Fast parallel IGA-ADS solver for time-dependent Maxwell's equations

We propose a simulator for time-dependent Maxwell's equations with linear computational cost. We employ B-spline basis functions as considered in the isogeometric analysis (IGA). We focus on non-stationary Maxwell's equations defined on a regular patch of elements. We employ the idea of alternating-directions splitting (ADS) and employ a second-order accurate time-integration scheme for the time-dependent Maxwell's equations in a weak form. After discretization, the resulting stiffness matrix exhibits a Kronecker product structure. Thus, it enables linear computational cost LU factorization. Additionally, we derive a formulation for absorbing boundary conditions (ABCs) suitable for direction splitting. We perform numerical simulations of the scattering problem (traveling pulse wave) to verify the ABC. We simulate the radiation of electromagnetic (EM) waves from the dipole antenna. We verify the order of the time integration scheme using a manufactured solution problem. We then simulate magnetotelluric measurements. Our simulator is implemented in a shared memory parallel machine, with the GALOIS library supporting the parallelization. We illustrate the parallel efficiency with strong and weak scalability tests corresponding to non-stationary Maxwell simulations.