Spectral element method for 3-D controlled-source electromagnetic forward modelling using unstructured hexahedral meshes

SUMMARY For forward modelling of realistic 3-D land-based controlled-source electromagnetic (EM) problems, we develop a parallel spectral element approach, blending the flexibility and versatility finite method in using unstructured grids with accuracy method. Complex-shaped structures topography are accommodated by hexahedral meshes, which elements can have curved edges non-planar faces. Our code is first algorithm EM geophysics that uses total field formulation (here electric field). Combining provides advantages dealing topography, particular, when transmitter located on rough surface topography. As further improvement over existing methods, our approach does not only allow for arbitrary distributions conductivity, but also magnetic permeability dielectric permittivity. The expanded terms high-order Lagrangian interpolants, element-wise integration weak form boundary value problem accomplished Gauss–Legendre–Lobatto quadrature. resulting complex-valued linear system equations solved direct solver MUMPS, and, subsequently, computed at points interest Faraday’s law. Five numerical examples comprehensively study benefits this algorithm. Comparisons to semi-analytical results confirm accurate representation responses indicate low dependency mesh discretization A convergence illuminates relation between high order polynomial approximation size their effects computational cost revealing yields very coarse meshes accompanied cost. presented experiments give evidence 2nd 3rd degree polynomials combination moderately discretized provide better trade-offs resources than lowest higher methods. To knowledge, final example includes pronounced two geometrically complicated conductive anomalies represents successful attempt supporting faces geophysics.