10.4122/1.1000000726
Ricciardi, Karen L.
Karen L.
Ricciardi
ricciard@math.umb.edu
Brill, Stephen H.
Stephen H.
Brill
brill@math.boisestate.edu
Ricciardi, Karen L.
Karen L.
Ricciardi
ricciard@math.umb.edu
Optimal collocation applied to a one-dimensional convection-diffusion equation using a hybrid optimization algorithm
XVI International Conference on Computational Methods in Water Resources
2006
2006
The method of collocation can be used to determine highly accurate
solutions to the one-dimensional steady-state convection-diffusion equation
(which can be used to model the transport of contaminants
dissolved in groundwater). This accuracy is dependent upon
sufficient refinement of the finite element mesh as well as
applying upstream weighting to the convective term through the
determination of collocation locations which meet specified
constraints. Due to an increase in computational intensity of the
application of the method of collocation associated with increases
in the mesh refinement, minimal mesh refinement is sought. A
hybrid method that utilizes a genetic algorithm and a
hill-climbing approach is used to determine the optimal mesh
refinement for a number of models differentiated by their velocity
fields. The genetic algorithm is used to determine a mesh
refinement that results in feasible collocation locations that is
close to optimal. Following the genetic algorithm, a hill-climbing
approach is used to determine a local optimal mesh refinement that
is feasible. In most cases the optimal mesh refinements
determined with this hybrid method are equal to or better than
previous mesh refinements determined through direct search
methods.