Detailed Description

Implementation of a static ODE solver compatible with non-linear materials.

We are trying to solve to following

$\begin{eqnarray*} \vect{R}(\vect{x}) - \vect{P} = 0 \end{eqnarray*}$

Where $\vect{R}$ is the (possibly non-linear) internal elastic force residual and $\vect{P}$ is the external force vector (for example, gravitation force or surface traction).

Following the Newton-Raphson method, we pose

$\begin{align*} \vect{F}(\vect{x}_{n+1}) &= \vect{R}(\vect{x}_{n+1}) - \vect{P}_n \\ \mat{J} = \frac{\partial \vect{F}}{\partial \vect{x}_{n+1}} \bigg\rvert_{\vect{x}_{n+1}^i} &= \mat{K}(\vect{x}_{n+1}) \end{align*}$

where $\vect{x}_{n+1}$ is the unknown position vector at the th time step. We then iteratively solve

$\begin{align*} \mat{K}(\vect{x}_{n+1}^i) \left [ \Delta \vect{x}_{n+1}^{i+1} \right ] &= - \vect{F}(\vect{x}_{n+1}^i) \\ \vect{x}_{n+1}^{i+1} &= \vect{x}_{n+1}^{i} + \Delta \vect{x}_{n+1}^{i+1} \end{align*}$

#include <StaticODESolver.h>

Inheritance diagram for SofaCaribou::ode::StaticODESolver:

Public Types
template<typename T >
using	Data = sofa::core::objectmodel::Data< T >

Public Types inherited from SofaCaribou::ode::NewtonRaphsonSolver
template<typename T >
using	Data = sofa::core::objectmodel::Data< T >

template<typename T >
using	Link = sofa::core::objectmodel::SingleLink< NewtonRaphsonSolver, T, sofa::core::objectmodel::BaseLink::FLAG_STRONGLINK >

Public Member Functions
	SOFA_CLASS (StaticODESolver, NewtonRaphsonSolver)

Public Member Functions inherited from SofaCaribou::ode::NewtonRaphsonSolver
	SOFA_CLASS (NewtonRaphsonSolver, sofa::core::behavior::OdeSolver)

void	init () override

void	solve (const sofa::core::ExecParams *params, SReal dt, sofa::core::MultiVecCoordId x_id, sofa::core::MultiVecDerivId v_id) override

auto	iteration_times () const -> const std::vector< UNSIGNED_INTEGER_TYPE > &
	List of times (in nanoseconds) that each Newton-Raphson iteration took to compute in the last call to Solve().

auto	squared_residuals () const -> const std::vector< FLOATING_POINT_TYPE > &
	The list of squared residual norms (\|\|r\|\|^2) of every newton iterations of the last solve call.

auto	squared_initial_residual () const -> const FLOATING_POINT_TYPE &
	The initial squared residual (\|\|r0\|\|^2) of the last solve call.

The documentation for this class was generated from the following files:

/home/jnbrunet/sources/caribou/src/Plugin/Ode/StaticODESolver.h
/home/jnbrunet/sources/caribou/src/Plugin/Ode/StaticODESolver.cpp

Detailed Description

Public Types

Public Member Functions