The name is absent



108

We take the SVD of this matrix, V = UΣXτ, and choose a strong reduced system
size
ks < Ns. The POD matrix is then the first ks columns of U, i.e. U = (7(:, 1 : fcs).
Now we define the reduced variable by

vs = Uvs, vs ∈ Rfes, U ∈ R,jv≡×fej

and then we substitute into (4.16) to obtain

∂t


Q I zs 0
(c∕2)C Hs

0


oʃl 1

Φ   2πα∆a?


ξ

⅞ιw(t)^
. ш.


0

N(Uvs(t), ws(t))


Multiplying through by the projection matrices U and Uτ, we obtain the IRKA+P0D

reduced system
where the new “Hines” matrix is now completely dense, but of dimension
(kw + ks) ×
( kw
4- ks ).

∂t


(Zs 0) U ^
U7 HsU


’ 0_l , ɪ ∣^BIw(t)

UτΦ] 27rα∆rr [uτIs(t)


0
UrN(Uvs,ws)


(4.17)


The final step is to reduce the nonlinear term, which follows the same procedure
as in §3.2.2. In this way we obtain a basis for the nonlinear term by taking snapshots
of N, and then using the DEIM to obtain the set of
ks spatial interpolation points z.



More intriguing information

1. The name is absent
2. Heterogeneity of Investors and Asset Pricing in a Risk-Value World
3. The name is absent
4. FASTER TRAINING IN NONLINEAR ICA USING MISEP
5. Luce Irigaray and divine matter
6. How we might be able to understand the brain
7. Segmentación en la era de la globalización: ¿Cómo encontrar un segmento nuevo de mercado?
8. The bank lending channel of monetary policy: identification and estimation using Portuguese micro bank data
9. Modeling industrial location decisions in U.S. counties
10. The name is absent