradient operator depending on whether

lapNonPeriodic2D() Returns a two-dimensional mimetic laplacian operator

lap3D(k, m, dx, n, dy, o, dz, dc, nc)#

PURPOSE#

Returns a three-dimensional mimetic Laplacian operator depending on whether

SYNOPSIS#

function lap3D

DESCRIPTION#

or not the operator will contain a periodic boundary condition type
a0 U + b0 dU/dn = g,
(optional) dc : a0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
(optional) nc : b0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)

               k : Order of accuracy
               m : Number of cells along x-axis
              dx : Step size along x-axis
               n : Number of cells along y-axis
              dy : Step size along y-axis
               o : Number of cells along z-axis
              dz : Step size along z-axis

CROSS-REFERENCE INFORMATION#

This function calls:

grad3D() Returns a three-dimensional mimetic gradient operator depending on whether

lapNonPeriodic3D() Returns a three-dimensional mimetic laplacian operator

div3D() Returns a three-dimensional mimetic divergence operator depending on whether

Interpolation Functions#

Node to Center Interpolation#

interpolNodesToCenters1D(k, m)#

PURPOSE#

interpolation operator from nodal coordinates to staggered centers

SYNOPSIS#

function interpolNodesToCenters1D

DESCRIPTION#

m is the number of cells in the logical x-axis
nodal logical coordinates are [1:1:m]
centers logical coordinates [1,1.5:m-0.5,m]

CROSS-REFERENCE INFORMATION#

This function calls:

interpolFacesToCentersG1D() 1D interpolation from faces to centers

interpolNodesToCenters2D(k, m, n)#

PURPOSE#

interpolation operator from nodal coordinates to staggered centers

SYNOPSIS#

function interpolNodesToCenters2D

DESCRIPTION#

m, n, are the number of cells in the logical x-, y- axes
nodal logical coordinates are [1:1:m]x[1:1:n]
centers logical coordinates [1,1.5:m-0.5,m]x[1,1.5:n-0.5,n]

CROSS-REFERENCE INFORMATION#

This function calls:

interpolFacesToCentersG1D() 1D interpolation from faces to centers

interpolNodesToCenters3D(k, m, n, o)#

PURPOSE#

interpolation operator from nodal coordinates to staggered centers

SYNOPSIS#

function interpolNodesToCenters3D

DESCRIPTION#

m, n, o, are the number of cells in the logical x-, y-, z- axes
nodal logical coordinates are [1:1:m]x[1:1:n]x[1:1:o]
centers logical coordinates [1,1.5:m-0.5,m]x[1,1.5:n-0.5,n]x[1,1.5:o-0.5,o]

CROSS-REFERENCE INFORMATION#

This function calls:

interpolFacesToCentersG1D() 1D interpolation from faces to centers

Center to Node Interpolation#

interpolCentersToNodes1D(k, m)#

PURPOSE#

interpolation operator from nodal coordinates to staggered centers

SYNOPSIS#

function interpolCentersToNodes1D

DESCRIPTION#

m is the number of cells in the logical x-axis
nodal logical coordinates are [1:1:m]
centers logical coordinates [1,1.5:m-0.5,m]

CROSS-REFERENCE INFORMATION#

This function calls:

interpolCentersToFacesD1D() 1D interpolation from centers to faces.

interpolCentersToNodes2D(k, m, n)#

PURPOSE#

interpolation operator from staggered to nodes

SYNOPSIS#

function interpolCentersToNodes2D

DESCRIPTION#

m, n, are the number of cells in the logical x-, y- axes
nodal logical coordinates are [1:1:m]x[1:1:n]
centers logical coordinates [1,1.5:m-0.5,m]x[1,1.5:n-0.5,n]

CROSS-REFERENCE INFORMATION#

This function calls:

interpolCentersToFacesD1D() 1D interpolation from centers to faces.

interpolCentersToNodes3D(k, m, n, o)#

PURPOSE#

interpolation operator from staggered to nodes

SYNOPSIS#

function interpolCentersToNodes3D

DESCRIPTION#

m, n, o, are the number of cells in the logical x-, y-, z- axes
nodal logical coordinates are [1:1:m]x[1:1:n]x[1:1:o]
centers logical coordinates [1,1.5:m-0.5,m]x[1,1.5:n-0.5,n]x[1,1.5:o-0.5,o]

CROSS-REFERENCE INFORMATION#

This function calls:

interpolCentersToFacesD1D() 1D interpolation from centers to faces.

Face Interpolation#

interpolFacesToCentersG1D(k, m)#

PURPOSE#

1D interpolation from faces to centers

SYNOPSIS#

function interpolFacesToCentersG1D

DESCRIPTION#

centers logical coordinates [1,1.5:m-0.5,m]
m is the number of cells in the logical x-axis

CROSS-REFERENCE INFORMATION#

This function is called by:

interpolNodesToCenters3D() interpolation operator from nodal coordinates to staggered centers

interpolFacesToCentersG2D() 2D interpolation from faces to centers

interpolFacesToCentersG3D() 3D interpolation from faces to centers

interpolNodesToCenters1D() interpolation operator from nodal coordinates to staggered centers

interpolNodesToCenters2D() interpolation operator from nodal coordinates to staggered centers

interpolFacesToCentersG2D(k, m, n)#

PURPOSE#

2D interpolation from faces to centers

SYNOPSIS#

function interpolFacesToCentersG2D

DESCRIPTION#

centers logical coordinates [1,1.5:m-0.5,m]x[1,1.5:n-0.5,n]
m, n, are the number of cells in the logical x- and y- axes

CROSS-REFERENCE INFORMATION#

This function calls:

interpolFacesToCentersG1D() 1D interpolation from faces to centers

interpolFacesToCentersG3D(k, m, n, o)#

PURPOSE#

3D interpolation from faces to centers

SYNOPSIS#

function interpolFacesToCentersG3D

DESCRIPTION#

centers logical coordinates [1,1.5:m-0.5,m]x[1,1.5:n-0.5,n]x[1,1.5:o-0.5,o]
m, n, o, are the number of cells in the logical x-, y-, z- axes

CROSS-REFERENCE INFORMATION#

This function calls:

interpolFacesToCentersG1D() 1D interpolation from faces to centers

General Interpolation#

interpol(m, c)#

PURPOSE#

Returns a m+1 by m+2 one-dimensional interpolator of 2nd-order

SYNOPSIS#

function interpol

DESCRIPTION#

m : Number of cells
c : Left interpolation coeff.

CROSS-REFERENCE INFORMATION#

This function is called by:

interpol2D() Returns a two-dimensional interpolator of 2nd-order

interpol3D() Returns a three-dimensional interpolator of 2nd-order

interpol2D(m, n, c1, c2)#

PURPOSE#

Returns a two-dimensional interpolator of 2nd-order

SYNOPSIS#

function interpol2D

DESCRIPTION#

 m : Number of cells along x-axis
 n : Number of cells along y-axis
c1 : Left interpolation coeff.
c2 : Bottom interpolation coeff.

CROSS-REFERENCE INFORMATION#

This function calls:

interpol() Returns a m+1 by m+2 one-dimensional interpolator of 2nd-order

interpol3D(m, n, o, c1, c2, c3)#

PURPOSE#

Returns a three-dimensional interpolator of 2nd-order

SYNOPSIS#

function interpol3D

DESCRIPTION#

 m : Number of cells along x-axis
 n : Number of cells along y-axis
 o : Number of cells along z-axis
c1 : Left interpolation coeff.
c2 : Bottom interpolation coeff.
c3 : Front interpolation coeff.

CROSS-REFERENCE INFORMATION#

This function calls:

interpol() Returns a m+1 by m+2 one-dimensional interpolator of 2nd-order

interpolD(m, c)#

PURPOSE#

Returns a m+2 by m+1 one-dimensional interpolator of 2nd-order

SYNOPSIS#

function interpolD

DESCRIPTION#

m : Number of cells
c : Left interpolation coeff.

CROSS-REFERENCE INFORMATION#

This function is called by:

interpolD2D() Returns a two-dimensional interpolator of 2nd-order

interpolD3D() Returns a three-dimensional interpolator of 2nd-order

interpolD2D(m, n, c1, c2)#

PURPOSE#

Returns a two-dimensional interpolator of 2nd-order

SYNOPSIS#

function interpolD2D

DESCRIPTION#

 m : Number of cells along x-axis
 n : Number of cells along y-axis
c1 : Left interpolation coeff.
c2 : Bottom interpolation coeff.

CROSS-REFERENCE INFORMATION#

This function calls:

interpolD() Returns a m+2 by m+1 one-dimensional interpolator of 2nd-order

interpolD3D(m, n, o, c1, c2, c3)#

PURPOSE#

Returns a three-dimensional interpolator of 2nd-order

SYNOPSIS#

function interpolD3D

DESCRIPTION#

 m : Number of cells along x-axis
 n : Number of cells along y-axis
 o : Number of cells along z-axis
c1 : Left interpolation coeff.
c2 : Bottom interpolation coeff.
c3 : Front interpolation coeff.

CROSS-REFERENCE INFORMATION#

This function calls:

interpolD() Returns a m+2 by m+1 one-dimensional interpolator of 2nd-order

Boundary Conditions#

General Boundary Conditions#

addScalarBC1D(A, b, k, m, dx, dc, nc, v)#

PURPOSE#

Separates cases non-periodic and periodic for dealing with boundary data

SYNOPSIS#

function addScalarBC1D

DESCRIPTION#

output
input

              A0 : Linear operator with boundary conditions added
              b0 : Right hand side with boundary conditions added
               A : Linear operator without boundary conditions added
               b : Right hand side without boundary conditions added
               k : Order of accuracy
               m : Number of cells
              dx : Step size
              dc : a0 (2x1 vector for left and right vertices, resp.)
              nc : b0 (2x1 vector for left and right vertices, resp.)
               v : g (2x1 vector for left and right vertices, resp.)

CROSS-REFERENCE INFORMATION#

This function calls:

addScalarBC1Drhs() This function uses the non-periodic boundary condition type of each vertex

addScalarBC1Dlhs() This functions uses geometry and boundary type conditions to create

addScalarBC1Dlhs(k, m, dx, dc, nc)#

PURPOSE#

This functions uses geometry and boundary type conditions to create

SYNOPSIS#

function addScalarBC1Dlhs

DESCRIPTION#

modifications of matrix A associated to each of the boundary faces.
output
input

              Al : modification of matrix A due to left boundary condition
              Ar : modification of matrix A due to right boundary condition
               k : Order of accuracy
               m : Number of cells
              dx : Step size
              dc : Dirichlet coefficient (2x1 vector for left and right vertices, resp.)
              nc : Neumann coefficient (2x1 vector for left and right vertices, resp.)

CROSS-REFERENCE INFORMATION#

This function calls:

grad() Returns a one-dimensional mimetic gradient operator depending on whether

This function is called by:

addScalarBC1D() Separates cases non-periodic and periodic for dealing with boundary data

addScalarBC2Dlhs() This functions uses geometry and boundary type conditions to create

addScalarBC3Dlhs() This functions uses geometry and boundary type conditions to create

addScalarBC1Drhs(b, v, vec)#

PURPOSE#

This function uses the non-periodic boundary condition type of each vertex

SYNOPSIS#

function addScalarBC1Drhs

DESCRIPTION#

and the rhs b values associated to left, and right vertices to modify the rhs vector b.
output
input

               b : Right hand side with boundary conditions added
               b : Right hand side without boundary conditions added
               v : value (2x1 vector for left and right vertices, resp.)
             vec : vector with indices of rhs associated to bc

CROSS-REFERENCE INFORMATION#

This function is called by:

addScalarBC1D() Separates cases non-periodic and periodic for dealing with boundary data

addScalarBC2D(A, b, k, m, dx, n, dy, dc, nc, v)#

PURPOSE#

This function assumes that the unknown u, which represents the discrete

SYNOPSIS#

function addScalarBC2D

DESCRIPTION#

solution the continuous second-order 2D PDE operator
L U = f,
with continuous boundary condition
a0 U + b0 dU/dn = g,
are given at the 2D cell centers and boundary face centers. Furthermore,
all discrete calculations are performed at the 2D cell centers and boundary
face centers.
The function receives as input quantities associated to the discrete
analog of the continuous problem given by the squared linear system
A u = b
where A is the discrete analog of L and b is the discrete analog of g,
both constructed by the user without boundary conditions.
The function output is the modified square linear system
A u = b
where both A and b include boundary condition information.
The boundary condition is always one of the following forms:
For Dirichlet set: a0 not equal zero and b0 = 0.
For Neumann set  : a0 = 0 and b0 not equal zero.
For Robin set    : both a0 and b0 not equal zero.
For Periodic set : both a0 = 0 and b0 = 0.
For periodic bc, it is assumed that not only u but also du/dn are the same
in both extremes of the domain since a second-order PDE is assumed.
Periodic boundary conditions can be applied along some axes and
non-periodic to some others.
For consistence with the way boundary operators are calculated to avoid
overwriting of the values v, the left and right boundary conditions are
assumed to be column vectors of (m+2)*n components, and the bottom and
top faces are assumed to be vectors of (m+2)*(n+2) components.
The order of these components is as follows:
For left and right edges, the ordering is the one given by columns vectors
where x increases. For bottom and top faces, the ordering is the one given
by columns vectors where y increases.
The code assumes the following assertions:
assert(k >= 2, 'k >= 2');
assert(mod(k, 2) == 0, 'k % 2 = 0');
assert(m >= 2*k+1, ['m >= ' num2str(2*k+1) ' for k = ' num2str(k)]);
output
input

               A : Linear operator with boundary conditions added
               b : Right hand side with boundary conditions added
               A : Linear operator without boundary conditions added
               b : Right hand side without boundary conditions added
               k : Order of accuracy
               m : Number of horizontal cells
              dx : Step size horizontal cells
               n : Number of vertical cells
              dy : Step size of vertical cells
              dc : a0 (4x1 vector for left, right, bottom, top boundaries, resp.)
              nc : b0 (4x1 vector for left, right, bottom, top boundaries, resp.)
               v : g (4x1 vector of arrays for left, right, bottom, top boundaries, resp.)

CROSS-REFERENCE INFORMATION#

This function calls:

addScalarBC2Dlhs() This functions uses geometry and boundary type conditions to create

addScalarBC2Drhs() function b = addBC2Drhs(b, m, n, dc, nc, v, vec)

addScalarBC2Dlhs(k, m, dx, n, dy, dc, nc)#

PURPOSE#

This functions uses geometry and boundary type conditions to create

SYNOPSIS#

function addScalarBC2Dlhs

DESCRIPTION#

modifications of matrix A associated to each of the boundary edges.
output
input

            Abcl : Matrix coefficients associated to boundary conditions for left edge
            Abcr : Matrix coefficients associated to boundary conditions for right edge
            Abcb : Matrix coefficients associated to boundary conditions for bottom edge
            Abct : Matrix coefficients associated to boundary conditions for top edge
               k : Order of accuracy
               m : Number of the horizontal cells
              dx : Step size
               n : Number of the vertical cells
              dy : Horizontal cell size
              dc : a0 (4x1 vector for left, right, bottom, top boundaries, resp.)
              nc : b0 (4x1 vector for left, right, bottom, top boundaries resp.)

CROSS-REFERENCE INFORMATION#

This function calls:

addScalarBC1Dlhs() This functions uses geometry and boundary type conditions to create

This function is called by:

addScalarBC2D() This function assumes that the unknown u, which represents the discrete

addScalarBC2Drhs(b, dc, nc, v, rl, rr, rb, rt)#

PURPOSE#

function b = addBC2Drhs(b, m, n, dc, nc, v, vec)

SYNOPSIS#

function b = addBC2Drhs(b, m, n, dc, nc, v, vec)

DESCRIPTION#

This function uses the boundary condition type of each face and the rhs b
indices and values associated to left, right, bottom, top, front, back
faces to modify the rhs vector b.
output
input

               b : Right hand side with boundary conditions added
               b : Right hand side without boundary conditions added
              dc : a0 (4x1 vector for left, right, bottom, top boundary types, resp.)
              nc : b0 (4x1 vector for left, right, bottom, top boundary types, resp.)
               v : g (4x1 vector of arrays for left, right, bottom, top boundaries, resp.)
              rl : indices of rhs left indices
              rr : indices of rhs right indices
              rb : indices of rhs bottom indices
              rt : indices of rhs top indices
             vec : vector with indices of rhs associated to bc

CROSS-REFERENCE INFORMATION#

This function is called by:

addScalarBC2D() This function assumes that the unknown u, which represents the discrete

addScalarBC3D(A, b, k, m, dx, n, dy, o, dz, dc, nc, v)#

PURPOSE#

This function assumes that the unknown u, which represents the discrete

SYNOPSIS#

function addScalarBC3D

DESCRIPTION#

solution the continuous second-order 3D PDE operator
L U = f,
with continuous boundary condition
a0 U + b0 dU/dn = g,
are given at the 3D cell centers and boundary face centers. Furthermore,
all discrete calculations are performed at the 3D cell centers and boundary
face centers.
The function receives as input quantities associated to the discrete
analog of the continuous problem given by the squared linear system
A u = b
where A is the discrete analog of L and b is the discrete analog of g,
both constructed by the user without boundary conditions.
The function output is the modified square linear system
A u = b
where both A and b include boundary condition information.
The boundary condition is always one of the following forms:
For Dirichlet set: a0 not equal zero and b0 = 0.
For Neumann set  : a0 = 0 and b0 not equal zero.
For Robin set    : both a0 and b0 not equal zero.
For Periodic set : both a0 = 0 and b0 = 0.
For periodic bc, it is assumed that not only u but also du/dn are the same
in both extremes of the domain since a second-order PDE is assumed.
Periodic boundary conditions can be applied along some axes and
non-periodic to some others.
For consistence with the way boundary operators are calculated to avoid
overwriting of the values v, the left and right boundary conditions are
assumed to be column vectors of n*o components, the bottom and top
boundary conditions are assumed to be column vectors of (m+2)*o
components, and the front and back faces are assumed to be vectors of
(m+2)*(n+2) components.
The order of these components is as follows:
For left and right faces, the ordering is the one by columns of the
matrix where y increase along rows, and z increase along columns.
For bottom and top faces, the ordering is the one by columns of the
matrix where x increase along rows, and z increase along columns.
For front and back faces, the ordering is the one by columns of the
matrix where x increase along rows, and y increase along columns.
The code assumes the following assertions:
assert(k >= 2, 'k >= 2');
assert(mod(k, 2) == 0, 'k % 2 = 0');
assert(m >= 2*k+1, ['m >= ' num2str(2*k+1) ' for k = ' num2str(k)]);
output
input

               A : Linear operator with boundary conditions added
               b : Right hand side with boundary conditions added
               A : Linear operator without boundary conditions added
               b : Right hand side without boundary conditions added
               k : Order of accuracy
               m : Number of horizontal cells
              dx : Step size of horizontal
               n : Number of vertical cells
              dy : Step size of vertical cells
               o : Number of depth cells
              dz : Step size of depth cells
              dc : a0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
              nc : b0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
               v : g (6x1 vector of arrays for left, right, bottom, top, front, back boundaries, resp.)

CROSS-REFERENCE INFORMATION#

This function calls:

addScalarBC3Drhs() This function uses the boundary condition type of each face and the rhs b

addScalarBC3Dlhs() This functions uses geometry and boundary type conditions to create

addScalarBC3Dlhs(k, m, dx, n, dy, o, dz, dc, nc)#

PURPOSE#

This functions uses geometry and boundary type conditions to create

SYNOPSIS#

function addScalarBC3Dlhs

DESCRIPTION#

modifications of matrix A associated to each of the boundary faces.
output
input

            Abcl : Matrix coefficients associated to boundary conditions for left face
            Abcr : Matrix coefficients associated to boundary conditions for right face
            Abcb : Matrix coefficients associated to boundary conditions for bottom face
            Abct : Matrix coefficients associated to boundary conditions for top face
            Abcf : Matrix coefficients associated to boundary conditions for front face
            Abcz : Matrix coefficients associated to boundary conditions for back face
               k : Order of accuracy
               m : Number of the horizontal cells
              dx : Step size
               n : Number of the vertical cells
              dy : Horizonttal cell size
               o : Number of the depth cells
              dz : Depth cell size
              dc : a0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
              nc : b0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)

CROSS-REFERENCE INFORMATION#

This function calls:

addScalarBC1Dlhs() This functions uses geometry and boundary type conditions to create

This function is called by:

addScalarBC3D() This function assumes that the unknown u, which represents the discrete

addScalarBC3Drhs(b, dc, nc, v, rl, rr, rb, rt, rf, rz)#

PURPOSE#

This function uses the boundary condition type of each face and the rhs b

SYNOPSIS#

function addScalarBC3Drhs

DESCRIPTION#

indices and values associated to left, right, bottom, top, front, back
faces to modify the rhs vector b.
output
input

               b : Right hand side with boundary conditions added
               b : Right hand side without boundary conditions added
              dc : a0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
              nc : b0 (6x1 vector for left, right, bottom, top, front, back boundary types, resp.)
               v : g (6x1 vector of arrays for left, right, bottom, top, front, back boundaries, resp.)
              rl : indices of rhs left indices
              rr : indices of rhs right indices
              rb : indices of rhs bottom indices
              rt : indices of rhs top indices
              rf : indices of rhs front indices
              rz : indices of rhs back indices

CROSS-REFERENCE INFORMATION#

This function is called by:

addScalarBC3D() This function assumes that the unknown u, which represents the discrete

Neumann Boundary Conditions#

neumann2DCurv(G, m, n, b)#

PURPOSE#

Returns a 2D curvilinear Neumann BC operator

SYNOPSIS#

function neumann2DCurv

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

neumann3DCurv(G, m, n, o, b)#

PURPOSE#

Returns a 3D curvilinear Neumann BC operator

SYNOPSIS#

function neumann3DCurv

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

Robin Boundary Conditions#

robinBC(k, m, dx, a, b)#

PURPOSE#

Returns a m+2 by m+2 one-dimensional mimetic boundary operator that

SYNOPSIS#

function robinBC

DESCRIPTION#

imposes a boundary condition of Robin's type

               k : Order of accuracy
               m : Number of cells
              dx : Step size
               a : Dirichlet Coefficient
               b : Neumann Coefficient

CROSS-REFERENCE INFORMATION#

This function calls:

grad() Returns a one-dimensional mimetic gradient operator depending on whether

This function is called by:

robinBC2D() Returns a two-dimensional mimetic boundary operator that

robinBC3D() Returns a three-dimensional mimetic boundary operator that

robinBC2D(k, m, dx, n, dy, a, b)#

PURPOSE#

Returns a two-dimensional mimetic boundary operator that

SYNOPSIS#

function robinBC2D

DESCRIPTION#

imposes a boundary condition of Robin's type

               k : Order of accuracy
               m : Number of cells along x-axis
              dx : Step size along x-axis
               n : Number of cells along y-axis
              dy : Step size along y-axis
               a : Dirichlet Coefficient
               b : Neumann Coefficient

CROSS-REFERENCE INFORMATION#

This function calls:

robinBC() Returns a m+2 by m+2 one-dimensional mimetic boundary operator that

robinBC3D(k, m, dx, n, dy, o, dz, a, b)#

PURPOSE#

Returns a three-dimensional mimetic boundary operator that

SYNOPSIS#

function robinBC3D

DESCRIPTION#

imposes a boundary condition of Robin's type

               k : Order of accuracy
               m : Number of cells along x-axis
              dx : Step size along x-axis
               n : Number of cells along y-axis
              dy : Step size along y-axis
               o : Number of cells along z-axis
              dz : Step size along z-axis
               a : Dirichlet Coefficient
               b : Neumann Coefficient

CROSS-REFERENCE INFORMATION#

This function calls:

robinBC() Returns a m+2 by m+2 one-dimensional mimetic boundary operator that

Mixed Boundary Conditions#

mixedBC(k, m, dx, left, coeffs_left, right, coeffs_right)#

PURPOSE#

Constructs a 1D mimetic mixed boundary conditions operator

SYNOPSIS#

function mixedBC

DESCRIPTION#

           k : Order of accuracy
           m : Number of cells
          dx : Step size
        left : Type of boundary condition at the left boundary ('Dirichlet', 'Neumann', 'Robin')
 coeffs_left : Coefficients for the left boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
       right : Type of boundary condition at the right boundary ('Dirichlet', 'Neumann', 'Robin')
coeffs_right : Coefficients for the right boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)

CROSS-REFERENCE INFORMATION#

This function calls:

grad() Returns a one-dimensional mimetic gradient operator depending on whether

This function is called by:

mixedBC3D() Constructs a 3D mimetic mixed boundary conditions operator

mixedBC2D() Constructs a 2D mimetic mixed boundary conditions operator

mixedBC2D(k, m, dx, n, dy, left, coeffs_left, right, coeffs_right, bottom, coeffs_bottom, top, coeffs_top)#

PURPOSE#

Constructs a 2D mimetic mixed boundary conditions operator

SYNOPSIS#

function mixedBC2D

DESCRIPTION#

            k : Order of accuracy
            m : Number of cells in x-direction
           dx : Step size in x-direction
            n : Number of cells in y-direction
           dy : Step size in y-direction
         left : Type of boundary condition at the left boundary ('Dirichlet', 'Neumann', 'Robin')
  coeffs_left : Coefficients for the left boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
        right : Type of boundary condition at the right boundary ('Dirichlet', 'Neumann', 'Robin')
 coeffs_right : Coefficients for the right boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
       bottom : Type of boundary condition at the bottom boundary ('Dirichlet', 'Neumann', 'Robin')
coeffs_bottom : Coefficients for the bottom boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
          top : Type of boundary condition at the top boundary ('Dirichlet', 'Neumann', 'Robin')
   coeffs_top : Coefficients for the top boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)

CROSS-REFERENCE INFORMATION#

This function calls:

mixedBC() Constructs a 1D mimetic mixed boundary conditions operator

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)#

PURPOSE#

Constructs a 3D mimetic mixed boundary conditions operator

SYNOPSIS#

function mixedBC3D

DESCRIPTION#

            k : Order of accuracy
            m : Number of cells in x-direction
           dx : Step size in x-direction
            n : Number of cells in y-direction
           dy : Step size in y-direction
            o : Number of cells in z-direction
           dz : Step size in z-direction
         left : Type of boundary condition at the left boundary ('Dirichlet', 'Neumann', 'Robin')
  coeffs_left : Coefficients for the left boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
        right : Type of boundary condition at the right boundary ('Dirichlet', 'Neumann', 'Robin')
 coeffs_right : Coefficients for the right boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
       bottom : Type of boundary condition at the bottom boundary ('Dirichlet', 'Neumann', 'Robin')
coeffs_bottom : Coefficients for the bottom boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
          top : Type of boundary condition at the top boundary ('Dirichlet', 'Neumann', 'Robin')
   coeffs_top : Coefficients for the top boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
        front : Type of boundary condition at the front boundary ('Dirichlet', 'Neumann', 'Robin')
 coeffs_front : Coefficients for the front boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)
         back : Type of boundary condition at the back boundary ('Dirichlet', 'Neumann', 'Robin')
  coeffs_back : Coefficients for the back boundary condition (a, b for Robin, otherwise coeff. for Dirichlet or Neumann)

CROSS-REFERENCE INFORMATION#

This function calls:

mixedBC() Constructs a 1D mimetic mixed boundary conditions operator

Grid Generation and Transformation#

Grid Generation#

gridGen(method, grid_name, m, n, plot_grid, varargin)#

PURPOSE#

Returns X and Y which are both m by n matrices that contains the physical

SYNOPSIS#

function gridGen

DESCRIPTION#

coordinates

       grid_name : String with the name of the grid folder
               m : Number of nodes along the horizontal axis
               n : Number of nodes along the vertical axis
       plot_grid : If true -> plot the grid
        varargin : Maximum number of iterations (Required for TTM)

CROSS-REFERENCE INFORMATION#

This function calls:

ttm() https://www.sciencedirect.com/science/article/pii/0022247X78902172?via%3Dihub

tfi() https://en.wikipedia.org/wiki/Transfinite_interpolation

tfi(grid_name, m, n, plot_grid)#

PURPOSE#

Returns X and Y which are both m by n matrices that contains the physical

SYNOPSIS#

function tfi

DESCRIPTION#

coordinates

       grid_name : String with the name of the grid folder
               m : Number of nodes along the horizontal axis
               n : Number of nodes along the vertical axis
       plot_grid : If defined -> grid will be plotted

CROSS-REFERENCE INFORMATION#

This function is called by:

gridGen() Returns X and Y which are both m by n matrices that contains the physical

Jacobian Calculation#

jacobian2D(k, X, Y)#

PURPOSE#

returns:: Determinant of the Jacobian (XeYn - XnYe)

SYNOPSIS#

function jacobian2D

DESCRIPTION#

Xe : dx/de metric
Xn : dx/dn metric
Ye : dy/de metric
Yn : dy/dn metric
 k : Order of accuracy
 X : x-coordinates (physical) of meshgrid
 Y : y-coordinates (physical) of meshgrid

CROSS-REFERENCE INFORMATION#

This function calls:

nodal2D() Returns a two-dimensional operator that approximates the first-order

This function is called by:

nodal2DCurv()

div2DCurv()

grad2DCurv() Returns a 2D curvilinear mimetic gradient

jacobian3D(k, X, Y, Z)#

PURPOSE#

returns:: Determinant of the Jacobian

SYNOPSIS#

function jacobian3D

DESCRIPTION#

Xe : dx/de metric
Xn : dx/dn metric
Xc : dx/dc metric
Ye : dy/de metric
Yn : dy/dn metric
Yc : dy/dc metric
Ze : dz/de metric
Zn : dz/dn metric
Zc : dz/dc metric
 k : Order of accuracy
 X : x-coordinates (physical) of meshgrid
 Y : y-coordinates (physical) of meshgrid
 Z : z-coordinates (physical) of meshgrid

CROSS-REFERENCE INFORMATION#

This function calls:

nodal3D() Returns a three-dimensional operator that approximates the first-order

This function is called by:

div3DCurv()

grad3DCurv() Returns a 3D curvilinear mimetic gradient

nodal3DCurv()

Nodal Operators#

nodal(k, m, dx)#

PURPOSE#

Returns a m+1 by m+1 one-dimensional operator that approximates the

SYNOPSIS#

function nodal

DESCRIPTION#

first-order derivatives on a uniform nodal grid

               k : Order of accuracy
               m : Number of nodes
              dx : Step size

CROSS-REFERENCE INFORMATION#

This function is called by:

nodal2D() Returns a two-dimensional operator that approximates the first-order

nodal3D() Returns a three-dimensional operator that approximates the first-order

nodal2D(k, m, dx, n, dy)#

PURPOSE#

Returns a two-dimensional operator that approximates the first-order

SYNOPSIS#

function nodal2D

DESCRIPTION#

derivatives on a uniform nodal grid

               k : Order of accuracy
               m : Number of nodes along x-axis
              dx : Step size along x-axis
               n : Number of nodes along y-axis
              dy : Step size along y-axis

CROSS-REFERENCE INFORMATION#

This function calls:

nodal() Returns a m+1 by m+1 one-dimensional operator that approximates the

This function is called by:

nodal2DCurv()

jacobian2D() Returns:

nodal2DCurv(k, X, Y)#

nodal3D(k, m, dx, n, dy, o, dz)#

PURPOSE#

Returns a three-dimensional operator that approximates the first-order

SYNOPSIS#

function nodal3D

DESCRIPTION#

derivatives on a uniform nodal grid

               k : Order of accuracy
               m : Number of nodes along x-axis
              dx : Step size along x-axis
               n : Number of nodes along y-axis
              dy : Step size along y-axis
               o : Number of nodes along z-axis
              dz : Step size along z-axis

CROSS-REFERENCE INFORMATION#

This function calls:

nodal() Returns a m+1 by m+1 one-dimensional operator that approximates the

This function is called by:

nodal3DCurv()

jacobian3D() Returns:

nodal3DCurv(k, X, Y, Z)#

sidedNodal(m, dx, type)#

PURPOSE#

Returns a m+1 by m+1 one-dimensional sided approximation for uniformly

SYNOPSIS#

function sidedNodal

DESCRIPTION#

spaced data points. This function is handy for advective terms.

               m : Number of cells
              dx : Step size
            type : 'backward', 'forward' or 'centered'

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

Mimetic Weights#

weightsP(k, m, dx)#

PURPOSE#

Returns the m+1 weights of P

SYNOPSIS#

function weightsP

DESCRIPTION#

 k : Order of accuracy
 m : Number of cells
dx : Step size

CROSS-REFERENCE INFORMATION#

This function calls:

grad() Returns a one-dimensional mimetic gradient operator depending on whether

This function is called by:

weightsP2D() Returns the 2mn+m+n weights of P in 2-D

mimeticB() Returns a m+2 by m+1 one-dimensional mimetic boundary operator

weightsP2D(k, m, dx, n, dy)#

PURPOSE#

Returns the 2mn+m+n weights of P in 2-D

SYNOPSIS#

function weightsP2D

DESCRIPTION#

 k : Order of accuracy
 m : Number of cells along x-axis
dx : Step size along x-axis
 n : Number of cells along y-axis
dy : Step size along y-axis

CROSS-REFERENCE INFORMATION#

This function calls:

weightsP() Returns the m+1 weights of P

weightsQ(k, m, dx)#

PURPOSE#

Returns the m+2 weights of Q

SYNOPSIS#

function weightsQ

DESCRIPTION#

 k : Order of accuracy
 m : Number of cells
dx : Step size

CROSS-REFERENCE INFORMATION#

This function calls:

div() Returns a one-dimensional mimetic divergence operator depending on whether

This function is called by:

mimeticB() Returns a m+2 by m+1 one-dimensional mimetic boundary operator

weightsQ2D(m, n, d)#

PURPOSE#

Returns the (m+2)(n+2) weights of Q in 2-D

SYNOPSIS#

function weightsQ2D

DESCRIPTION#

Only works for 2nd-order 2-D Mimetic divergence operator

               m : Number of cells along x-axis
               n : Number of cells along y-axis
               d : Step size (assuming d = dx = dy)

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

Utility Functions#

amean(X)#

PURPOSE#

Returns the arithmetic mean for every two pairs in a column vector

SYNOPSIS#

function amean

DESCRIPTION#

And, Y(1) = X(1), Y(end) = X(end)

               X : Column vector

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

hmean(X)#

PURPOSE#

Returns the harmonic mean for every two pairs in a column vector

SYNOPSIS#

function hmean

DESCRIPTION#

And, Y(1) = X(1), Y(end) = X(end)

               X : Column vector

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

rk4(func, tspan, dt, y0)#

PURPOSE#

Explicit Runge-Kutta 4th-order method

SYNOPSIS#

function rk4

DESCRIPTION#

Returns : t (evaluation points) and y (solutions) of the specified ODE
   func : Function handler
  tspan : [t0 tf]
     dt : Step size
     y0 : Initial conditions

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

ttm(grid_name, m, n, iters, plot_grid)#

PURPOSE#

Returns X and Y which are both m by n matrices that contains the physical

SYNOPSIS#

function ttm

DESCRIPTION#

coordinates

       grid_name : String with the name of the grid folder
               m : Number of nodes along the horizontal axis
               n : Number of nodes along the vertical axis
       plot_grid : If defined -> grid will be plotted

CROSS-REFERENCE INFORMATION#

This function is called by:

gridGen() Returns X and Y which are both m by n matrices that contains the physical

boundaryIdx2D(m, n)#

PURPOSE#

Returns the indices of the nodes that lie on the boundary of a 2D nodal

SYNOPSIS#

function boundaryIdx2D

DESCRIPTION#

grid

               m : Number of nodes along x-axis
               n : Number of nodes along y-axis

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

DI2(m, n, type)#

DI3(m, n, o, type)#

GI1(M, m, n, type)#

GI13(M, m, n, o, type)#

GI2(M, m, n, type)#

mimeticB(k, m)#

PURPOSE#

Returns a m+2 by m+1 one-dimensional mimetic boundary operator

SYNOPSIS#

function mimeticB

DESCRIPTION#

k : Order of accuracy
m : Number of cells

CROSS-REFERENCE INFORMATION#

This function calls:

div() Returns a one-dimensional mimetic divergence operator depending on whether

weightsQ() Returns the m+2 weights of Q

grad() Returns a one-dimensional mimetic gradient operator depending on whether

weightsP() Returns the m+1 weights of P

tensorGrad2D(K, G)#

PURPOSE#

Returns a two-dimensional flux operator

SYNOPSIS#

function tensorGrad2D

DESCRIPTION#

K : Tensor (e.g. diffusion tensor)
G : 2D mimetic gradient operator

CROSS-REFERENCE INFORMATION#

No cross-reference information found. This typically means this function neither calls nor is called by other functions in the codebase.

MATLAB/Octave API

Contents

MATLAB/Octave API#

Differential Operators#

Gradient Operators#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

Divergence Operators#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

Curl Operators#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

Laplacian Operators#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#

PURPOSE#

SYNOPSIS#

DESCRIPTION#

CROSS-REFERENCE INFORMATION#