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13 Cards in this Set
- Front
- Back
MPP Banded Sparse GE FLOPs |
1D: 5N ~ 5h^-1 2D: O(N^4) ~ O(h^-4) 3D: O(N^7) ~ O(H^-7) |
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MPP Banded Sparse GE Storage |
1D: 4N ~ 4h^-1 2D: 2N^3 ~ 2h^-3 3D: 2N^5 ~ 2H^-5 |
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MPP residual computation FLOPs |
1D: 6N ~ 6h^-1 2D: 10N^2 ~ 10h^-2 3D: 14N^3 ~ 14H^-3 |
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MPP residual computation Storage |
1D: 2N ~ 2h^-1 2D: 2N^2 ~ 2h^-2 3D: 2N^3 ~ 2H^-3 |
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GE FLOPs |
(2/3)N^3 |
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Back solve FLOPs |
N^2 |
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Multiplying Ax |
2N^2 - N |
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Solve Tridiag Ax = b |
GE = 5N - 5 BS = 3N-2 |
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J_0_(x) |
(1/2)xTAx - xTb |
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FOR with MPP |
rho(u^(n+1) - u^(n)) = f - Au^n uij^(n+1) = (1/rho)(fij +ui+1j^n + ui-1j^n + uij+1^n + uij-1^n) |
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Steepest Descent Algorithm |
A: SPD; guess x0, r0 = b-Ax0 For n = 1:Itmax dn = rn alphn = (dnTrn/dnTAdn) xn+1 = xn + alphndn rn+1 = {b - Axn+1, or rn - alphnAdn} Test for convergence |
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Conjugate Gradient Method Algorithm |
Given x0, r0 = b - Ax0, d0 = r0 alphn = (dnTrn/dnTAdn) xn+1 = xn + alphndn rn+1 = {b - Axn+1, or rn - alphnAdn} Test for Convergence In divergent Bn+1 = rnTrn/rn+1Trn+1 dn+1 = rn+1 + Bn+1dn |
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<x,d>A |
xTAd = bTd for symmetric matrices |