4. Interpolation Design

4.1. Requirements

This document describes incorporating “ENZO interpolation” into Enzo-E; in particular, the “SecondOrderA” method. This method requires an extra layer of coarse-level cells compared to the basic “trilinear interpolation” previously implemented in Enzo-E. Implementing this requires additional communication, since this augmented coarse-grid array overlaps multiple additional blocks.

In ENZO’s SecondOrderA interpolation method, multiple additional blocks intersect the extended array of coarse values (red) required for computing the interpolated ghost zone values (blue) for the fine block (green) that intersects a coarse block.

4.2. Design

We decompose the operations required according to the role of blocks for each interpolation. Note a given block may participate in multiple roles for different block faces. There are three main block roles involved in an interpolation:

1. Sending block

   1. sends its overlapped cell values to the receiver

2. Extra block

   1. sends its overlapped cell values to the receiver

3. Receiving block

   1. receives data from sending and extra blocks

   2. copies incoming data to padded array

   3. copies its own overlapped cells to the padded array

   4. calls the interpolation operation using the padded array to compute the interpolated ghost cell values

Some minor operations are not included, such as extra blocks that are in the same level as the receiving block need to “coarsen” their values before sending to the receiving block in operation 3.

4.2.1. Sending Block

The sending block must send its data to the receiving block, as it does for all other refresh operations. The main difference is it requires an additional layer of padding when sending. This is handled by the method Block::refresh_load_field_face_() in control_refresh.cpp

4.2.2. Extra Block

In addition to the sending block, some extra blocks must also send their overlapped cell data to the receiving block. This requires an extra loop and some additional logic for a block to determine that it must participate in an interpolation operation not as the sender or receiver. This is handled in the Block::refresh_load_extra_face_() method, which can be found in the control_refresh.cpp source file. Depending on the relative mesh refinement level, an extra block may be handled

4.2.3. Receiving Block

4.3. Milestones

4.4. Tasks