Using GIS for the design of groundwater models motivates the search for numerical methods that do not require the discretization of the flow domain: GIS are natively vectorized. Numerical methods that relie on the discretization of the boundaries rather than the domain offer the advantage of retaining the native description of information in vector form as provided by the GIS, thus reducing the loss inherent to raterization and subsequent vextorization. The Analytical Element Method is especially promising. However, it lacks the capacity to handle a specific type of object, NURBS curves. The functions necessary to allow the inclusion of these curves in the AEM are derived, and examples are provided. Their versatility is presented, also showing that existing smooth curves can be represented as NURBS, thus allowing backward compatibility, should they be replaced. A method is offered to allow for faster model response when using these curvilinear elements, based on the Direct Boundary Integral Method. Standard line elements are also improved to allow greater precision and control in the speed-improving scheme.
