A fast multipole boundary element method (FMBEM) is presented for diffusion problems based on a dual reciprocity formulation. In the dual reciprocity formulation, domain integrals that arise from solving the timedependent boundary value problems are transformed into boundary integrals by constructing particular solutions. The time-derivatives in the governing differential equation are approximated with a first-order finite difference timestepping scheme. Discontinuous linear elements, which are known to give more accurate results than constant or linear elements, are used in the implementation to discretize the boundary integral equations, in combination with the fast multipole method for speeding up the solution. Three numerical examples of diffusion are presented. The performance of the developed FMBEM is compared with that of a conventional BEM and a commercial finite element program. The results show that the developed FMBEM can be a reliable and efficient tool for solving diffusion problems.

• Fast multipole accelerated dual reciprocity boundary element method for diffusion problems
• Fast multipole accelerated dual reciprocity boundary element method for diffusion problems