Speed-up of Magnetic-Electric Matrices Assembly Computation by Means of a Multi GPUs Environment

This paper deals with an accelerated implementation of the assembly of the matrices accounting for the magnetic-electric interactions arising from an integral formulation of the eddy current problem. The use of integral formulations leads to fully populated matrices whose assembly requires a computational effort of O(N2), N being the number of degrees of freedoms (DoFs) related to the finite element discretization. Although the inversion procedure is O(N3) for a direct method, the assembly for “medium size” problems can be very time consuming. In this work we prove that a significant speed-up can be achieved by means of an optimized “ad-hoc” use of GPUs. The price to be “paid” is a challenging implementation if compared to traditional parallel systems (CPUs based). Two kinds of applications are considered: one in the framework of Non-Destructive Testing (NDT), the other in the field of plasma fusion devices modellingThis paper deals with an accelerated implementation of the assembly of the matrices accounting for the magnetic-electric interactions arising from an integral formulation of the eddy current problem. The use of integral formulations leads to fully populated matrices whose assembly requires a computational effort of O(N^2) , N being the number of degrees of freedoms related to the finite-element discretization. Although the inversion procedure is O(N^3) for a direct method, the assembly for medium size problems can be very time consuming. In this paper, we prove that a significant speedup can be achieved by means of an optimized ad hoc use of graphical processing units. The price to be paid is a challenging implementation if compared with the traditional parallel systems (CPUs based). Two kinds of applications are considered: one in the framework of non-destructive testing and the other in the field of plasma fusion devices modeling