A Novel Solution of Underdetermined Equations for DGTD based on Prior knowledge

To accelerate solving transient electromagnetic problems by discontinuous Galerkin time domain (DGTD) method, a solution of underdetermined equations is established based on prior knowledge. In the proposed method, nodal basis function and a leapfrog scheme are used to Maxwell curl equations for spatial and time discretization. Electromagnetic fields in each element of computation domain are updated individually by applying conventional DGTD in initial time. When the electromagnetic wave covers the domain, the fields of all elements are updated as a whole. The underdetermined equations are established by randomly extracting rows from global mass matrix. Taking the results of a few previous time steps as the prior knowledge, a sparse transform is constructed. Then the underdetermined system of equations can be solved by recovery algorithms. Meanwhile,in order to maintain the advantage of low computational complexity, a restart mechanism is presented. The validity of the proposed method is verified by numerical experiments.