<p dir="ltr">A novel computational electromagnetic (CEM) solver using potential-based formulations and discrete exterior calculus (DEC) is proposed. The proposed solver consists of two parts: the DEC A-Phi solver and the DEC F-Psi solver. A and Phi are the magnetic vector potential and electric scalar potential of the electromagnetic (EM) field, respectively; F and Psi are the electric vector potential and magnetic scalar potential, respectively. The two solvers are dual to each other, and most research is carried out with respect to the DEC A-Phi solver.</p><p dir="ltr">Systematical approach for constructing the DEC A-Phi matrix equations is provided in this thesis, including the construction of incidence matrices, Hodge star operators and different boundary conditions. The DEC A-Phi solver is proved to be broadband stable from DC to optics, while classical CEM solvers suffer from stability issues at low frequencies (also known as the low-frequency breakdown). The proposed solver is ideal for broadband and multi-scale analysis, which is of great importance in modern industry.</p><p dir="ltr">To empower the proposed solver with the ability to solve industry problems with large number of unknowns, iterative solvers are preferred. The error-minimization mechanism buried in iterative solvers allows user to control the effect of numerical error accumulation to the solution vector. Proper preconditioners are almost always needed to accelerate the convergence of iterative solvers in large scale problems. In this thesis, preconditioning schemes for the proposed solver are studied.</p><p dir="ltr">In the DEC A-Phi solver, current sources can be applied easily, but it is difficult to implement voltage sources. To incorporate voltage sources in the potential-based solver, the DEC F-Psi solver is proposed. The DEC A-Phi and F-Psi solvers are dual formulations to each other, and the construction of the F-Psi solver can be generalized from the A-Phi solver straightforward.</p>