Dynamic load balancing. Overview.

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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.

• 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.

The combustion zone
CH4 concentration
CO concentration
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Dynamic load balancing. Problem statement.

• 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

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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

When a task is processed, the result should be
returned to the corresponding processor
regardless where it was obtained
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Dynamic load balancing.Issues.

• Algorithm is based on collective farm, but is
  devoid of its
• shortcoming. 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 are
• stored 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.

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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

speedup
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