[Getfem-users] transient problems in Getfem

[Andriy Andreykiv]

Dear Yves, dear Getfem users

I was wondering about the general strategy for first order transient problems in Getfem.

If some problem is described by 

    C*du/dt + K*u = RHS

then something like K is conveniently taken into account with time dispatchers (either theta or midpoint).

What I don't understand is the general strategy for an arbitrary C brick. Getfem has functionality like add_basic_d_on_dt_brick.

But this function is specific to a mass matrix. I find it a bit not general enough to build a brick for every C like matrix.

The manual on time dispatchers also says that 

"The same brick as for the -method can be used to represent a first order time derivative."

but I"m not completely sure how this can be achieved. In the beginning I thought that I can create a list of 

bricks that go into C and pass them to 

   getfem::add_theta_method_dispatcher(model,transient_bricks_derivative,"1/dt");

but this is not entirely correct, because in that case Getfem will be setting the coefficients like this:

      md.matrix_coeff_of_brick(ib) = 1/dT;

      md.rhs_coeffs_of_brick(ib)[0] = 1/dT;

      md.rhs_coeffs_of_brick(ib)[1] = 1- 1/dT; 

while I need something like this:

      md.matrix_coeff_of_brick(ib) = 1/dT;

      md.rhs_coeffs_of_brick(ib)[0] = 1/dT;

      md.rhs_coeffs_of_brick(ib)[1] = - 1/dT;

Well, this is all easy to solve by creating another dispatcher which allows me 

to add any C-like brick (which is being multiplied by first order derivative du/dt )

(I used this solution to develop poroelastic formulation for structural-flow coupling)

struct first_order_derivative_dispatcher: public theta_method_dispatcher{

    void set_dispatch_coeff(const model &md, size_type ib) const {

      scalar_type dt;

      if (md.is_complex())

        dt = gmm::real(md.complex_variable(param_names[0])[0]);

      else

        dt = md.real_variable(param_names[0])[0];

      md.matrix_coeff_of_brick(ib) = 1.0/dt;

      md.rhs_coeffs_of_brick(ib)[0] = 1.0/dt;

      md.rhs_coeffs_of_brick(ib)[1] = -1.0/dt;

    }

  void add_first_order_derivative_dispatcher

  (model &md, dal::bit_vector ibricks, const std::string &dt) {

    pdispatcher pdispatch = new first_order_derivative_dispatcher(dt);

    for (dal::bv_visitor i(ibricks); !i.finished(); ++i)

      md.add_time_dispatcher(i, pdispatch);

  }

but I resent the fact if I might be re-inventing a wheel in this case.

Thanks in advance,

                               Andriy