Engee documentation

DASKR.jl

This is a wrapper package for importing solvers from DASKR into the SciML interface. DASKR.jl is not automatically included by DifferentialEquations.jl. To use this algorithm, you will need to install and use the package:

using Pkg
Pkg.add("DASKR")
using DASKR

These methods can be used independently of the rest of DifferentialEquations.jl.

DAE Solver APIs

function daskr(;linear_solver=:Dense,
                  jac_upper=0,jac_lower=0,max_order = 5,
                  non_negativity_enforcement = 0,
                  non_negativity_enforcement_array = nothing,
                  max_krylov_iters = nothing,
                  num_krylov_vectors = nothing,
                  max_number_krylov_restarts = 5,
                  krylov_convergence_test_constant = 0.05,
                  exclude_algebraic_errors = false)

This is a wrapper for the well-known DASKR algorithm.

DASKR is a solver for systems of differential-algebraic equations (DAEs). It includes options for both direct and iterative (Krylov) methods for the solution of the linear systems arising at each (implicit) time step. DASKR is a variant of the DASPK package [1]. In addition to all the capabilities of DASPK, DASKR includes the ability to find the roots of a given set of functions while integrating the DAE system.

In contrast to the older DASSL package, DASKR includes a procedure for calculating consistent initial conditions for a large class of problems (which includes semi-explicit index-1 systems) [2]. This procedure includes options for inequality constraints on selected components. The package also includes an option to omit the algebraic components from the local error control.

Linear Solver Choice

Choices for the linear solver are:

  • :Dense

  • :Banded

  • :SPIGMR, a Krylov method

Other Keyword Arguments

  • jac_upper=0,jac_lower=0: used for setting the upper and lower bands for a banded Jacobian. Defaults to 0. Ignored unless the linear solver is :Banded.

  • max_order = 5: the maximum order of the BDF method.

  • non_negativity_enforcement = 0, whether to enforce non-negativty in the solution. Defaults to 0 or false, can be set to 1 to enable.

  • non_negativity_enforcement_array = nothing, an array of 0’s and 1’s for specifying non-negativity enforcement to a subset of states.

  • max_krylov_iters=nothing: maximum number of iterations for the Krylov subspace linear solver before rejecting a step. Defaults to nothing or an automatic detection.

  • num_krylov_vectors=nothing: maximum number of history states in the GMRES vector. Defaults to nothing or an automatic choice

  • max_number_krylov_restarts=5: If you figure out what this is, open an issue or PR.

  • krylov_convergence_test_constant = 0.05: Some constant in DASKR’s convergence test.

  • exclude_algebraic_errors = false: whether algebraic variables are included in the adaptive time stepping error check. Defaults to false.