AbstractMagnetic inversion methods based on structured grids have been used extensively in geomagnetic research. Nevertheless, structured grids limit the modeling capability and accuracy of models with arbitrary geometries. To address these challenges, 3‐D magnetic numerical forward modeling and inversion methods using an unstructured tetrahedral grid based on a partial differential equation (PDE) framework are proposed. The methods are derived from Maxwell's partial equations and constructed using the finite element method. Arbitrary undulating topographies, complex geometries, and demagnetization effects can be represented exactly, leading to high‐accuracy forward modeling and inversion solutions. The proposed methods are suitable for both local‐ and global‐scale magnetic data interpretation, for example, in mineral exploration and tectonic research. A synthetic example and real airborne magnetic survey data collected from Mount Iliamna, Alaska, USA, are tested. The results demonstrate that the novel methods significantly improve the capability and accuracy of magnetic data interpretation.