Parallel Generalized Finite Element Method for Magnetic Multiparticle Problems - Basermann, Achim; Tsukerman, Igor (High Performance Computing for Computational Science - VECPAR 2004, 2005)
A parallel version of the Generalized Finite Element Method is applied to multiparticle problems. The main advantage of the method is that only a regular hexahedral grid is needed; the particles do not have to be meshed and are represented by special basis functions approximating the field behavior near the particles. A general-purpose parallel Schur complement solver with incomplete LU preconditioning (A. Basermann) showed excellent performance for the varying problem size, number of processors and number of particles. In fact, the scaling of the computational time with respect to the number of processors was slightly superlinear due to cache effects. Future research plans include parallel implementation of the new Flexible Local Approximation MEthod (FLAME) that incorporates desirable local approximating functions (e.g. dipole harmonics near particles) into the difference scheme.