A finite-element time-domain forward solver for electromagnetic methods with complex-shaped loop sources

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. E117-E132 ◽  
Author(s):  
Jianhui Li ◽  
Xushan Lu ◽  
Colin G. Farquharson ◽  
Xiangyun Hu
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Time Domain ◽  
Real Life ◽  
Euler Method ◽  
Stratified Medium ◽  
Tetrahedral Mesh ◽  
Fe Method ◽  
Circular Loop ◽  
Backward Euler

A finite-element time-domain (FETD) electromagnetic forward solver for a complex-shaped transmitting loop is presented. Any complex-shaped source can be viewed as a combination of electric dipoles (EDs), each of which can be further decomposed into two horizontal EDs along the [Formula: see text]- and [Formula: see text]-directions and one vertical ED along the [Formula: see text]-direction. Using this method, a complex-shaped loop can be easily handled when implementing an FE method based on the total-field algorithm and an unstructured tetrahedral mesh. The FETD solver that we developed used a vector FE method and the first-order backward Euler method to discretize in space and time, respectively. Unstructured tetrahedral girds combined with a local refinement technique was used to exactly delineate topography and a deformed loop. This FETD solver was tested by the five following scenarios: a rectangular loop on a flat-surface half-space, a circular loop on a stratified medium, a rectangular loop laid on a slope-surface half-space, a rectangular loop laid on a slope with a conductive cubic body, and a complex-shaped loop on a real-life topography. The results of this FETD solver agreed well with the ones evaluated by the analytic methods for the first three examples, and with a frequency-domain FE solver combined with a cosine transform for the last two examples.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

Finite-Element Modeling of Time-Domain Controlled-Source Electromagnetic Survey with Weighted Laguerre Polynomials

Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Qingtao Sun ◽  
Runren Zhang ◽  
Yunyun Hu
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Laguerre Polynomials ◽  
Time Integration ◽  
Sampling Interval ◽  
Controlled Source ◽  
Time Integration Method ◽  
Transient Electromagnetic ◽  
Backward Euler ◽  
Land Survey

To facilitate the modeling of time-domain controlled-source electromagnetic survey, we propose an efficient finite-element method with weighted Laguerre polynomials, which shows a much lower computational complexity than conventional time integration methods. The proposed method allows sampling the field at arbitrary time steps and also its accuracy is determined by the number of polynomials, instead of the time sampling interval. Analysis is given regarding the optimization of the polynomial number to be used and the criterion of selecting the time scale factor. Two numerical examples in marine and land survey environments are included to demonstrate the superiority of the proposed method over the existing backward Euler time integration method. The proposed method is expected to facilitate the modeling of transient electromagnetic surveys in the geophysical regime.

FINITE ELEMENT IMPLEMENTATION OF A SUPER-ELASTIC CONSTITUTIVE MODEL FOR TRANSFORMATION RATCHETTING OF NiTi ALLOY

2012 ◽  
Vol 09 (01) ◽  
pp. 1240022 ◽  
Author(s):  
Q. H. KAN ◽  
G. Z. KANG ◽  
S. J. GUO
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Niti Alloy ◽  
Cyclic Stress ◽  
Euler Method ◽  
Convergence Criterion ◽  
Integration Algorithm ◽  
Finite Element Implementation ◽  
Backward Euler ◽  
Forward Transformation

In the previous work, a new constitutive model describing the transformation ratchetting of super-elastic NiTi alloy was proposed. The finite element implementation of the proposed model is discussed in this work, because such implementation is necessary to launch a numerical analysis for the cyclic stress–strain responses of NiTi alloy devices including the transformation ratchetting. During the implementation, a new stress integration algorithm is adopted, and a new expression of the consistent tangent modulus is derived for the forward transformation and the reverse transformation. The finite element implementation is elaborated by the user subroutine of UMAT in ABAQUS based on backward Euler method. The accumulated error during cyclic transformation is controlled by a robust convergence criterion. Finally, the validity of such implementation is verified by several numerical examples.

scholarly journals Development of a continuum plasticity model for the commercial finite element code ABAQUS

2011 ◽  
Vol 2 (2) ◽  
pp. 275-283
Author(s):  
M. Safaei ◽  
W. De Waele
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Euler Method ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Implicit Integration ◽  
Backward Euler ◽  
User Material Subroutine ◽  
Von Mises ◽  
Future Work

The present work relates to the development of computational material models for sheet metalforming simulations. In this specific study, an implicit scheme with consistent Jacobian is used forintegration of large deformation formulation and plane stress elements. As a privilege to the explicitscheme, the implicit integration scheme is unconditionally stable. The backward Euler method is used toupdate trial stress values lying outside the yield surface by correcting them back to the yield surface atevery time increment. In this study, the implicit integration of isotropic hardening with the von Mises yieldcriterion is discussed in detail. In future work it will be implemented into the commercial finite element codeABAQUS by means of a user material subroutine.

Time‐domain simulation of SH-wave‐induced electromagnetic field in heterogeneous porous media: A fast finite‐element algorithm

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 448-461 ◽  
Author(s):  
Qiyu Han ◽  
Zhijing (Zee) Wang
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Time Domain ◽  
Heterogeneous Porous Media ◽  
Matrix Equations ◽  
Time Domain Simulation ◽  
Sh Wave ◽  
Fe Method ◽  
Streaming Current ◽  
The Time Domain

When a horizontally polarized rotational mechanical wave (SH-wave) travels through a porous rock, acceleration of the rock frame induces a streaming current in the SH particle motion plane. This streaming current is parallel to the particle displacement and has an associated electromagnetic (EM) field. This phenomenon is often described as the electroseismic (EOS) conversion. Numerically, the EOS phenomenon can be simulated in either the frequency or the time domain. Frequency‐domain numerical simulation has huge memory and computational requirements. Traditional time‐domain simulation, on the other hand, must restrict the time steps to be very small to satisfy stability conditions, resulting in large workload. In this paper, we present a fast finite‐element (FE) method simulating the EOS conversion in the time domain. In our method, we decompose the large 2-D FE matrix equations into a set of 1-D matrix equations and solve the problem using the approximate 1-D multistep process. We present numerical examples of 1-D and 2-D models to illustrate the coevolution of the seismic and electromagnetic fields. Our simulation results show that the diffusive electrical field is induced from the spatial variations of mechanical and electrical properties of the porous media due to the imbalance of the induced electric current. Besides the direct SH-wave itself, the transmitted waves, multiple waves, reflected waves, and diffracted waves also induce diffusive electrical fields. The EOS conversion is potentially useful for reservoir characterization, but the EOS data may be difficult to interpret due to the complexity of the superposed wave fields. The diffusive nature of the induced EM fields suggests that antennas should be positioned close to the target of interest in in‐situ measurements. As a result, borehole EOS surveys are likely to be more practical than surface surveys.

scholarly journals Unloading Behavior of Elastic-power-law Strain Hardening Materials Indented by Elastic Indenter

2021 ◽  
Author(s):  
Chuanqing Chen ◽  
Qiao Wang ◽  
Hui Wang ◽  
Huaiping Ding ◽  
Wei Hu ◽  
...  
Keyword(s):  
Finite Element ◽  
Strain Hardening ◽  
Half Space ◽  
Elastic Deformation ◽  
Power Law ◽  
Elastic Sphere ◽  
Fe Method ◽  
Cavity Profile ◽  
Relationship Of

Abstract Both strain hardening and indenter elastic deformation usually cannot be neglected in engineering contacts. By the finite element (FE) method, this paper investigates the unloading behavior of elastic-power-law strain-hardening half-space frictionlessly indented by elastic sphere for systematic materials. The effects of strain hardening and indenter elasticity on the unloading curve, cavity profile during unloading and residual indentation are analyzed. The unloading curve is observed to follow a power-law relationship, whose exponent is sensitive to strain hardening but independent upon indenter elastic deformation. Based on the power-law relationship of the unloading curve and the expression of the residual indentation fitted from the FE data, an explicit theoretical unloading law is developed. Its suitability is validated numerically and experimentally by strain hardening materials contacted by elastic indenter or rigid flat.

scholarly journals Formulative Visualization of Numerical Methods for Solving Non-Linear Ordinary Differential Equations

2021 ◽  
Vol 2 (2) ◽  
pp. 79-88
Author(s):  
Jeevan Kafle ◽  
Bhogendra Kumar Thakur ◽  
Grishma Acharya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Real Life ◽  
Euler Method ◽  
Linear Ordinary Differential Equations ◽  
Life Problems ◽  
Backward Euler ◽  
Non Linear ◽  
Runge Kutta

Many physical problems in the real world are frequently modeled by ordinary differential equations (ODEs). Real-life problems are usually non-linear, numerical methods are therefore needed to approximate their solution. We consider different numerical methods viz., Explicit (Forward) and Implicit (Backward) Euler method, Classical second-order Runge-Kutta (RK2) method (Heun’s method or Improved Euler method), Third-order Runge-Kutta (RK3) method, Fourth-order Runge-Kutta (RK4) method, and Butcher fifth-order Runge-Kutta (BRK5) method which are popular classical iteration methods of approximating solutions of ODEs. Moreover, an intuitive explanation of those methods is also be presented, comparing among them and also with exact solutions with necessary visualizations. Finally, we analyze the error and accuracy of these methods with the help of suitable mathematical programming software.

Study on the Dispersion Curves of Rayleigh Wave in Foundation of Obstacles

2011 ◽  
Vol 90-93 ◽  
pp. 2193-2199
Author(s):  
Fang Ding He ◽  
Guang Jun Guo ◽  
Zhi Gang Dou ◽  
Yang Yang
Keyword(s):  
Finite Element ◽  
Rayleigh Wave ◽  
Half Space ◽  
Time Domain ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Displacement Curve ◽  
Rayleigh Wave Dispersion ◽  
Water Drain

It is difficult to accurately identify dispersion curves of Rayleigh wave for the foundation with obstacles. Displacement curve of time-domain of half-space foundation have been obtained with the finite element in the paper. Then time-domain curve have been transformed Rayleigh wave dispersion curves. Rayleigh wave dispersion curves have been analysed in half-space foundation with water drain pipes. The results show that, there are reflection waves at the receiving signals in front of the obstacles, there are no reflection waves behind the obstacles basically. The location and spacing of the sensor have a greater impact on the results. The results provide the reference for the recognition of dispersion curves and disposition patterns of the sensors.

3D multinary inversion of CSEM data based on finite element method with unstructured mesh

Geophysics ◽  
2020 ◽  
pp. 1-60
Author(s):  
Hongzhu Cai ◽  
Zhidan Long ◽  
Wei Lin ◽  
Jianhui Li ◽  
Pinrong Lin ◽  
...  
Keyword(s):  
Finite Element ◽  
Mineral Exploration ◽  
A Priori ◽  
Ground Truth ◽  
Tetrahedral Mesh ◽  
A Priori Information ◽  
Fe Method ◽  
Geological Interpretation ◽  
Clustering Model ◽  
Priori Information

In controlled-source electromagnetic (CSEM) inversion with conventional regularization, the reconstructed conductivity image is usually blurry and only has limited resolution. To effectively obtain more compact conductivity models, we apply the concept of multinary transformation to CSEM inversion based on the finite element (FE) method with unstructured tetrahedral mesh. Within the framework of multinary inversion, the model conductivities are only allowed to be clustered within the designed values which is usually obtained from other a priori information or the conventional inversion. The synthetic studies show that the multinary inversion produces conductivity images with clearer model boundaries comparing to both the maximum smoothness inversion and the focusing inversion for realistic geoelectric models. We further applied the developed method to a land CSEM survey for mineral exploration. The multinary inversion results are closer to the ground truth comparing to the conventional maximum smoothness inversion and the focusing inversion. The developed method and numerical algorithm provide a new approach and workflow for CSEM inversion when the models need to have clear boundaries and clustering model values. Such geoelectric models could be very useful for geological interpretation in oil and mineral exploration when the a priori information (such as the estimated conductivity values) of the exploration targets is known.

Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

2013 ◽  
Vol 3 (3) ◽  
pp. 209-227
Author(s):  
Yuelong Tang ◽  
Yanping Chen
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problems ◽  
Finite Element Approximation ◽  
Euler Method ◽  
Time Dependent ◽  
Control Problems ◽  
Element Approximation ◽  
Time Discretisation ◽  
Backward Euler

AbstractIn this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the L2 projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

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