p-adaptive numerical methods for particle transport

A p-adaptive method is applied to the discrete ordinates form of the monoenergetic transport equation in one dimension. Discontinuous spatial discretizations of arbitrary accuracy are generated in a finite element context using the computer algebra program MAPLE. Source code for the high order methods is produced automatically by MAPLE and then implemented in a discrete ordinates neutral particle transport code in an adaptive fashion. The degree, p, of the polynomial representation used on a mesh cell is varied during the course of the source iterations and the corresponding order of accuracy increased or decreased according to some selected tolerance specification. The accuracy and other numerical properties of the method are investigated and the results of numerical computations are presented.