A sparse matrix open boundary method for finite element analysis

A novel implicit mapping method for handling exterior- and far-field problems is described. The method provides a way of maintaining sparsity. Several boundary methods are compared, and the implicit mapping approach is described in detail. In terms of complexity the proposed method is more expensive than a hybrid or ballooning method, but this cost is offset for many problems by its simplicity and the fact that far-field values are readily available. In addition, the method can be used to extend the range of boundary conditions available in a standard finite-element package to include inhomogeneous Neumann conditions.>