function plan = plate_fem_plan(params)
% PLATE_FEM_PLAN  Sizes and estimates of a finite-element run, before it runs.
%
%   plan = plate_fem_plan(params) reports the mesh and its unknowns, the
%   number of modes to expect below 0.47 fs, the pendulum frequency of the
%   thread, the Hertz estimates of the contact and the plate's coincidence
%   frequency.  Cheap: no matrix is assembled.  The eigensolve's cost grows
%   a little faster than the number of unknowns; the strike stage's with the
%   number of samples times the number of modes.

P = plate_setup(params);
plan = plate_plan_common(params, P);
nx = params.fem.mesh_x;
ny = params.fem.mesh_y;
ndof = 3 * (nx + 1) * (ny + 1);
plan.method = 'fem';
plan.ndof = ndof;
plan.nx = nx;
plan.ny = ny;
plan.dx = params.plate.width / nx;
plan.dy = params.plate.height / ny;
plan.work = ndof^1.3;
plan.size_note = sprintf('%d x %d Q4 elements, %d unknowns', nx, ny, ndof);
if nx < 4 || ny < 4
    plan.notes{end + 1} = 'the mesh needs at least 4 elements per side';
end
if nx < 48 || ny < 48
    plan.notes{end + 1} = 'full-integration Q4 locks in shear on a thin plate: below 48 x 48 the partials are several percent high (the reference used 80 x 80)';
end
end