> On Mar 11, 2019, at 11:11 PM, Maahi Talukder <[email protected]> wrote:
>
> Hi
> Thank you so much for explanation.
>
> So when you say connecting two points on the grid in the matrix entry, what
> do you mean by that? Do you mean that matrix entry is calculated using two
> points ( (i,j) and (i',j') ) on the grid?
I mean the value of the finite difference "stencil" that connects the two
points.
Take a look at src/ksp/ksp/examples/tutorials/ex22f.F90. The inner most loop
do 30,i=xs,xs+xm-1
row(MatStencil_i) = i
row(MatStencil_j) = j
row(MatStencil_k) = k
....
sets one row of the matrix which has 7 nonzero columns corresponding to the 6
neighbors of the (i,j,k) point plus the diagonal entry which connects with
itself.
> And when you talked about thinking about the vector, how is it that the
> entry in the vector is a function of both i and j?
For each (i,j) point on the mesh there is a vector entry. When indexing into
vectors we use a single index value m; that has to be computed based on the two
values of the logical coordinates on the mesh i and j.
> Will it be the same if my dof = 1 ie solving for only one thing at each grid
> point?
Yes it doesn't have anything to do with dof. The stencil_c value is used for
multiple degrees of freedom per grid point.
>
>
> Regards,
> Maahi Talukder
>
> On Mon, Mar 11, 2019 at 11:11 PM Smith, Barry F. <[email protected]> wrote:
>
>
> > On Mar 11, 2019, at 10:01 PM, Maahi Talukder <[email protected]> wrote:
> >
> > Hi
> > Thank you for your explanation.
> > So is it so that it always connects two points?
>
> Entries in matrices represent the connection between points in a vector
> (including the diagonal entries that are connections between a point and
> itself).
>
> I think you are "over-thinking" MatStencil. It is just a handy way of
> managing the mapping from a grid point to an entry in a vector. And similarly
> from two grid points and an entry in a matrix.
>
> > I am still hazy on the concept. Could you suggest me some more elaborate
> > book or something to go through so that I can grasp the whole concept? How
> > about your book ' Domain Decomposition'? Does it cover this topic?
>
> No, it doesn't discuss this issue.
>
> Barry
>
> > Please let me know
> >
> > Regards,
> > Maahi Talukder
> >
> > On Mon, Mar 11, 2019 at 9:46 PM Smith, Barry F. <[email protected]> wrote:
> >
> >
> > > 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
> >
>
