institute for mathematical modeling ras 1 dynamic load balancing. overview. simulation of combustion...

Institute for Mathematical Modeling RAS

1

Dynamic load balancing.Overview.

Simulation of combustion problems using multiprocessor computer systems• For the "chemical part" of the problem the computational costs are very expensive and each point depends

strongly on values of temperature and species concentration and can not be predetermined before calculation. In our case the calculation of chemical reactions requires more than 90% of total computational time. The reason of such fact is that in some of chemical processes the time of reactions is very small in comparison to gas dynamic time.

5%

65%

CH4

30%

The combustion zone • Many of the species exist and react only in the quite narrow region - in the flame front. The equal number of numerical points per processor does not imply the load balancing automatically therefore the special software was developed. The modified "processor farm" principles with master controlled data exchange between worker-nodes were used to achieve load balancing for chemical kinetic part.

CH4 concentration CO concentration

M.IakobovskiM.Iakobovski


2M.IakobovskiM.Iakobovski


3

The system of equations, governing gas-dynamic and chemical kinetic processes under combustion, expressed in operator form is the following:

Here A is a nonlinear operator, - density, y(i) - mass fraction of the i-th species, u, v - components of velocity along x and y respectively, p - pressure, E - total energy, I - mass velocity of formation of substance in all responses.

I. Gasdynamic block (GD):

GD block is approximated via half-implicit finite-difference scheme

II. Block of chemical kinetics (CHEM):

Dynamic load balancing. Problem statement.

,fAt

UU

U , , , ,( )y u v Ei T

f iT( , , , , )0 0 0 0

0 UU

At

U UU U

j jj j

tA A

1

11

20

.

d

dtf

U , T

if )0,0,0,,0(



4

Dynamic load balancing.Goals.

The main goal was to develop a library for dynamic load balancing of loosely coupled distributed tasks when using a heterogeneous multiprocessor systems

Independent tasks are assigned to the nodes of the mesh, which is distributed over processors according to the domain decomposition method

1 3 5 7 9

11 13 15 17 19 21 23 25 27 29

Р1

0.00

5.00

10.00

15.00

20.00

25.00

Calculation time using domain decomposition

ideal time

the number of processor

sec p r o c e s s i n g t i me

When a task is processed, the result should be returned to the corresponding processor regardless where it was obtained



5

Algorithm is based on collective farm, but is devoid of itsshortcoming. It is achieved due to a great reduction of traffic as each processing node possesses equal controlling features.Two (or more) processes are executed on each node - communication (control) process and operating process (or processes).

Algorithm for load balancing is based on the following principles:• each processor primarily operates its local points (that arestored in its memory);• the processor can request points from the others provided that a) all local points are calculated or transferred for handling to other processors; b) transmission of points for handling to otherprocessors and handling of local pointsare fulfilled simultaneously.

Dynamic load balancing.Issues.

A

D

B

E

C

A

D

B

E

C

A

D

B

E

C

task

Calculation process

Control process

Processor



6

Dynamic load balancing. Status.

• The dynamic load balancing library was developed. The library allows to efficiently schedule the stream of tasks, which are distributed according to the domain decomposition method.

• The library provides efficient use of metacomputers. The mesh may be stored within one or both clusters

• An approach is offered to the integration of more than two clusters forsolving combustion problems

High speed network Mbyte/sec

Low speed network

Client

Server

32 processors 12 processors

1.00

6.00

11.00

16.00

21.00

26.00

31.00

36.00

41.00

1 5 9 13 17 21 25 29 33 37 41 45

Np

speedup

Cluster1

CFD

Cluster2 Chemical

Cluster4 Chemical

Cluster3 Chemical

Control


institute for mathematical modeling ras 1 dynamic load balancing. overview. simulation of combustion...

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