An Efficient Algorithm for Surface Integral Equation Based on Mesh-Free Scheme

Efficient strategy for parallelisation of multilevel fast multipole algorithm using CUDA

“…The MLFMA has been widely used in combination with the MoM and its computational benefits have been illustrated in several publications [4][5][6].…”

“…As previously shown, the aggregation term is calculated using expression (11). For its numerical computation, a number of angular samples over the unit sphere are obtained: ( 15) where k^k is the unit vector over the unit sphere of the sample k. Using the Gaussian quadrature method described in (6), the integrals can be computed as a weighted addition of points, so (15) can be approximated as (16) where w u and w v are the coefficients of the Gauss quadrature method at points p u and p v , respectively, T i (p u , p v ) is the value of the Basis Function of the subdomain i at point (p u , p v ), and…”

“…As the size of the geometry grows, the problem becomes computationally expensive very quickly, and this is the reason for the emergence of several techniques whose objective is to make larger problems manageable. Three of these efficient approaches are the characteristic basis function method (CBFM) [2], the fast multipole method (FMM) [3] and its multilevel approach, the multilevel fast multipole algorithm (MLFMA) [4][5][6]. The FMM and MLFMA compute the coupling matrix by only storing the interactions between geometrically close elements and consider the interactions between distant elements by means of efficient matrix-vector multiplications in the iterative process.…”