Space-time finite elements derived by convolution for the efficient solution of transient eddy current problems

A procedure for transient-eddy-current analysis is reported that is more efficient than conventional methods. Convolution in the time domain is used to convert the time operator into a symmetric form. A projective method is used to approximate the solution in the time domain by nth-order polynomials. The result is a general prismatic space-time finite element that is defined for any order of discretization in both time and space. First- to third-order time-finite-element matrices are calculated and tabulated. The stability and convergence of the method has been demonstrated numerically. The solution of two test cases is presented: a simple problem in one spatial dimension and the two-dimensional Felix cylinder problem