Node-based methods: A unifying approach to developing numerical techniques

This paper presents a node-based method that unifies the existing numerical techniques. It is based on the method of weighted residuals (MWR) that is built around spatial nodes representing a solution domain. With proper imposition of relationships among nodes and incorporation of circuit/network physics and mathematical principles, the node-based method can include existing mesh-based and non-mesh-based methods. Consequently, a new horizon for computational electromagnetics is created and explored. Further new developments/applications can then be carried out in a unifying manner. A recently developed leap-frog meshless method is presented as an example.