Search code examples
differential-equationsmodelicadymola

In Dymola to solve DAEs, why use the DASSL algorithm after performing the Patelides algorithm?

I am confused about the solving DAEs process in Dymola. So I made an example to explore it.
Here is the screenshot of the example scheme and control equations

enter image description here

Based on the following definition of variables, I think the solving DAEs process is to

  1. choose the state variables
  2. using an integrator to calculate the state variables according to their derivatives.
  3. calculate the other variables.

enter image description here

I build the model in Dymola with the following debug settings.

enter image description here

Since the DAE's index in my model is 3, there is a need to do index reduction, after using the Pantelides Algorithm, Dymola would adding more differentiated equations to the DAE system.
The translate log verified my deduction. enter image description here

enter image description here enter image description here

Now, according to the equation browser, it is apparent the DAE system has been modified into a BLT form, I think I could just use the newton method with the current equation system, but Dymola would use the DASSL algorithm. And apparently, DASSL would do build the Structural Jacobian Matrix from scratch again, so during the initialization(using Pantelides Algorithm) and simulation(using DASSL Algorithm) processes, different Structural Jacobian Matrix would be used.

enter image description here

My question is:
After using Pantelides Algorithm to do index reduction and partitioning, I could solve the equations with Newton Method, but why does Dymola have to do partitioning again and use DASSL Algorithm?

enter image description here

In addition, I compared the Structural Jacobian Matrix in initialization and simulation process in Wolfram System Modeler, which showed these two matrices are different.

enter image description here

Solution

  • After using Pantelides Algorithm to do index reduction and partitioning, I could solve the equations with Newton Method, but why does Dymola have to do partitioning again and use DASSL Algorithm?

    The simple answer is: it doesn't have to do either additional partitioning or use DASSL. You can just click a few buttons and change the algorithm to cvode, Runge-Kutta, Euler, etc. I'm a bit unsure, but I don't think Dymola does any additional partitioning for DASSL in ODE mode (I know for sure that OpenModelica's DASSL algorithm does not - although it's a little silly using a DAE solver to solve an ODE system). If you run the simulation in DAE mode, you can perhaps even skip index reduction (depending on the index of the system).

    What the integration method (e.g. dassl) does is actually solve the system time step by time step. What Pantelides algorithm does is index reduction (in Modelica tools usually to ODE form, which is what most of the integration methods require).