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.

An Axisymmetric Single-Path Model for Gas Transport in the Conducting Airways

2005 ◽  
Vol 128 (1) ◽  
pp. 69-75 ◽  
Author(s):  
Srinath Madasu ◽  
Ali Borhan ◽  
James S. Ultman
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Diffusion Processes ◽  
Path Model ◽  
Navier Stokes ◽  
Straight Tube ◽  
Element Analysis ◽  
Continuity Equations ◽  
Longitudinal Position ◽  
Single Path

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel’s symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%–30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.

Three dimensional controlled-source electromagnetic forward modeling by edge-based finite element with a divergence correction

Geophysics ◽  
2021 ◽  
pp. 1-71
Author(s):  
Wenwu Tang ◽  
Yaoguo Li ◽  
Jianxin Liu ◽  
Juzhi Deng
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Normal Component ◽  
Solution Process ◽  
Iterative Solution ◽  
Controlled Source ◽  
Correction Technique ◽  
Speed Up ◽  
Edge Based ◽  
Minimal Residual

We present an edge-based finite element modeling algorithm with a divergence correction for calculating controlled-source electromagnetic (CSEM) responses of a 3D conductivity earth model. We solve a curl-curl equation to directly calculate the secondary electric field in order to eliminate the source singularity. The choice of the edge-based finite element method enables us to properly handle the discontinuity of the normal component of electric fields across conductivity boundaries. Although we can solve the resulting complex-symmetric linear system of equations efficiently by a quasi-minimal residual method preconditioned with an incomplete Cholesky decomposition for the high frequency band, the iterative solution process encounters a common problem in the field formulation and does not converge within a practically feasible number of iterations for low frequencies. To overcome this difficulty and to accelerate the iterative solution process in general, we combine a divergence correction technique with the secondary field solution using the quasi-minimal residual solver. We have found that applying the divergence correction intermittently during the iterative solution process ensures the calculation of sufficiently accurate electric and magnetic fields and can significantly speed up the solution process by more than an order of magnitude. We have tested the efficiency and accuracy of the proposed algorithm with 1D and 3D models, and have found that the divergence correction technique is able to guide the electric field to satisfy the boundary conditions across conductivity interfaces. Although there is a computational overhead required for applying the divergence correction, that cost is significantly offset by the substantial gains in the solution accuracy and speed-up. The work makes the field-based curl-curl formulation using edge elements an efficient and practical method for CSEM simulations.

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.

A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos

2015 ◽  
Vol 5 (2) ◽  
pp. 192-208 ◽  
Author(s):  
Ning Li ◽  
Bo Meng ◽  
Xinlong Feng ◽  
Dongwei Gui
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Finite Element ◽  
Finite Difference ◽  
Stochastic Differential Equation ◽  
Numerical Experiments ◽  
Polynomial Chaos ◽  
Numerical Solutions ◽  
Numerical Comparison ◽  
Fe Method

AbstractA numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

Modeling the Multiphysics Wrinkling Instability of Ionic Polymer Composite Plates for Artificial Muscle Applications

2016 ◽  
Author(s):  
John G. Michopoulos ◽  
Athanasios P. Iliopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Polymer Composite ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Artificial Muscle ◽  
Composite Plates ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Ionic Polymer

In this paper we first present the derivation of the governing equations that describe the multiphysics behavior of Ionic Polymer Composite Plates (IPMC). This is done in a manner that accounts for their non-linear large deflection deformation under the influence of mechanical, electrical, thermal and multicomponent mass transport fields. We subsequently present numerical solutions of the system of these equations via the use of the finite element method for a case of a specific rectangular plate. Emphasis is given in identifying the multiphysics based wrinkling instability behavior that manifest near the corners of these plates due to multiphysics stimuli.

AN EFFICIENT PSEUDO THREE-DIMENSIONAL FINITE ELEMENT MODEL: PRESENTATION AND ANALYSIS OF TWO SOIL/FOUNDATION INTERACTION PROBLEMS

2005 ◽  
Vol 02 (02) ◽  
pp. 231-253 ◽  
Author(s):  
DJ. AMAR BOUZID ◽  
P. A. VERMEER ◽  
B. TILIOUINE ◽  
M. MIR
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Element Model ◽  
Combined Loading ◽  
Shear Stresses ◽  
Fe Method ◽  
Dimensional Finite Element ◽  
Soil Foundation ◽  
Three Dimensional Finite Element

A pseudo-three-dimensional numerical model has been developed for the analysis of full 3D soil problems under combined loading. The procedure called Vertical Slices Model takes advantage of finite element (FE) 2D numerical solutions in plane stress for building approximate 3D solutions by replacing the inter-slice interactions by fictitious body forces. Continuum slices are successively analyzed by the combination of the explicit 2D finite element (FE) method and finite difference (FD) method in iterative process. The three-dimensional aspect of the considered problem is preserved by satisfying the continuity of shear stresses developed at the inter-slices. The theory of the vertical slices model is developed first, and then encoded in a Fortran computer program. Next, the prediction capabilities of this program are illustrated with two classical geotechnical applications, namely; the laterally and the axially loaded single piles embedded in homogeneous and non-homogeneous elastic soils. Although approximate, the model proved its ability to capture the behavior of the two boundary value problems. Then, in terms of stiffness factors the approach is used to predict the behavior of an embedded rigid square footing and a pile under combined loading in a half-space where the stiffness shows a power law variation with depth.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

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