ConstrainedSystems.jl

Tools for solving constrained dynamical systems
Author JuliaIBPM
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June 2020

ConstrainedSystems.jl

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

du/dt = A u - B1T f + r1(u,t)

B2 u = r2(u,t)

u(0) = u0

where u is a state vector, A is a linear operator with an associated matrix exponential (integrating factor), and f 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).

It should be noted that the DifferentialEquations.jl package provides a nearly comprehensive set of tools for differential equations. However, the current package provides functionality for constrained systems.

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

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