1. A computer-implemented method for automatically generating a computation mesh for use with an analytical tool, the computation mesh having a plurality of ξ-grid lines and η-grid lines intersecting at mesh points positioned with respect to an inner boundary and an outer boundary, the method comprising: receiving using the computer from a user information corresponding to a shape to be analyzed using the analytical tool, a ξ-grid line mesh parameter value corresponding to a desired number of ξ-grid lines for the computation mesh, and an η-grid line mesh parameter value corresponding to a desired number of η-grid lines for the computation mesh; solving using the computer one or more mesh equations for a plurality of point locations without the need for additional information from the user, said solving including: determining if the η-grid line mesh parameter value exceeds a threshold resolution parameter, wherein the one or more mesh equations depend on an outer boundary distance parameter; determining the outer boundary distance parameter as a function of an inner boundary distance parameter and the natural log of the η-grid line mesh parameter value, if the η-grid line mesh parameter value exceeds the threshold resolution parameter; and determining the outer boundary distance parameter as a function of an inner boundary distance parameter and the square root of the η-grid line mesh parameter value, if the η-grid line mesh parameter value does not exceed the threshold resolution parameter; generating the computation mesh as a function of the plurality of point locations; and outputting one or more indicia representing the computational mesh.