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poisson-bak
Course: M 171, Fall 2009School: University of Iowa
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of Rates Convergence Iteration Methods for Poisson's Equation Consider the discretization (8.8.1) of page 557 for Poisson's equation. De ne p21 ; 2 = 1 ; 2 sin2 2N ! = 1+ Rate of Convergence Jacobi Gauss-Seidel SOR For the SOR method, r ! ;1 0 ! 2 8 < (M (!)) = : 1 4 ! ;1 ! + (! )2 + 4 (1 ; !) q ! ! ! 2 Let MJ , MGS , and MSOR denote number the of iterations needed to reduce the iteration...
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of Rates Convergence Iteration Methods for Poisson's Equation
Consider the discretization (8.8.1) of page 557 for Poisson's equation. De ne p21 ; 2 = 1 ; 2 sin2 2N ! = 1+
Rate of Convergence
Jacobi Gauss-Seidel SOR For the SOR method,
r
!
;1
0
!
2
8 < (M (!)) = :
1 4
!
;1
!
+ (! )2 + 4 (1 ; !)
q
! !
!
2
Let MJ , MGS , and MSOR denote number the of iterations needed to reduce the iteration error by a factor of 10, for the Jacobi, Gauss-Seidel, and SOR methods, respectively.
2
!
MJ MGS MSOR
;1
N = 10 :9510565 :9045085 :527864
46 23 4...
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