Interpolating Shape Functions

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Presentation transcript:

Interpolating Shape Functions Wednesday, 10/16/2002

Local Interpolation (1D)

Local Shape Function (1D)

1D Shape Function in Local Coordinate System

1D Shape Function

Global Shape Function (1D)

Out of Cell Shape Function is 0

2D Shape Function 1D Shape Function

2D Interpolation Surface

Interpolation Surface

Shape Function (2D)

Bilinear Shape Function

2D Shape Function

2D Global Shape Function L is half of the cell size

Out of Cell Shape Function is Zero

Properties of Shape Function (1) Partition of unity (2) Positive (3) Kronecker delta m and n are grid nodes. (4) Interpolation (5) Smooth everywhere, except at nodes where they are continuous.