Transcript Slide 1 - NSC - Linköping University

GridModelica
High Level Modeling on the Grid
Kaj Nyström
Dept. of Computer and Information Science,
Linköping University
MathCore Engineering AB
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Modeling – The way of doing things
• Modeling (like talk) is cheap, considering the
alternatives
• Modeling is almost always possible
• Modeling gives extensive data even where physical
measuring might not always be possible, or is too
expensive.
• Modeling is fast, especially on large systems
Limiting factors:
• Model complexity
• Computational power
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Modeling – The way of doing things(2)
Factors limiting usage of modeling
• Conservative engineers
• Domain knowledge
• Model complexity
• Computational power
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Modeling – Dealing with complexity
• Traditionally high performance models have been
written in C or Fortran.
• The Modelica language provides an object oriented
approach to modeling.
Main benefits from our point of view:
• Acausal: No need to do the mathematical dirtywork
yourself anymore.
• Connection oriented: Well defined interface between
all components (very useful for parallelization).
• Reusable: Extensive object libraries exists.
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Modeling – Dealing with complexity(2)
Example: The DC-motor
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Modeling – Dealing with complexity(3)
Example: The DC-motor, modelica source code
model dcmotor
Modelica.Electrical.Analog.Basic.Resistor Resistor1;
Modelica.Electrical.Analog.Basic.Ground Ground1;
Modelica.Electrical.Analog.Basic.Inductor Inductor1;
Modelica.Electrical.Analog.Basic.EMF EMF1;
Modelica.Electrical.Analog.Sources.ConstantVoltage ConstantVoltage1;
Modelica.Electrical.Analog.Basic.Resistor Resistor2(R=10);
equation
connect(Resistor1.p, ConstantVoltage1.p) ;
connect(Resistor1.n, Inductor1.p);
connect(Inductor1.n, EMF1.p);
connect(ConstantVoltage1.n, Ground1.p);
connect(EMF1.n, Ground1.p);
connect(EMF1.flange_b, Inertia1.flange_a);
connect(Resistor2.p, Resistor1.p);
connect(Resistor2.n, Resistor1.n);
end dcmotor;
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Modeling – Dealing with complexity(4)
Another example: A robot, including visualization
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Problem 2: Computational Power
• The Grid is the solution (?) – Computational power
for the masses.
• Nordugrid middleware
• Resources: Nordugrid and our own cluster
This provides the computational power we need
but it also just brings us to the next (big) problem:
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Problem no 2: Computational Power
• The Grid is the solution (?) – Computational power
for the masses.
• Nordugrid middleware
• Resources: Nordugrid and our own cluster
This provides the computational power we need
but it just brings us to the next (big) problem:
Partitioning!
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Partitioning models on the Grid
An example:
a+b+c+d=10
a+b+c=2
c-d=-2
a+b-d=4
How would you solve this system?
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Partitioning models on the Grid (2)
The grid has special features/misfeatures:
• Latency, latency, latency, latency…
• Heterogenity
• Close to infinite resources
• Unpredictability
• Unreliability
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Partitining the models
We attack the problem on different levels
• High level partitioning - New Modelica constructs to
enable parallelism.
• Medium level partitioning - Shared level memory
model (GridNestStep).
• Low level partitioning – Parallelizing the generated
C-code.
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High Level Partitioning
• Partitioning at Modelica model level
• Done by adding partitioning constructs to the
language and modification of the Modelica compiler.
Considered methods are:
• Weak Operators/Variables (Francesco Casella)
• Transmission Line Modeling method (Christos
Christopoulos)
• Modelica specific ideas
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High Level Partitioning (2)
The weak variables method
1. Partition the model into physical domains
2. Identify boundary variables
3. Treat these variables as parameters on both sides
of boundary.
4. Use fast fixed step solvers but with different stepsize for both subsystems
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High Level Partitioning (3)
The transmission line modeling method
1. Partition the model fast and slow subsystems
2. Insert delaying TLM-element between subsystems
3. Calculate approximate loss in precision and
compensate if possible
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Medium Level Partitioning
Grid level parallelization
with GridNestStep
• Shared memory model
for the grid
• Specific adaption for
the grid is neccesary,
maximize time between
syncs is absolutely
vital.
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Low Level Partitioning
Primarily by task merging and common parallelization
techniques in parallel solvers
Task merging:
• Partition code very fine grained
• Achive parallelism by a sequence of duplicating
tasks and merging very small jobs, depending on
computational and communication cost.
• This can be done adaptively for large jobs
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Wrap up
• Parallelizing solving of large equation systems is
hard.
• Latency is our worst enemy
• Different variants of speculative execution might be
our best friends
• The grid might be a hype, but it is a useful hype.
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Thank you for your attention
Questions?
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