5.2 psb_ovrl — Overlap Update

These subroutines applies an overlap operator to the input vector:

where:

x

is the global dense submatrix x

Q

is the overlap operator; it is the composition of two operators P_a and P^T.

Type:

Synchronous.

On Entry

x

global dense matrix x.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type psb_T_vect_type containing numbers of type specified in Table 18.

desc_a

contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type.

update

Update operator.

update = psb_none_

Do nothing;

update = psb_add_

Sum overlap entries, i.e. apply P^T;

update = psb_avg_

Average overlap entries, i.e. apply P_aP^T;

Scope: global
Intent: in.
Default: update_type = psb_avg_
Scope: global
Specified as: a integer variable.

work

the work array.
Scope: local
Type: optional
Intent: inout.
Specified as: a one dimensional array of the same type of x.

On Return

x

global dense result matrix x.
Scope: local
Type: required
Intent: inout.
Specified as: an array of rank one or two containing numbers of type specified in Table 18.

info

Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.

Notes

1. If there is no overlap in the data distribution associated with the descriptor, no operations are performed;
2. The operator P^T performs the reduction sum of overlap elements; it is a “prolongation” operator P^T that replicates overlap elements, accounting for the physical replication of data;
3. The operator P_a performs a scaling on the overlap elements by the amount of replication; thus, when combined with the reduction operator, it implements the average of replicated elements over all of their instances.

Example of use Consider the discretization mesh depicted in fig. 8, partitioned among two processes as shown by the dashed lines, with an overlap of 1 extra layer with respect to the partition of fig. 7; the data distribution is such that each process will own 40 entries in the index space, with an overlap of 16 entries placed at local indices 25 through 40; the halo will run from local index 41 through local index 48.. If process 0 assigns an initial value of 1 to its entries in the x vector, and process 1 assigns a value of 2, then after a call to psb_ovrl with psb_avg_ and a call to psb_halo_ the contents of the local vectors will be the following (showing a transition among the two subdomains)