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Interpolations

Interpolations. Achi Brandt. Two Dimensional Interpolation. First direction Second direction Bileanear. Bicubic … Bipolynomial. Linear Interpolation 2h →h.  ”second order” interpolation. P-order interpolation. Linear interpolation: p = 2 Cubic interpolation: p = 4. u (x j ). u (x).

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Interpolations

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  1. Interpolations Achi Brandt

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

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

  4. P-order interpolation Linear interpolation: p = 2 Cubic interpolation: p = 4 u (xj) u (x) Xi+p Xi+2 Xi+1 X

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

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

  7. 1-D linear interpolation2h h Adjoint h 2h transfer(anterpolation) = = = =

  8. Coarse-Grid Aliasing

  9. Coarse-Grid Aliasing

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