  This article presents an immersed virtual element method for solving a class
of interface problems that combines the advantages of both body-fitted mesh
methods and unfitted mesh methods. A background body-fitted mesh is generated
initially. On those interface elements, virtual element spaces are constructed
as solution spaces to local interface problems, and exact sequences can be
established for these new spaces involving discontinuous coefficients. The
discontinuous coefficients of interface problems are recast as Hodge star
operators that are the key to project immersed virtual functions to classic
immersed finite element (IFE) functions for computing numerical solutions. An a
priori convergence analysis is established robust with respect to the interface
location. The proposed method is capable of handling more complicated interface
element configuration and provides better performance than the conventional
penalty-type IFE method for the H(curl)-interface problem arising from Maxwell
equations. It also brings a connection between various methods such as
body-fitted methods, IFE methods, virtual element methods, etc.
