Accurate matrix-free time-domain method in three-dimensional unstructured meshes

We develop an accurate 3-D matrix-free time-domain method independent of the element shape used for discretization. The accuracy and stability of the proposed method are shown to be theoretically guaranteed. No dual mesh is needed. The tangential continuity of the fields is satisfied across the element interface. Numerical experiments on unstructured 3-D meshes with arbitrarily shaped tetrahedron and triangular prism elements have validated the accuracy and generality of the proposed method.