psb_ovrl -- Overlap Update

These subroutines applies an overlap operator to the input vector:

$$x \leftarrow Q x$$

where:

$x$

is the global dense submatrix $x$

$Q$

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

Table 15: Data types

$x$	Subroutine
Short Precision Real	psb_ovrl
Long Precision Real	psb_ovrl
Short Precision Complex	psb_ovrl
Long Precision Complex	psb_ovrl

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 vdatapsb_T_vect_type containing numbers of type specified in Table 15.

desc_a

contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type descdatapsb_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 15.

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.

Figure 8: Sample discretization mesh.

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)

Process 0				Process 1
I	GLOB(I)	X(I)		I	GLOB(I)	X(I)
1	1	1.0		1	33	1.5
2	2	1.0		2	34	1.5
3	3	1.0		3	35	1.5
4	4	1.0		4	36	1.5
5	5	1.0		5	37	1.5
6	6	1.0		6	38	1.5
7	7	1.0		7	39	1.5
8	8	1.0		8	40	1.5
9	9	1.0		9	41	2.0
10	10	1.0		10	42	2.0
11	11	1.0		11	43	2.0
12	12	1.0		12	44	2.0
13	13	1.0		13	45	2.0
14	14	1.0		14	46	2.0
15	15	1.0		15	47	2.0
16	16	1.0		16	48	2.0
17	17	1.0		17	49	2.0
18	18	1.0		18	50	2.0
19	19	1.0		19	51	2.0
20	20	1.0		20	52	2.0
21	21	1.0		21	53	2.0
22	22	1.0		22	54	2.0
23	23	1.0		23	55	2.0
24	24	1.0		24	56	2.0
25	25	1.5		25	57	2.0
26	26	1.5		26	58	2.0
27	27	1.5		27	59	2.0
28	28	1.5		28	60	2.0
29	29	1.5		29	61	2.0
30	30	1.5		30	62	2.0
31	31	1.5		31	63	2.0
32	32	1.5		32	64	2.0
33	33	1.5		33	25	1.5
34	34	1.5		34	26	1.5
35	35	1.5		35	27	1.5
36	36	1.5		36	28	1.5
37	37	1.5		37	29	1.5
38	38	1.5		38	30	1.5
39	39	1.5		39	31	1.5
40	40	1.5		40	32	1.5
41	41	2.0		41	17	1.0
42	42	2.0		42	18	1.0
43	43	2.0		43	19	1.0
44	44	2.0		44	20	1.0
45	45	2.0		45	21	1.0
46	46	2.0		46	22	1.0
47	47	2.0		47	23	1.0
48	48	2.0		48	24	1.0