SIDD: Short Range Interactions for Distributed Data

1. SIDD: Short Range Interactions for Distributed Data A new algorithm for solid-boundary communication. Sean Mauch Caltech October, 2003

2. Communicating the Solid Mesh Boundary • In the coupled Eulerian/Lagrangian VTF simulation, both the solid mesh and the fluid grid are distributed over a number of processors. • This simulation may require communicating the boundary of the solid to a group of processors. • To couple the solid solver and the fluid solver, the boundary of the solid mesh is communicated to the fluid processors. • In contact detection and correction the boundary of the solid is communicated to the solid processors. • Currently this communication is done by assembling the entire boundary (Gather-Send-Broadcast). This approach may not be feasible for very large meshes. • We are developing a new point-to-point algorithm for these problems. SIDD (Short-range Interactions for Distributed Data) uses bounding box information to determine communication patterns. 2

3. The Solid Mesh and the Fluid Grid • The solid mesh and the fluid grid are distributed over a number of processors. The fluid grid needs the boundary of the solid to enforce boundary conditions at the solid/fluid interface. Solid mesh. Fluid grid. 3

4. The Boundary of the Solid is Distributed • The boundary of the solid is distributed over the 9 solid processors. 4

5. The Gather-Send-Broadcast Algorithm • The solid processors gather the boundary onto the solid server. The solid server sends the boundary to the fluid server. The fluid server broadcasts the boundary to the 8 fluid processors. 5

6. Advantages/Disadvantages of GSB • Advantages: • Easy to implement. • The number of communications is small. • Disadvantages: • The average size of a communication is large. • Assembling the solid boundary may be costly or infeasible for large meshes. • Each fluid processor receives the entire boundary, though it only needs the portion that intersects its domain. • After receiving the entire boundary, each fluid processor extracts the relevant portion. This may be costly for large problems. 6

7. Bounding Boxes for the Solid and Fluid • Each solid processor makes a bounding box around its portion of the boundary. • Each fluid processor makes a bounding box that contains its region of interest. Any portion of the solid boundary in the region of interest could influence the fluid grid. 7

8. SIDD Algorithm: Gather and Exchange • The solid and fluid processors gather their bounding boxes. • Then the servers exchange the bounding boxes. 8

9. SIDD Algorithm: Broadcast • The solid server broadcasts the fluid bounding boxes. • The fluid server broadcasts the solid boundary bounding boxes. 9

10. SIDD Algorithm: Point to Point • Each solid processor knows where to send its portion of the boundary. • Each fluid processor knows from where to receive the relevant portions of the boundary. • Point-to-point communication from the solid to the fluid processors. 10

11. Features of the SIDD Algorithm • Instead of communicating the entire boundary, only the bounding box information is gathered and broadcasted. • It reduces the storage overhead for the boundary. • The number of communications is increased, but the volume of the communications is decreased. • The SIDD algorithm has better theoretical complexity for large problems. We expect that it will perform better than the gather-send-broadcast algorithm for these cases. • The SIDD algorithm does not depend on any special distribution of the data. 11