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 salome-med  6.5.0
OverlapDEC

The \c OverlapDEC enables the \ref InterpKerRemapGlobal "conservative remapping" of fields between two parallel codes.
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The \c OverlapDEC enables the \ref InterpKerRemapGlobal "conservative remapping" of fields between two parallel codes.

This remapping is based on the computation of intersection volumes on a same processor group. On this processor group are defined two field-templates called A and B. The computation is possible for 3D meshes, 2D meshes, 3D-surface meshes, 1D meshes and 2D-curve meshes. Dimensions must be similar for the distribution templates A and B. The main difference with InterpKernelDEC is that this DEC manages 2 field templates on each processor of the processor group (A and B) called source and target. Furthermore all processors in processor group cooperates in global interpolation matrix computation. In this respect InterpKernelIDEC is a specialization of OverlapDEC.

## Algorithm Description

Let's consider the following use case that is ran in ParaMEDMEMTest_OverlapDEC.cxx to describes the different steps of the computation. The processor group contains 3 processors.

Example showing the use case in order to explain the different steps.

### Step 1 : Bounding box exchange and global interaction between procs computation.

In order to reduce as much as possible the amount of communications between distant processors, every processor computes a bounding box for A and B. Then a AllToAll communication is performed so that every processor can compute the global interactions between processor. This computation leads every processor to compute the same global TODO list expressed as a list of pair. A pair (x,y) means that proc x fieldtemplate A can interact with fieltemplate B of proc y because the two bounding boxes interact. In the example above this computation leads to the following a global TODO list :

(0,0),(0,1),(1,0),(1,2),(2,0),(2,1),(2,2)

Here the pair (0,2) does not appear because the bounding box of fieldtemplateA of proc#2 does not intersect that of fieldtemplate B on proc#0.

Stage performed by ParaMEDMEM::OverlapElementLocator::computeBoundingBoxes.

### Step 2 : Computation of local TODO list

Starting from the global interaction previously computed in Step 1, each proc computes the TODO list per proc. The following rules is chosen : a pair (x,y) can be treated by either proc #x or proc #y, in order to reduce the amount of data transfert among processors. The algorithm chosen for load balancing is the following : Each processor has an empty local TODO list at the beginning. Then for each pair (k,m) in global TODO list, if proc::k has less temporary local list than proc::m pair, (k,m) is added to temparary local TODO list of proc::k. If proc::m has less temporary local TODO list than proc::k pair, (k,m) is added to temporary local TODO list of proc::m. If proc::k and proc::m have the same amount of temporary local TODO list pair, (k,m) is added to temporary local TODO list of proc::k.

In the example above this computation leads to the following local TODO list :

• proc#0 : (0,0)
• proc#1 : (0,1),(1,0)
• proc#2 : (1,2),(2,0),(2,1),(2,2)

The algorithm described here is not perfect for this use case, we hope to enhance it soon.

At this stage each proc knows precisely its local TODO list (with regard to interpolation). The local TODO list of other procs than local is kept for future computations.

### Step 3 : Matrix echange between procs

Knowing the local TODO list, the aim now is to exchange field-templates between procs. Each proc computes knowing TODO list per proc computed in Step 2 the exchange TODO list :

In the example above the exchange TODO list gives the following results :

Sending TODO list per proc :

• proc #0 : Send fieldtemplate A to Proc#1, Send fieldtemplate B to Proc#1, Send fieldtemplate B to Proc#2
• Proc #1 : Send fieldtemplate A to Proc#2, Send fieldtemplate B to Proc#2
• Proc #2 : No send.

Receiving TODO list per proc :

• proc #0 : No receiving
• proc #1 : receiving fieldtemplate A from Proc#0, receiving fieldtemplate B from Proc#0
• proc #2 : receiving fieldtemplate B from Proc#0, receiving fieldtemplate A from Proc#1, receiving fieldtemplate B from Proc#1

To avoid as much as possible large volumes of transfers between procs, only relevant parts of meshes are sent. In order for proc::k to send fieldtemplate A to fieldtemplate B of proc #m., proc::k computes the part of mesh A contained in the boundingbox B of proc::m. It implies that the corresponding cellIds or nodeIds of the corresponding part are sent to proc #m too.

Let's consider the couple (k,m) in the TODO list. This couple is treated by either k or m as seen in here in Step2.

As will be dealt in Step 6, for final matrix-vector computations, the resulting matrix of the couple (k,m) whereever it is computed (proc #k or proc #m) will be stored in proc::m.

• If proc #k is in charge (performs the matrix computation) for this couple (k,m), target ids (cells or nodes) of the mesh in proc #m are renumbered, because proc #m has seelected a sub mesh of the target mesh to avoid large amounts of data to transfer. In this case as proc #m is ultimately in charge of the matrix, proc #k must keep preciously the source ids needed to be sent to proc::m. No problem will appear for matrix assembling in proc m for source ids because no restriction was done. Concerning source ids to be sent for the matrix-vector computation, proc k will know precisely which source ids field values to send to proc #m. This is embodied by OverlapMapping::keepTracksOfTargetIds in proc m.
• If proc #m is in charge (performs matrix computation) for this couple (k,m), source ids (cells or nodes) of the mesh in proc #k are renumbered, because proc #k has selected a sub mesh of the source mesh to avoid large amounts of data to transfer. In this case as proc #k is ultimately in charge of the matrix, proc #m receives the source ids from remote proc #k, and thus the matrix is directly correct, no need for renumbering as in Step 5. However proc #k must keep track of the ids sent to proc #m for te matrix-vector computation. This is incarnated by OverlapMapping::keepTracksOfSourceIds in proc k.

This step is performed in ParaMEDMEM::OverlapElementLocator::exchangeMeshes method.

### Step 4 : Computation of the interpolation matrix

After mesh exchange in Step3 each processor has all the required information to treat its local TODO list computed in Step2. This step is potentially CPU costly, which is why the local TODO list per proc is expected to be as well balanced as possible.

The interpolation is performed as Remapper does.

This operation is performed by OverlapInterpolationMatrix::addContribution method.

### Step 5 : Global matrix construction.

After having performed the TODO list at the end of Step4 we need to assemble the final matrix.

The final aim is to have a distributed matrix on each proc::k. In order to reduce data exchange during the matrix product process, is built using sizeof(Proc group) std::vector< std::map<int,double> >.

For a proc::k, it is necessary to fetch info of all matrices built in Step4 where the first element in pair (i,j) is equal to k.

After this step, the matrix repartition is the following after a call to ParaMEDMEM::OverlapMapping::prepare :

• proc#0 : (0,0),(1,0),(2,0)
• proc#1 : (0,1),(2,1)
• proc#2 : (1,2),(2,2)

Tuple (2,1) computed on proc 2 is stored in proc 1 after execution of the function "prepare". This is an example of item 0 in Step2. Tuple (0,1) computed on proc 1 is stored in proc 1 too. This is an example of item 1 in Step2.

In the end ParaMEDMEM::OverlapMapping::_proc_ids_to_send_vector_st will contain :

• Proc#0 : 0,1
• Proc#1 : 0,2
• Proc#2 : 0,1,2

In the end ParaMEDMEM::OverlapMapping::_proc_ids_to_recv_vector_st will contain :

• Proc#0 : 0,1,2
• Proc#1 : 0,2
• Proc#2 : 1,2

The method in charge to perform this is : ParaMEDMEM::OverlapMapping::prepare.