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Ice-shelf problem

Gridap Example

Solving an example ice-shelf problem with Gridap. Brief description of the modules are below:

  • dispersion.jl: Contains functions to compute the roots of the dispersion equation. Solving roots of non-linear equations, for example

  • FEMSolve.jl: Contains functions to solve the FEM problems using Julia and to build the reduced system. Currently the full implementation is available for thin-plate problems. Will be extended to linear elasticity.

  • nonLocal.jl: To obtain the non-local boundary condition on the ocean-cavity interface. A robin-type boundary condition, where the derivative is related to the potential in the form of an integral equation.

  • solver.jl: Main routine to get the user-data and solve the problem.

Sample outputs

Some sample outputs showing the displacement of the ice when forced by a long incident wave. The shelf is rigidly fixed at one end.

Disp Disp

Reference

Ilyas, M., Meylan, M. H., Lamichhane, B., & Bennetts, L. G. (2018). Time-domain and modal response of ice shelves to wave forcing using the finite element method. J. Fluids Struct., 80, 113–131.

Computing function at a point

feval.jl Contains the routines to compute the function at a point. Dependency: PolygonOps.jl for locating the polygon in which the point is located.

  • The function
evalAtPoint.evaluate(uh,P)

does the operation using a naive approach. Results show the difference between the computation time.

  • The method
evalAtPoint.evaluate_optim(uh,P)

uses lazy_map to perform the computations and hence optimised (There is definitely room for improvement ...). Dispatch the routine to Gridap.evaluate using

Gridap.evaluate(uh::SingleFieldFEFunction, P::Point) = sum(unique(evaluate_optim(uh,P)))

and is done inside feval.jl.

Example

  • Compute the solution on a 500 x 500 cartesian grid.
  • Use
valAtPoint.evaluate(uh,Point(√2-1,√3-1))

and compare with

evalAtPoint.evaluate_optim(uh,Point(√2-1,√3-1))

The time taken by the naive approach is ~10x larger than the optimised version. The bulk of the time is taken by the (external)inpolygon function which is used to find the location of the point in the discretization. This part of the code could be optimised further ...

Compare

Interpolating Lagrange elements

Check out this task list for full details. I will update the info of the scripts shortly.