Tools for solving constrained dynamical systems

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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 - B1T 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 B1T 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 B1T 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.