Finite Element Time-Domain Body-of-Revolution Maxwell Solver based on Discrete Exterior Calculus

We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a TE/TM field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particle-in-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.Comment: 42 pages, 19 figure

Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface

Near-surface applied electromagnetic geophysics is experiencing an explosive period of growth with many innovative techniques and applications presently emergent and others certain to be forthcoming. An attempt is made here to bring together and describe some of the most notable advances. This is a difficult task since papers describing electromagnetic induction methods are widely dispersed throughout the scientific literature. The traditional topics discussed herein include modeling, inversion, heterogeneity, anisotropy, target recognition, logging, and airborne electromagnetics (EM). Several new or emerging techniques are introduced including landmine detection, biogeophysics, interferometry, shallow-water electromagnetics, radiomagnetotellurics, and airborne unexploded ordnance (UXO) discrimination. Representative case histories that illustrate the range of exciting new geoscience that has been enabled by the developing techniques are presented from important application areas such as hydrogeology, contamination, UXO and landmines, soils and agriculture, archeology, and hazards and climat

A three-dimensional numerical investigation of the thermo-hydro-mechanical behaviour of a large-scale prototype repository

This thesis describes the modelling of the thermo-hydro-mechanical behaviour of a large-scale experiment, carried out at SKB's underground research laboratory in Aspo, Sweden. The experiment, known as the Prototype Repository Project, was constructed in highly fractured granite rock and is scheduled to last 20 years. Results from the experiment are collected systematically by SKB from the initial rock characterisation to the highly instrumented installed material. The model applied is the thermo-hydro-mechanical model previously developed at the Geoenvironmental Research Centre (GRC). The GRC's current model was extended to successfully accommodate three-dimensional THM behaviour, including the development of a high-performance computing algorithm using both multi-threaded and message-passing programming paradigms to enable simulations to be completed in significantly reduced time. Model simulations have been conducted of both the pre-placement stage of the experiment and the post-placement operational phase. The results of the pre-placement phase have been used to aid the calibration of the simulation and provide confidence in the development of the operational phase simulation. In the pre-placement phase simulation, a pragmatic approach using a combination of an effective continuum model and a number of key discontinuities was employed. A domain of 100 x 100 x 160m was used, discretised into over 550,000 finite-elements. The simulations were able to reproduce three-dimensional highly anisotropic flow conditions shown in the experimental results. The post-placement operational stage was then simulated in three-dimensions using the same rock domain as for the pre-placement analyses, including the buffer material, and discretised into over 920,000 elements. A number of key features, including the anisotropic hydraulic behaviour, were captured. It was concluded that the geological conditions, backfill re-saturation and buffer re-saturation, including the micro-structural effects of the bentonite, are all important to the simulation of a high-level waste repository. Long term simulation results were also presented. A number of aspects were explored using two-dimensional analyses, including the macro/micro- structural interactions of the bentonite buffer. A time-dependant form of the hydraulic conductivity relationship was developed and yielded significantly improved results in long-term analyses. The behaviour of a fracture intersecting a deposition-hole was also investigated highlighting the importance of discrete fractures on hydration behaviour

Development and application of 2D and 3D transient electromagnetic inverse solutions based on adjoint Green functions: A feasibility study for the spatial reconstruction of conductivity distributions by means of sensitivities

To enhance interpretation capabilities of transient electromagnetic (TEM) methods, a multidimensional inverse solution is introduced, which allows for a explicit sensitivity calculation with reduced computational effort. The main conservation of computational load is obtained by solving Maxwell's equations directly in time domain. This is achieved by means of a high efficient Krylov-subspace technique that is particularly developed for the fast computation of EM fields in the diffusive regime. Traditional modeling procedures for Maxwell's equations yields solutions independently for every frequency or, in the time domain, at a given time through explicit time stepping. Because of this, frequency domain methods are rendered extremely time consuming for multi-frequency simulations. Likewise the stability conditions required by explicit time stepping techniques often result in highly inefficient calculations for large diffusion times and conductivity contrasts. The computation of sensitivities is carried out using the adjoint Green functions approach. For time domain applications, it is realized by convolution of the background electrical field information, originating from the primary signal, with the impulse response of the receiver acting as secondary source. In principle, the adjoint formulation may be extended allowing for a fast gradient calculation without calculating and storing the whole sensitivity matrix but just the gradient of the data residual. This technique, which is also known as migration, is widely used for seismic and, to some extend, for EM methods as well. However, the sensitivity matrix, which is not easily given by migration techniques, plays a central role in resolution analysis and would therefore be discarded. But, since it allows one to discriminate features in the a posteriori model which are data or regularization driven, it would therefore be very likely additional information to have. The additional cost of its storage and explicit computation is comparable low disbursement to the gain of a posteriori model resolution analysis. Inversion of TEM data arising from various types of sources is approached by two different methods. Both methods reconstruct the subsurface electrical conductivity properties directly in the time domain. A principal difference is given by the space dimensions of the inversion problems to be solved and the type of the optimization procedure. For two-dimensional (2D) models, the ill-posed and non-linear inverse problem is solved by means of a regularized Gauss-Newton type of optimization. For three-dimensional (3D) problems, due to the increase of complexity, a simpler, gradient based minimization scheme is presented. The 2D inversion is successfully applied to a long offset (LO)TEM survey conducted in the Arava basin (Jordan), where the joint interpretation of 168 transient soundings support the same subsurface conductivity structure as the one derived by inversion of a Magnetotelluric (MT) experiment. The 3D application to synthetic data demonstrates, that the spatial conductivity distribution can be reconstructed either by deep or shallow TEM sounding methods

a feasibility study for the spatial reconstruction of conductivity distributions by means of sensitivities

To enhance interpretation capabilities of transient electromagnetic (TEM) methods, a multidimensional inverse solution is introduced, which allows for a explicit sensitivity calculation with reduced computational effort. The main conservation of computational load is obtained by solving Maxwell's equations directly in time domain. This is achieved by means of a high efficient Krylov-subspace technique that is particularly developed for the fast computation of EM fields in the diffusive regime. Traditional modeling procedures for Maxwell's equations yields solutions independently for every frequency or, in the time domain, at a given time through explicit time stepping. Because of this, frequency domain methods are rendered extremely time consuming for multi-frequency simulations. Likewise the stability conditions required by explicit time stepping techniques often result in highly inefficient calculations for large diffusion times and conductivity contrasts. The computation of sensitivities is carried out using the adjoint Green functions approach. For time domain applications, it is realized by convolution of the background electrical field information, originating from the primary signal, with the impulse response of the receiver acting as secondary source. In principle, the adjoint formulation may be extended allowing for a fast gradient calculation without calculating and storing the whole sensitivity matrix but just the gradient of the data residual. This technique, which is also known as migration, is widely used for seismic and, to some extend, for EM methods as well. However, the sensitivity matrix, which is not easily given by migration techniques, plays a central role in resolution analysis and would therefore be discarded ...thesi