Tools for solving constrained dynamical systems

Documentation	Build Status

This package contains several tools for solving and advancing (large-scale) dynamical systems with constraints. These systems generically have the form

dy/dt = L y - B₁^T z + r₁(y,t)

B₂ y + C z = r₂(y,t)

y(0) = y₀

where y is a state vector, L is a linear operator with an associated matrix exponential (integrating factor), and z is a constraint force vector (i.e., Lagrange multipliers).

Some of the key components of this package are

• Tools for solving linear algebra problems with constraints and associated Lagrange multipliers, known generically as saddle point systems. The sizes of these systems might be large.

• Time integrators that can incorporate these constraints, such as half-explicit Runge-Kutta (HERK) and integrating factor Runge-Kutta (IFRK), or their combination (IF-HERK). These extend the tools in the DifferentialEquations.jl package, and utilize the same basic syntax for setting up a problem and solving it.

• Allowance for variable constraint operators B₁^T and B₂, through the use of a variable parameter argument and an associated parameter update function.

• The ability to add an auxiliary (unconstrained) system of equations that the constraint operators B₁^T and B₂ depend upon.

The package is agnostic to the type of systems, and might arise from, e.g., fluid dynamics or rigid-body mechanics.