3-D marine controlled-source electromagnetic modelling in an anisotropic medium using a Wavelet–Galerkin method with a secondary potential formulation

2019 ◽  
Vol 219 (1) ◽  
pp. 373-393
Author(s):  
Hanbo Chen ◽  
Tonglin Li
Keyword(s):  
Galerkin Method ◽  
Anisotropic Medium ◽  
Hankel Transform ◽  
Fe Method ◽  
Controlled Source ◽  
Wavelet Galerkin Method ◽  
Potential Formulation ◽  
Sparse System ◽  
Electromagnetic Modelling ◽  
Modelling Problems

SUMMARY This paper presents a new algorithm for solving 3-D MCSEM modelling problems in an anisotropic medium using a Wavelet–Galerkin method (WGM) based on compactly supported Daubechies wavelets which are differentiable according to the requirement. In order to avoid the source singularity, we adopted a secondary potential formulation for the quasi-static Maxwell's equation. The primary field on the modelling domain is calculated using fast Hankel transform. The domain can be discretized by locally intensive nodes to deal with the model's complexity, which is observed to improve the accuracy of the solution. The sparse system of the WGM equations is solved using the direct solver MUMPS. This study's algorithm is then applied to calculate the response of the MCSEM in isotropic and anisotropic mediums. The results generated are verified against with solution obtained by FE method and confirmed the performance of the algorithm presented in this study.

3D controlled-source electromagnetic edge-based finite element modeling of conductive and permeable heterogeneities

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. F215-F226 ◽  
Author(s):  
Souvik Mukherjee ◽  
Mark E. Everett
Keyword(s):  
Finite Element ◽  
Magnetic Permeability ◽  
Numerical Solutions ◽  
Governing Equations ◽  
Fe Method ◽  
Controlled Source ◽  
Continuity Equations ◽  
Potential Formulation ◽  
Edge Based ◽  
Further Development

A new 3D controlled-source electromagnetic finite element (FE) modeling algorithm is presented which is capable of handling local inhomogeneities in the magnetic permeability and electrical conductivity distribution of buried geologic and anthropogenic structures. An ungauged, coupled-potential formulation of the governing electromagnetic vector diffusion and scalar continuity equations is used. The formulation introduces magnetic reluctivity, the inverse of magnetic permeability, to facilitate a separation of secondary and primary potentials. The governing equations are solved using a tetrahedral edge-based FE method. The postprocessing steps to obtain electromagnetic fields are outlined. The code is validated for non-magnetic and permeable conductive structures by comparisons against analytic and previously published numerical solutions. Some limitations of the implementation are explored and directions are proposed for its further development.

scholarly journals Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Quasilinearization Method ◽  
Nonlinear Boundary Value Problems ◽  
Wavelet Galerkin Method ◽  
Nonlinear Boundary Value ◽  
Quasilinearization Technique

A numerical method is proposed by wavelet-Galerkin and quasilinearization approach for nonlinear boundary value problems. Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is implemented to linearized differential equations. In each iteration of quasilinearization technique, solution is updated by wavelet-Galerkin method. In order to demonstrate the applicability of proposed method, we consider the various nonlinear boundary value problems.

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