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Summary form only given. The surface integral equation formulation is applicable to homogeneous material only. If there is a slight change of dielectric contrast within the volume, or there is a small portion of the material region that has inhomogeneous permittivity, the SIE will no longer be valid. It has been proposed that an additional volume integral equation be introduced to model the inhomogeneous part of the material region. The idea is to use the induced volume current for the region that has dielectric contrast which is different from the majority of the dielectric region. This is called the hybrid PMCHWT and VIE formulation. In this presentation, we apply this method to calculate the scattering by three-dimensional material scatterers. Our formulation uses the quadrilateral mesh for the surface modeling and hexahedron mesh for the volume modeling. Methods to treat the singular integrals for various integral operators are discussed, and validation numerical results will be shown.