An ID Tucker-FFT-Accelerated Volume Integral Equation Solver for Magneto-Quasi-Static Analysis of Multiscale Voxelized Geometries

An algorithm combining a tensor decomposition and fast Fourier transform (FFT) is proposed for rapid iterative solution of volume integral equations (VIEs). The proposed scheme partitions the system matrix into admissible and inadmissible blocks. Interactions between basis functions within inadmissible blocks are accounted for by fast Fourier transform (FFT) acceleration, while a new tensor decomposition algorithm called interpolative decomposition (ID) Tucker (ID Tucker) is leveraged to handle interactions within admissible blocks by compressing them after converting them to six-dimensional arrays. The proposed ID Tucker-FFT acceleration scheme is integrated into a VIE solver for magneto-quasi-static (MQS) analysis applicable to voxelized geometries with uniform or multiscale mesh. Numerical results demonstrate that ID Tucker can achieve memory reductions up to two orders of magnitude larger than that can be achieved by singular value decomposition (SVD) when compressing interactions between two well-separated blocks. Furthermore, the proposed ID Tucker accelerated VIE solver requires 226x/46x less memory and 16x/23x less computational time compared to FFT/ID SVD accelerated VIE solvers for MQS analysis of well-separated interconnect structures, respectively.