SpECTRE  v2024.03.19
Elasticity::FirstOrderSystem< Dim > Struct Template Reference

The linear elasticity equation formulated as a set of coupled first-order PDEs. More...

#include <FirstOrderSystem.hpp>

Public Types

using primal_fields = tmpl::list< Tags::Displacement< Dim > >
 
using primal_fluxes = tmpl::list< Tags::MinusStress< Dim > >
 
using background_fields = tmpl::list<>
 
using inv_metric_tag = void
 
using fluxes_computer = Fluxes< Dim >
 
using sources_computer = void
 
using boundary_conditions_base = elliptic::BoundaryConditions::BoundaryCondition< Dim >
 

Static Public Attributes

static constexpr size_t volume_dim = Dim
 

Detailed Description

template<size_t Dim>
struct Elasticity::FirstOrderSystem< Dim >

The linear elasticity equation formulated as a set of coupled first-order PDEs.

This system formulates the elasticity equation (see Elasticity):

\begin{align*} \nabla_i T^{ij} = f_\mathrm{ext}^j \\ T^{ij} = -Y^{ijkl} \nabla_{(k} \xi_{l)} \end{align*}

The system can be formulated in terms of these fluxes and sources (see elliptic::protocols::FirstOrderSystem):

\begin{align*} F^{ij} &= -T^{ij} = Y^{ijkl} \nabla_{(k} \xi_{l)} \\ S^j &= 0 \\ f^j &= f_\mathrm{ext}^j \text{.} \end{align*}


The documentation for this struct was generated from the following file: