Schur Complement Based Parallel Finite Element Analysis Coupled

1. Széchenyi István Universityhttp://uni.sze.hu Department of Automationhttp://automatizalas.sze.hu Laboratory of ElectromagneticFieldhttp://emt.sze.hu Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical Equations Dániel Marcsa, Miklós Kuczmann Széchenyi István University (Hungary)Department of Automation, Laboratory of ElectromagneticField Research Centre of VehicleIndustry E-mail: marcsad@sze.hu The 15th International ConferenceonComputationalProblems of ElectricalEngineering 9th-12th, September, 2014, Terchová-Vrátna dolina, SlovakRepublik

2. Formulation Equation of thinconductors Formulation with magnetic vector potential 2D model Discretization Finiteelement Ni(x, y) Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

3. Movement Modelling Slidingsurfacetechnique Firstorderinterpolation Interpolationmatrix Mechanicalequation Maxwell’sstresstensormethod Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

4. SchurComplementMethod • The solution of the sub-problems is “easier” than the original • The original problem does not fit into the available memory space Motivations Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

5. SchurComplementMethod ajis the vector of the right hand side defined inside the sub-domain. Equation of sub-domain aГ is the coupling of the interface unknowns. Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

6. SchurComplementMethod The movementmodeling is additionalinterprocesscommunication. Stator Rotor Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

7. Parallel Solver Parallel preconditionedconjugategradientsolver with Jacobi preconditioner with Neumann-Neumann preconditoner Interprocesscommunication (dataexchange) Parallel part (local operation) Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

8. Benchmark 4-pole 3-phase 3kW induction motor Gmsh 2D modell withend-winding inductance Anti-periodicboundarycondition Anti-periodicboundarycondition Discretization and partitioning Solvedtheproblem by parallel way GmshwithMetis Matlab Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

9. SimulationResults Simulationresults of induction motor Transientwaveform of rotor speed Transientwaveform of phasecurrents Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

10. Speedup Jacobi Neumann-Neumann Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

11. Efficiency Jacobi Neumann-Neumann Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

12. Performance of theSolver Jacobi Neumann-Neumann Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa

13. Conclusions and Future Works • The implemented programis workproperly, as the results of test problem are shows. • The numerical experiments show the work of the implementedprogram is depend on the size of the problem, butindependentfromtheinternalunknowns. • Implemented the presented methods for 3D parallel finite element method. • Used the finiteelementmodelin a controlloop, and forthecontrol design. Schur Complement Based Parallel Finite Element Analysis Coupled With Circuit and Mechanical EquationsDániel Marcsa