kajny@ida.liu.se

1. GridModelica High Level Modeling on the Grid Kaj Nyström Dept. of Computer and Information Science, Linköping University MathCore Engineering AB kajny@ida.liu.se kajny@ida.liu.se

2. 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 kajny@ida.liu.se

3. Modeling – The way of doing things(2) • Factors limiting usage of modeling • Conservative engineers • Domain knowledge • Model complexity • Computational power kajny@ida.liu.se

4. 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 betweenall components (very useful for parallelization). • Reusable: Extensive object libraries exists. kajny@ida.liu.se

5. Modeling – Dealing with complexity(2) Example: The DC-motor kajny@ida.liu.se

6. 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; kajny@ida.liu.se

7. Modeling – Dealing with complexity(4) Another example: A robot, including visualization kajny@ida.liu.se

8. 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 needbut it also just brings us to the next (big) problem: kajny@ida.liu.se

9. 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 needbut it just brings us to the next (big) problem: • Partitioning! kajny@ida.liu.se

10. Partitioning models on the Grid An example: a+b+c+d=10a+b+c=2c-d=-2a+b-d=4 How would you solve this system? kajny@ida.liu.se

11. Partitioning models on the Grid (2) • The grid has special features/misfeatures: • Latency, latency, latency, latency… • Heterogenity • Close to infinite resources • Unpredictability • Unreliability kajny@ida.liu.se

12. 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. kajny@ida.liu.se

13. 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 kajny@ida.liu.se

14. High Level Partitioning (2) • The weak variables method • Partition the model into physical domains • Identify boundary variables • Treat these variables as parameters on both sides of boundary. • Use fast fixed step solvers but with different step-size for both subsystems kajny@ida.liu.se

15. High Level Partitioning (3) • The transmission line modeling method • Partition the model fast and slow subsystems • Insert delaying TLM-element between subsystems • Calculate approximate loss in precision and compensate if possible kajny@ida.liu.se

16. 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. kajny@ida.liu.se

17. 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 kajny@ida.liu.se

18. 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. kajny@ida.liu.se

19. Thank you for your attention Questions? kajny@ida.liu.se