On Tue, Aug 20, 2013 at 3:06 PM, Matthew Knepley <[email protected]> wrote:
> On Tue, Aug 20, 2013 at 7:19 AM, Bishesh Khanal <[email protected]>wrote: > >> Hi all, >> In solving problems such as laplacian/poisson equations with dirichlet >> boundary conditions with finite difference methods, I set explicity the >> required values to the diagonal of the boundary rows of the system matrix, >> and the corresponding rhs vector. >> i.e. typically my matrix building loop would be like: >> >> e.g. in 2d problems, using DMDA: >> >> FOR (i=0 to xn-1, j = 0 to yn-1) >> set row.i = i, row. j = j >> IF (i = 0 or xn-1) or (j = 0 or yn-1) >> set diagonal value of matrix A to 1 in current row. >> ELSE >> normal interior points: set the values accordingly >> ENDIF >> ENDFOR >> >> Is there another preferred method instead of doing this ? I saw functions >> such as MatZeroRows() >> when following the answer in the FAQ regarding this at: >> http://www.mcs.anl.gov/petsc/documentation/faq.html#redistribute >> >> but I did not understand what it is trying to say in the last sentence of >> the answer "An alternative approach is ... into the load" >> > > Since those values are fixed, you do not really have to solve for them. > You can eliminate them from your > system entirely. Imagine you take the matrix you produce, plug in the > values to X, act with the part of the > matrix that hits them A_ID X, and move that to the RHS, then eliminate > the row for Dirichlet values. > Now I understand the concept, thanks! So how do I efficiently do this with petsc functions when I am using DMDA which contains the boundary points too? Conceptually the steps would be the following, I think, but which petsc functions would enable me to do this efficiently, for example, without explicitly creating the new matrix A1 in the following and instead informing KSP about it ? 1) First create the big system matrix (from DM da) including the identity rows for Dirichlet points and corresponding rhs, Lets say Ax = b. 2) Initialize x with zero, then set the desired Dirichlet values on corresponding boundary points of x. 3) Create a new matrix, A1 with zeros everywhere except the row,col positions corresponding to Dirchlet points where put -1. 4) Get b1 by multiplying A1 with x. 5) Update rhs with b = b + b1. 6) Now update A by removing its rows and columns that correspond to the Dirichlet points, and remove corresponding rows of b and x. 7) Solve Ax=b > Matt > > Thanks, >> Bishesh >> > > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener >
