Public Types | Public Member Functions | List of all members
SofaCaribou::ode::StaticODESolver Class Reference

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 $n$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: