A mixed solving procedure for ungauged 3D edge finite element analysis

A new mixed procedure for solving the system of algebraic equations generated by the edge finite element method (EFEM) for ungauged vector potential formulation is proposed. The singularity of the matrix of the system obtained by ungauged vector formulation results in unstable and nonuniform convergence rates of the Preconditioned Conjugate Gradient (PCG) iteration procedure. The proposed method uses the excellent initial convergence rate of the PCG procedure, and enables switching from the PCG procedure to the Gauss-Seidel procedure when numerical instability of the former method occurs, continuing with a slower but more stable convergence rate. The proposed mixed PCG-Gauss-Seidel procedure requires monitoring of the PCG iteration process, however, it does not require generation of tree graphs, rearranging of unknowns inside the matrix of the system nor any additional memory.