Priori local grid refinement in the multigrid method Page: 4 of 14
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31
For equations with well behaved coefficients, it
suffices to take Ik1 to be bilinear interpolation and
Ik-1 to be (I 1)T or just injection. However, because
of the jump discontinuities in D, a more exotic choice of
these operators is required (1,5): We take Ik-1 ~ k-1
anu Ik-1 = (Jk)T, where J is as follows. Suppose
that at (IF+1,JF) a Gk, Lk has the pointwise templateTk
IF+I,JF+1
k
F+I,JF
Rk
RIF+1 ,JFand that
(IFJF) a Gk.
replacement:wk
IF+I,.JF+1
k
SIF+I,JF
k
WI+,JF(IC,JC) Gk-1
At (IF,JF),k
-RIF+2,JF+1
-IF+2,JF
k
-TIF+2 ,JFis the same point
Jk- is just givenk k-1 =k-1
(Jk-1v )IF,JF = I,JC
At (IF+l,JF), we have
k-1 k-1
k k-1 'IF+1,JF V CJC +IF+2,JF SIC+iJC
(k-1 )IF+1,JF k
IF+1,JF
where
IF+1,JF IF+I,JF+1 + IF+i,JF IF+1,JFIF+1,JF F+1,JF IF+1,JF + F+1,JF+1
(5)
as
by
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Dendy, Joel E. Priori local grid refinement in the multigrid method, article, January 1, 1983; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1212379/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.