Pre-Corrected Tensor Train Algorithm For Current Flow Modelling in 2D Multi-Conductor Transmission Lines

Pre-corrected Tensor Train (P-TT) fast iterative method is introduced for acceleration of Method of Moments (MoM) solution of the 2D Volume Electric Field Integral Equation (V-EFIE) in magneto-quasi-static regime. The method performs voxelization of the unstructured triangle mesh in MoM discretization through projection of the basis and test functions onto the regular grid of point sources. Subsequently, the Toeplitz matrix governing point-to-point interactions is represented as multi-dimensional tensor and decomposed into the product of smaller dimensional tensors (Tensor Train (TT)). The storage of the TT carriages and vectors pertinent to P-TT requires O(log N) and O(N) memory, respectively. Evaluation of the matrix-vector product requires O(N log N) operations. Resistance and inductance of the circular wire are extracted in broad range of frequencies with proposed P-TT algorithm and compared against analytical values.