Parallel Generalized Finite Element Method for Magnetic Multiparticle Problems

• Published in: High Performance Computing for Computational Science - VECPAR 2004 pp. 325 - 339
• Main Authors: Basermann, Achim, Tsukerman, Igor
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; Fast Multipole Method; Generalize Finite Element Method; Iterative Solver; Software; Sparse Linear System; Standard Finite Element Method; Harmonic; High performance; Parallel algorithm; Difference scheme; Cache memory; Grid; Special function; Distributed computing; Modeling; Function field; Finite element method; Polyhedron; Size effect; Schur complement; Preconditioning
• ISBN: 9783540254249; 3540254242
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11403937_26

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.