WIAS Preprint No. 382, (1997)

Parallelized numerical methods for large systems of differential-algebraic equations in industrial application


  • Borchardt, Jürgen
  • Grund, Friedrich
  • Horn, Dietmar

2010 Mathematics Subject Classification

  • 65Y05 65L05 65H10 65F50 80A30 92E20


  • Systems of differential-algebraic equations, Block partitioned systems, Newton-type methods, Gaussian elimination, Sparse-matrix techniques, Parallelization, Electric circuit simulation, Chemical process simulation.




Based on a hierarchical modular modeling the large nonlinear systems of differential algebraic equations arising from industrial applications in electric circuit simulation or in dynamic process simulation of chemical plants can be structured into subsystems. Parallelized numerical methods for solving such systems are considered at the level of nonlinear and linear equations. Merging subsystems to blocks and extending the systems of nonlinear equations resulting from backward differentiation formulas block-structured Newton-type methods can be used for their solution on parallel computers. A parallelized Gaussian elimination method using pseudo code techniques for the LU-factorization of the large sparse systems of linear equations is implemented. The methods are successfully used on parallel and vector computers for the time domain simulation of VLSI circuits as well as for the dynamic process simulation of complex chemical production plants.

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