1. Interpolations Achi Brandt

3. Two Dimensional Interpolation First direction Second direction Bileanear. Bicubic … Bipolynomial

4. Linear Interpolation 2h →h  ”second order” interpolation

5. P-order interpolation Linear interpolation: p = 2 Cubic interpolation: p = 4 u (x j ) u (x) X i+1 X i+2 X i+p X

6. Fine-to Coarse Transfer (Restriction) Injection Full Weighting

7. Linear interpolation: Second order transfers. General order, general dimension d:

9. 1-D linear interpolation 2h h Adjoint h 2h transfer (anterpolation) = = = =

10. Coarse-Grid Aliasing