> On Mar 11, 2019, at 7:07 PM, Maahi Talukder via petsc-users
> <[email protected]> wrote:
>
>
> Thank you for your reply.
>
> I still have some confusion. So if (i,j) is a point on the structured grid(
> Where "i" is the column and "j" is the row), and the information associated
> with the (i,j) point on the grid is stored in some (m,n) location of the
> matrix A (Where Ax =b),
Almost. Think about the vector (not the matrix) first. The point (i,j) on
the mesh has location m in the vector (m is a function of both i and j) Now
think about another point on the mesh (say next to the first point), call it
(i',j') this point also has a location in the vector, call it n. Now consider
the matrix entry containing the value that connects m and n. On the mesh it is
associated with the point (i,j) AND the point (i',j') hence the row in the
matrix is a function of the first point (i,j) while the column is a function of
the second point (i',j').
Now the diagonal entry in matrix a_{mm} has (i,j) for both "row" and "column"
stencils, but the off-diagonal entries a_{mn} has (i,j) for the row but (i',j')
for the column.
> I still don't
> understand why both of row(MatStencil_i,1) and row(MatStencil_j,1) are
> necessary? I mean is it something like mapping "i" from grid to its location
> in the matrix?
> Would you please explain that?
>
> Regards,
> Maahi
>
> On Mon, Mar 11, 2019 at 4:41 PM Patrick Sanan <[email protected]> wrote:
> There are two different types of rows and columns:
> 1. Rows and columns in a grid
> 2. Rows and columns in a matrix
>
> "i" and "j" refer to rows and columns in the grid, but "row" and "col"
> refer to rows and columns in the matrix.
>
>
>
> Am Mo., 11. März 2019 um 21:18 Uhr schrieb Maahi Talukder via petsc-users
> <[email protected]>:
> Hello all,
>
> I am trying to solve Poisson Equation on structured grid using 9-point
> stencil in 2D. Now to setup my matrix, I came across C structure MatStencil
> in ex22f.F90
>
> ...........................................................................................................
> call DMDAGetCorners
> (da,xs,ys,zs,xm,ym,zm,ierr)
>
>
> 107: do
> 10,k=zs,zs+zm-1
>
> 108: do
> 20,j=ys,ys+ym-1
>
> 109: do
> 30,i=xs,xs+xm-1
>
> 110:
> row(MatStencil_i) = i
>
> 111:
> row(MatStencil_j) = j
>
> 112:
> row(MatStencil_k) = k
>
> 113: if
> (i.eq.0 .or. j.eq.0 .or. k.eq.0 .or. i.eq.mx-1 .or. j.eq.my-1 .or.
> k.eq.mz-1) then
>
> 114:
> v(1) = 2.0*(HxHydHz + HxHzdHy + HyHzdHx)
>
> 115: call MatSetValuesStencil(jac,i1,row,i1,row,v,INSERT_VALUES
> ,ierr)
>
> 116: else
> 117:
> v(1) = -HxHydHz
>
> 118:
> col(MatStencil_i,1) = i
>
> 119:
> col(MatStencil_j,1) = j
>
> 120:
> col(MatStencil_k,1) = k-1
>
> 121:
> v(2) = -HxHzdHy
>
> 122:
> col(MatStencil_i,2) = i
>
> 123:
> col(MatStencil_j,2) = j-1
>
> 124:
> col(MatStencil_k,2) = k
>
> 125:
> v(3) = -HyHzdHx
>
> 126:
> col(MatStencil_i,3) = i-1
>
> 127:
> col(MatStencil_j,3) = j
>
> 128:
> col(MatStencil_k,3) = k
>
> 129:
> v(4) = 2.0*(HxHydHz + HxHzdHy + HyHzdHx)
>
> 130:
> col(MatStencil_i,4) = i
>
> 131:
> col(MatStencil_j,4) = j
>
> 132:
> col(MatStencil_k,4) = k
>
> 133:
> v(5) = -HyHzdHx
>
> 134:
> col(MatStencil_i,5) = i+1
>
> 135:
> col(MatStencil_j,5) = j
>
> 136:
> col(MatStencil_k,5) = k
>
> 137:
> v(6) = -HxHzdHy
>
> 138:
> col(MatStencil_i,6) = i
>
> 139:
> col(MatStencil_j,6) = j+1
>
> 140:
> col(MatStencil_k,6) = k
>
> 141:
> v(7) = -HxHydHz
>
> 142:
> col(MatStencil_i,7) = i
>
> 143:
> col(MatStencil_j,7) = j
>
> 144:
> col(MatStencil_k,7) = k+1
>
> 145: call MatSetValuesStencil(jac,i1,row,i7,col,v,INSERT_VALUES
> ,ierr)
>
> 146: endif
> .....................................................................................
> What I am confused about is what it means to have the value of row in i and j
> directions(row(MatStencil_i,1) & row(MatStencil_j,1)).
> Same confusion goes for the column values as well. I mean generally in a 2D
> Matrix row values are in j/y direction and column values are in i/x direction.
> Could you please explain that?
>
> Regards,
> Maahi Talukder
> Department of Mechanical Engineering
> Clarkson University
