Core algorithms for equation-based modeling
Author ModiaSim
6 Stars
Updated Last
1 Year Ago
Started In
February 2021


Stable The MIT License

ModiaBase is part of ModiaSim.

ModiaBase is usually used via Modia.

ModiaBase provides basic algorithms and functionality that is needed for equation-based modeling to transform a (potentially high-index) Differential-Algebraic Equation system (DAE), to an Ordinary Differential Equation system in state space form (ODE). It is used by Modia, but can also be utilized in another context. Especially the following functionality is provided:

  • Find a variable assignment of an equation system, in order to transform the equation system in a directed graph that can be further processed.

  • Find the strong components in a directed graph (with the algorithm of Tarjan) in order to find algebraic equation systems that must be solved together.

  • Sort an equation system (= transform to Block Lower Triangular form), in order determine the order in which the equations have to be evaluated.

  • Simplify linear Integer equations (remove alias variables/equations as well as redundant equations, provide definite values to variables that have an infinite number of solutions if this makes sense, make state constraints structurally visible). Many equations of object-oriented models are linear Integer equations and can be pre-processed exactly to simplify the equations and to remove (consistently) redundant or overdetermined equations.

  • Reduce the dimension of algebraic equation systems by tearing.

  • Find equations that need to be differentiated one or more times (with the algorithm of Pantelides) in order that the DAE can be transformed to an ODE.

  • Analytically differentiate the found equations.

  • Statically select ODE states and transform to ODE form (hereby identifying linear equation systems that must be solved during simulation).


Typically, a user installs Modia and does not need to install ModiaBase separately. If needed, ModiaBase is installed with (Julia >= 1.5 is required):

julia> ]add ModiaBase

Main Developers

License: MIT (expat)