### Table of Contents

The Chrono system contains all other objects being simulated, like bodies, links, etc. The system is the cornerstone of a Chrono simulation.

# ChSystem

A Chrono simulation system is an object of class ChSystem. See ChSystem for API details.

Note that ChSystem is an abstract class: you must instantiate one of its specializations. In detail you can use of these sublclasses:

- ChSystemNSC for
**Non Smooth Contacts**(NSC): in case of contacts a complementarity solver will take care of them using non-smooth dynamics; this is very efficient even with large time steps. - ChSystemSMC for
**SMooth Contacts**(SMC): contacts are handled using penalty methods, i.e. contacts are deformable;

If there are no contacts or collisions in your system, it is indifferent to use ChSystemNSC or ChSystemSMC.

- A ChSystem contains all items that participate in a simulation: bodies, constraints, numerical integrator type, integration tolerances, etc.
- Use the
`Add()`

,`Remove()`

functions to add elements to a system object

Recommended way of dealing with system objects:

- Create a ChSystemNSC or a ChSystemSMC
- Add body objects into it, see ChBody
- Add link objects into it, see ChLink
- Adjust parameters for the time integration and solver
- Run a dynamic simulation

Refer to demo_MBS_crank for a basic example.

In most cases there are three parameters to adjust:

**time stepper**: the time integration algorithm and its stepsize (when calling DoStepDynamics())**solver**; the algorithm that computes accelerations and reaction forces at each time step; setting a proper number of max iterations is crucial for iterative solvers e.g.`my_system.GetSolver()->AsIterative()->SetMaxIterations(400);`

**collision parameters**

A primer on tuning these parameters is provided below.

# Time steppers

Time steppers, also known as *time integrators*, are used to advance the simulation. They perform numerical integration and they advance the state of the system in time.

Technical and theoretical details on time integration are explained in several PDF documents available on the white papers page. For example the Integrator Whitepaper explains how implicit integrators are implemented in Chrono.

Time steppers can be changed in two ways:

- Using the
`my_system.SetTimestepper(...)`

function, to plug in a custom time-stepper, which is user-defined**[PREFERRED]** - Using the
`my_system.SetTimestepperType(...)`

function, to choose a ready-to-use, pre-packaged time-stepper

Example: changing the time stepper to an implicit numerical integrator

Summary of time-steppers:

`EULER_IMPLICIT_LINEARIZED`

- Default time stepper in Chrono
- Fast, no sub-iterations required
- First order accuracy
- Works for DVI contacts (hard contacts)
- Delivers first order accuracy for FEA
- Constraints kept closed using stabilization

`HHT`

- Implicit integrator, based on the Hilber-Hughes-Taylor formula
- Typically slower than the INT_EULER_IMPLICIT_LINEARIZED choice
- Sub-iterations required
- Second order accuracy, with adjustable numerical damping
- Currently can't be used for systems that handle contacts in a DVI approach; i.e., for hard contacts
- Delivers second order accuracy for FEA
- Constraints kept closed
*exactly*because of inner iterations.

`NEWMARK`

- Popular in the FEA community, similar properties as INT_HHT
- With the exception of one particular choice of parameters (in which it becomes the trapezoidal integration rule) it delivers first order accuracy

In the above, the meaning of 'first order' or 'second order' accuracy is that the global integration error goes to zero as the value of the time step (or square of the time step for a second order method).

Depending on the type of time-stepper used, there may be different parameters to adjust. Example:

See ChTimestepper API for details.

# Solvers

A solver is called by a time stepper to compute the unknown accelerations and unknown reaction forces at each time step of the simulation. Most often they represent the biggest computational bottleneck of the entire simulation.

Solvers can be changed in two ways:

- Using the
`my_system.SetSolver(...)`

function, to plug in a custom time-stepper, which is user-defined**[PREFERRED]** - Using the
`my_system.SetSolverType(...)`

function, to choose a ready-to-use, pre-packaged option

Example:

We recommend using one of the following iterative solvers:

`PSOR`

- low precision: convergence might stall, especially with odd mass ratios
- supports DVI (hard contacts, with complementarity)
- used most often for small problems, solution accuracy is not particularly important

`APGD`

- very good convergence, used most often for simulations in which high accuracy is desired
- supports DVI (hard contacts, with complementarity)

`BARZILAIBORWEIN`

- good convergence
- supports DVI (hard contacts, with complementarity)

- similar to
`APGD`

, might be more robust when using large mass ratios

`MINRES`

- good convergence
- supports FEA problems
- does not support DVI (hard contacts, with complementarity) for the moment.

`ADMM + PardisoMKL`

- supports FEA problems and DVI problems
- requires an inner linear solver; best choice is
`PardisoMKL`

(requires PARDISO_MKL module) otherwise it will use ChSolverSparseQR.

While using iterative solvers it is **highly recommended**, especially in case of systems with links/constraints, to increase the number of iterations until the links do not get violated anymore. This is done by:

Depending on the type of solver used, there may be different parameters to adjust. Advanced settings are not accessible directly from ChSystem, for instance:

See ChSolver API for further details.

# Other parameters

There are many integrator/solver settings that can affect the outcome of a simulation. For instance, see collision tolerances to gain a better understanding of the interplay between the accuracy in the collision detection and robustness of a simulation. We focus below on two important settings related to handling collisions in a simulation in which bodies collide with each other and/or with the ground.

### Max. recovery speed

Bodies in contact that interpenetrate for various reasons, e.g., small numerical integration error, inconsistent initial conditions, etc., will not 'escape' this contact violation at a speed faster than this threshold. The recovery speed is in general problem dependent and is controlled by user as shown below.

- Larger values allow a more aggressive correction of the penetration, yet this can lead to scenarios in which bodies in contact pop out fast or in stacking problems the stack becoming jittery, noisy

- A small threshold increases the risk that objects
*sink*into one another when integrator precision is low, for instance, when the solver has a small max number of iterations

### Min. bounce speed

When objects collide, if their incoming speed is lower than this threshold, a zero restitution coefficient is assumed. This helps to achieve more stable simulations of stacked objects.

- A higher value leads to more stable simulations but less physically realistic collisions
- Lower values lead to a more physically realistic time evolution but require small integration time steps otherwise objects may keep bounce erratically

# Theory

Additional information regarding the time integration strategies implemented in Chrono can be found on the white papers page.