Coupled Poisson–elasticity

This application composes a 1D-in-3D Poisson Problem with a 3D static elasticity Problem. The Poisson solution is multiplied by two, lifted from the representative cylinder, converted to a normal traction, and assembled against the elasticity displacement test field:

PoissonSolver<1,3> -> value -> lift -> normal traction
                                      -> test(displacement)
ElasticStaticProblem<3,3> ------------^

The executable is coupled_poisson_elasticity, from apps/app_coupled_poisson_elasticity.cc. Its input is tutorials/coupled_poisson_elasticity/coupled_poisson_elasticity.prm.in:

subsection Poisson
  set FE degree              = 2
  set Output directory       = @TEST_OUTPUT_DIR@/tutorial-output/coupled-poisson-elasticity
  set Dirichlet boundary ids = 0, 1
  subsection Domain
    set Initial refinement     = 1
    set Grid generator           = hyper_cube
    set Grid generator arguments = 0: 1: false
    set Triangulation type       = fullydistributed
  end
  subsection Right hand side
    set Function expression = 1
    set Variable names      = x,y,z,t
  end
  subsection Dirichlet boundary conditions
    set Function expression = 0
    set Variable names      = x,y,z,t
  end
end

subsection Pressure lift
  set Thickness = 0.2
  subsection Representative quadrature
    set Type = gauss
    set Number of points = 3
    set Number of repetitions = 1
  end
  subsection Cross section
    set Geometry type = hyper_ball
    set Refinement level = 1
    set Maximum basis degree = 0
    set Selected modes = 0
    set Quadrature type = gauss
    set Number of points = 4
    set Number of repetitions = 1
  end
end

subsection Elastic static
  set FE degree              = 1
  set Dirichlet boundary ids = 0
  set Neumann boundary ids   =
  set Output directory       = @TEST_OUTPUT_DIR@/tutorial-output/coupled-poisson-elasticity
  set Output name            = coupled_elasticity
  subsection Domain
    set Initial refinement     = 1
    set Grid generator           = hyper_cube
    set Grid generator arguments = 0: 1: false
    set Grid scale               = 1
    set Triangulation type       = fullydistributed
  end
  subsection Functions
    subsection Right hand side
      set Function expression = 0; 0; 0
      set Variable names      = x,y,z,t
    end
    subsection Dirichlet boundary conditions
      set Function expression = 0; 0; 0
      set Variable names      = x,y,z,t
    end
    subsection Neumann boundary conditions
      set Function expression = 0; 0; 0
      set Variable names      = x,y,z,t
    end
  end
end

The application calls setup() on each Problem and adds both Problems to a LinearAdapter. It forms the traction from their semantic Fields with make_lift(2. * value(poisson.solution), pressure_lift) * normal(surface) and adds the resulting weak_term against test(elastic.displacement). The adapter owns the execution vector and coupled solve. OutputHandler writes both semantic Fields directly from the adapter state.

Run the configured input with:

mpirun -np 1 ./build/coupled_poisson_elasticity_debug \
  build/tutorials/coupled_poisson_elasticity/coupled_poisson_elasticity.prm

The executable writes the pressure and displacement Fields below the configured output directory. Integration tests check the coupled residual, pressure scaling, and traction balance; the application test checks the configured output.