# Browsing by Author "Liu, Qing Huo"

###### Results Per Page

###### Sort Options

Item Open Access Adaptive Discontinuous Galerkin Methods Applied to Multiscale & Multiphysics Problems towards Large-scale Modeling & Joint Imaging(2019) Zhan, QiweiAdvanced numerical algorithms should be amenable to the scalability in the increasingly powerful supercomputer architectures, the adaptivity in the intricately multi-scale engineering problems, the efficiency in the extremely large-scale wave simulations, and the stability in the dynamically multi-phase coupling interfaces.

In this study, I will present a multi-scale \& multi-physics 3D wave propagation simulator to tackle these grand scientific challenges. This simulator is based on a unified high-order discontinuous Galerkin (DG) method, with adaptive nonconformal meshes, for efficient wave propagation modeling. This algorithm is compatible with a diverse portfolio of real-world geophysical/biomedical applications, ranging from longstanding tough problems: such as arbitrary anisotropic elastic/electromagnetic materials, viscoelastic materials, poroelastic materials, piezoelectric materials, and fluid-solid coupling, to recent challenging topics: such as fracture-wave interactions.

Meanwhile, I will also present some important theoretical improvements. Especially, I will show innovative Riemann solvers, inspired by physical meanings, in a unified mathematical framework, which are the key to guaranteeing the stability and accuracy of the DG methods and domain decomposition methods.

Item Open Access Compressed Sensing Based Image Restoration Algorithm with Prior Information: Software and Hardware Implementations for Image Guided Therapy(2012) Jian, YuchuanBased on the compressed sensing theorem, we present the integrated software and hardware platform for developing a total-variation based image restoration algorithm by applying prior image information and free-form deformation fields for image guided therapy. The core algorithm we developed solves the image restoration problem for handling missing structures in one image set with prior information, and it enhances the quality of the image and the anatomical information of the volume of the on-board computed tomographic (CT) with limited-angle projections. Through the use of the algorithm, prior anatomical CT scans were used to provide additional information to help reduce radiation doses associated with the improved quality of the image volume produced by on-board Cone-Beam CT, thus reducing the total radiation doses that patients receive and removing distortion artifacts in 3D Digital Tomosynthesis (DTS) and 4D-DTS. The proposed restoration algorithm enables the enhanced resolution of temporal image and provides more anatomical information than conventional reconstructed images.

The performance of the algorithm was determined and evaluated by two built-in parameters in the algorithm, i.e., B-spline resolution and the regularization factor. These parameters can be adjusted to meet different requirements in different imaging applications. Adjustments also can determine the flexibility and accuracy during the restoration of images. Preliminary results have been generated to evaluate the image similarity and deformation effect for phantoms and real patient's case using shifting deformation window. We incorporated a graphics processing unit (GPU) and visualization interface into the calculation platform, as the acceleration tools for medical image processing and analysis. By combining the imaging algorithm with a GPU implementation, we can make the restoration calculation within a reasonable time to enable real-time on-board visualization, and the platform potentially can be applied to solve complicated, clinical-imaging algorithms.

Item Open Access Discontinuous Galerkin Based Multi-Domain Multi-Solver Technique for Efficient Multiscale Electromagnetic Modeling(2017) Sun, QingtaoDiscontinuous Galerkin (DG) methods provide an efficient option for modeling multiscale problems. With the help of the Riemann solver (upwind flux), a discontinuous Galerkin based multi-domain multi-solver technique is introduced in this work for multiscale electromagnetic modeling. Specifically, the proposed technique allows multiple subdomains and multiple solvers. Through multiple subdomains, the original large linear system is reduced into multiple subsystems to solve, thus reducing computational complexity. Different subdomains can be non-conformal with each other. Different element types (tetrahedron, hexahedron, Yee's cell) and element sizes (h-refinement) can be used with different orders of basis functions (p-refinement). For different solvers, the finite element method, spectral element method and finite difference method are incorporated into the proposed technique. As is well known, the finite element method features great mesh flexibility for arbitrarily shaped objects, the spectral element method shows spectral accuracy with high order basis functions, and the finite difference method has great computational efficiency for time domain modeling. With multiple solvers the proposed technique can provide efficient solution for multiscale problems based on different element types. Considering the model geometry, for irregular and complicated structures the finite element method is used with small tetrahedron elements for local refinement, for simple structures the spectral method is used with high order basis functions based on hexahedron elements to exploit its spectral accuracy, and for perfectly matched layer (PML) and layered structures the finite different method is used to improve computational efficiency.

For time domain modeling, firstly hybrid spectral element-finite element method in time domain (hybrid SETD-FETD) is implemented based on the first-order Maxwell's curl equations. To facilitate modeling of electrically small problems, an efficient implicit non-iterative time integration method is proposed based the EB scheme for sequentially ordered systems. Compared with the previous Block-Thomas algorithm, the proposed block Lower-Diagonal-Upper (LDU) decomposition algorithm shows better performance in terms of CPU time and memory, due to the separation of surface unknowns from the volume unknowns.

Then a second-order wave equation based discontinuous Galerkin time domain (DGTD) framework is proposed with a modified Riemann solver to evaluate the flux. Compared with the first-order Maxwell's curl equations based DGTD methods, the new DGTD framework reduces the degrees of freedom for each subdomain by solving the E unknowns plus only surface H unknowns. By contrast, the first-order Maxwell's curl equations based DGTD methods require to solve all the E and B unknowns in each subdomain. To model open problems, a novel coupling method is proposed to incorporate PML into the wave equation based DGTD framework. The PML region is based on the first-order Maxwell's curl equations based DGTD framework with implicit Crank-Nicholson time integration while the physical region follows the wave equation based DGTD framework with implicit Newmark-beta time integration.

To further extend the existing hybrid methods, the hybrid FDTD-SETD-FETD method is proposed by incorporating the finite different time domain method (FDTD). In this work, completely non-conformal mesh is implemented for the first time to hybridize FDTD, SETD and FETD for 3D modeling. Based on the DGTD framework, a buffer zone is introduced between FDTD and SETD/FETD to facilitate the coupling procedure. A global leapfrog time integration is implemented to validate the proposed hybrid FDTD-SETD-FETD method, and the implicit-explicit time integration is proposed to improve its performance for practical applications. To remove the buffer zone, a more advanced hybridization technique is introduced, which shows better performance in terms of CPU time and memory. The corresponding explicit leapfrog and implicit-explicit time integration scheme are also given for the new hybrid FDTD-SETD-FETD method without buffer.

For frequency domain modeling, based on the second-order wave equation and time harmonic assumption, a discontinuous Galerkin frequency domain (DGFD) method is introduced with the Riemann solver for anisotropic media. To improve the accuracy and efficiency, a mixed total field/scattered field DGFD (TF/SF DGFD) formulation is given. For subdomains with sources and receivers, the scattered field based DGFD is used to improve accuracy while for the remaining subdomains the total field DGFD is used to improve efficiency. With TF/SF DGFD, the scattered field at the receivers can be directly obtained. In addition, some useful boundary conditions, including scattering boundary condition (SCBC), surface impedance boundary condition (SIBC) and impedance transition boundary condition (ITBC), are incorporated into the proposed DGFD framework to further improve its performance for geophysical exploration problems. SCBC is used to truncate the physical region, SIBC is for approximating the effect of thick imperfect conductor, and ITBC is for approximating thin imperfect conductor as a surface. ITBC is used for the first time in this work for fracture modeling, and shows good agreement with the reference.

Finally, a domain decomposition based inversion method is proposed based on the DGFD forward solver for inverse scattering problems. The inversion algorithm is given based on the Gauss-Newton method, and more importantly, the formulation related to domain decomposition is derived. With the advantage of domain decomposition, an adaptive inversion procedure is introduced to gradually improve the inversion resolution and accuracy.

Item Open Access Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method(2016) Dai, JunwenIn this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Item Embargo Efficient Simulations of Electromagnetic Induction Tool in a Deviated Borehole for Resistivity Inversions(2022) Zhong, YangFor the petroleum industry, layered medium subsurface detection plays an important role in discovering reservoirs and drilling wells. In geophysics, resistivity is an essential property for distinguishing formation layers or even small fractures. Well logging with electromagnetic induction tools can measure the subsurface resistivity. This measurement includes two steps: 1) directly measure the low-frequency response signals using the tool and 2) determine the subsurface geometric model and resistivity. The problem is that no formula can directly calculate the resistivity from the measured tool responses. A systematic solution is to combine forward electromagnetic simulations and inversion of the subsurface model. In this dissertation, two categories of inversion are investigated: Determine the proper subsurface model by 1) optimizing the objective function, such as data misfit, and 2) training a surrogate model for the inverse mapping. Many forward simulations are demanded for either estimating the data misfit of new candidate models or collecting data for training. Therefore, efficient electromagnetic simulation is critical for resistivity logging. From complex to simple, three types of simulation are discussed: 1) borehole simulation with real tool configuration, 2) borehole simulation with point sources as the virtual tool, and 3) simplified layered medium simulation with virtual tool. Three optimal methods are implemented, respectively: the domain decomposition method, the finite element boundary integral method, and the analytical method. The tool calibration and the borehole effects are studied in the comparison of these simulations. Ideally, the simplest forward simulation should be used in the inversion, and the additional effects can be extracted as correction terms. The optimization-based inversion of the formation model uses simulations of a virtual tool in the layered medium. The Occam inversion or Monte Carlo Markov chain can minimize the data misfit. Another special simulation for small fractures using the thin dielectric sheet approximate method collects the dataset of fracture models. Fracture parameters such as resistivity, extension, and tilt angle are accurately determined by machine learning methods. The surrogate model also tends to predict fracture properties correctly, even for the complete simulation result.

Item Open Access Electromagnetic Forward Modeling and Inversion for Geophysical Exploration(2015) Jia, YuElectromagnetic forward modeling and inversion methods have extensive applications in geophysical exploration, and large-scale controlled-source electromagnetic method has recently drawed lots of attention. However, to obtain a rigorous and efficient forward solver for this large-scale three-dimensional problem is difficult, since it usually requires to solve for a large number of unknowns from a system of equations describing the complicate scattering behavior of electromagnetic waves that happened within inhomogeneous media. As for the development of an efficient inversion solver, because of the nonlinear, non-unique and ill-posed properties of the problem, it is also a very challenging task.

In the first part of this dissertation, a fast three-dimensional nonlinear reconstruction method is proposed for controlled-source electromagnetic method. The borehole-to-surface and airborne electromagnetic survey methods are investigated using synthetic data. In this work, it is assumed that there is only electric contrast between the inhomogeneous object and the layered background medium, for the reason that the electric contrast is much more dominant than magnetic contrast in most cases of the earth formation. Therefore, only the EFIE is needed to solve. While the forward scattering problem is solved by the stabilized bi-conjugate gradient FFT (BCGS-FFT) method to give a rigorous and efficient modeling, the Bore iterative method along with the multiplicative regularization technique is used in the inversion through frequency hopping. In the inversion, to speed up the expensive computation of the sensitivity matrix relating every receiver station to every unknown element, a fast field evaluation (FFE) technique is proposed using the symmetry property of the layered medium Green's function combined with a database strategy. The conjugate-gradient method is then applied to minimize the cost function after each iteration. Due to the benefits of using 3D FFT acceleration, the proposed FFE technique as well as the recursive matrix method combined with an interpolation technique to evaluate the LMGF, the developed inversion solver is highly efficient, and requires very low computation time and memory. Numerical experiments for both 3D forward modeling and conductivity inversion are presented to show the accuracy and efficiency of the method.

Some recent research on artificial nanoparticles have demonstrated the improved performance in geophysical imaging using magnetodielectric materials with enhanced electric and magnetic contrasts. This gives a promising perspective to the future geophysical exploration by infusing well-designed artificial magnetodielectric materials into the subsurface objects, so that a significantly improved imaging can be achieved. As a preparation for this promising application, the second part of the dissertation presents an efficient method to solve the scattering problem of magnetodielectric materials with general anisotropy that are embedded in layered media. In this work, the volume integral equation is chosen as the target equation to solve, since it solves for fields in inhomogeneous media with less number of unknowns than the finite element method. However, for complicated materials as magnetodielectric materials with general anisotropy, it is a very challenging task, because it requires to simultaneously solve the electric field integral equation (EFIE) and magnetic field integral equation (MFIE). Besides that, the numerous evaluation of the layered medium Green's function (LMGF) for the stratified background formation adds on the difficulty and complexity of the problem. To my knowledge, there is no existing fast solver for the similar problem. In this dissertation, using the mixed order stabilized biconjugate-gradient fast Fourier transform (mixed-order BCGS-FFT) method, a fast forward modeling method is developed to solve this challenging problem. Several numerical examples are performed to validate the accuracy and efficiency of the proposed method.

Besides the above mentioned two topics, one-dimensional inversion method is presented in the third part to determine the tilted triaxial conductivity tensor in a dipping layered formation using triaxial induction measurements. The tilted triaxial conductivity tensor is described by three conductivity components and three Euler angles. Based on my knowledge, due to the highly nonlinear and ill-posed nature of the inverse problem, this study serves as the first work that investigates on the subject. There are six principal coordinate systems that can give the same conductivity tensor. Permutation is performed to eliminate the ambiguity of inversion results caused by the ambiguity of the principal coordinate system. Three new Euler angles after permutation for each layer can be found by solving a nonlinear equation. Numerical experiments are conducted on synthetic models to study the feasibility of determining triaxially anisotropic conductivity tensor from triaxial induction data. This project is accomplished during my internship in the Houston Formation Evaluation Integration Center (HFE) at Schlumberger, a world-leading oilfield service company.

Item Open Access Fluid Flow and Electromagnetic Fields Modeling for Geophysical Subsurface Sensing(2018) Hu, YunyunCrosswell electromagnetic (EM) fields measurement has been widely applied in oil industry which has a reservoir scale detection range. One of the limitation of this technique is that the EM singals are usually too weak to be detected. In order to overcome the disadvantage, nanoparticles (NP) designed with high contrast EM properties (conductivity, permittivity and magnetic permeability) are introduced to enhance the signals. They are injected into the formation and moving with the fluids. The movement of NP with the flow in a porous medium is modeled by solving the flow transport equations. The 3-D spectral-element time domain method (SETD) based on Gauss-Lobatto-Legendre (GLL) polynomials is employed to solve the flow equation to obtain the NP concentration distribution as a function of time. Since the method shows a spectral accuracy, i.e., the error decreases exponentially with the order of basis functions, less unknown is needed to achieve a given accuracy with a high order basis function.

The injected fluids with high contrast NP increase the electric conductivity and magnetic permeability in the flooded zone. The effective EM properties of the mixed fluids are calculated by the mixing theory, e.g., Bruggeman mixing rule. The increased EM property values produce higher EM signals in the receivers. The EM fields are then modeled by the volume integral equations (VIE), thus realizing the coupling of fluid flow and EM measurements. Based on the coupling, the detection range of the high contrast NP can be analyzed. Different types of NP are investigated under both electric and magnetic dipole sources.

The magnetic contrast NP excited by a magnetic dipole source can generate a detectable signal, while the electric contrast NP is more sensitive to an electric dipole. Using a magnetic dipole source, it is hard to generate detectable signals at receivers with high dielectric particles, however, increasing the frequency will improve the signals.

The coupling technique can also be used to evaluate the heterogeneity of the formation. When the high contrast agents are injected into a heterogeneous medium, e.g., with a low permeable region. The EM responses at the four producers are different. The signals at the producer near the barrier are lower than the other producers, since the fluids containing the high contrast NP is blocked. The proposed multiphysics coupling technique of fluid flow and EM measurements provides guidance for NP field application and help monitor the flow movement in reservoirs.

One of the applications of the high contrast agents is used for hydraulic fractures detection. Hydraulic fracturing is a technique to crack rocks by pumping high pressure fluid into a segment of a well. The created fractures serve as a pathway to release the hydrocarbon resource such as oil or natural gas from the rock. It is an efficient technology to increase the oil/gas production in tight formations. Successful fracture imaging is important to evaluate the created fractures. This is a part of a large project of the Advanced Energy Consortium (AEC) to image large-scale hydraulic fractures in deep underground with high contrast proppants injection. A group of small-scaled fracturing field tests are performed by AEC to investigate the feasibility of injecting high contrast proppants to detect fractures. The injected proppants are designed with high conductivity and permittivity to generate detectable signals at electrode-type sensors. To map the created fractures, an efficient 3-D EM inversion method with physical constraint on the inverted unknowns is developed to simultaneously reconstruct conductivity and permittivity profiles.

The inversion solver is firstly applied to a theoretical model with the noise-polluted synthetic data to reconstruct the fracture, and then applied to two hydraulic fracturing field tests with injected high conductive proppants, Loresco Coke Breeze and steel shot. The fracture conductivity and permittivity are reconstructed based on the scattered voltage signals which are the difference between the post-fracturing and pre-fracturing data. The post-fracturing data are the signals measured after the fracturing and the pre-fracturing data are measured before the fracturing. The difference signals are regarded as from the created fracture. The reconstructed fracture profiles are compared with the coring data to show the reliability of the inversion results. Their good agreement demonstrates the effectiveness of the inverse solver to estimate the fracture size and location.

In recent several decades, EM fields from layered media have attracted considerable attention concerning various applications including geophysical exploration, microwave remote sensing, wave propagation, microstrip circuits, antennas, etc. Especially, the EM waves in anisotropic laminates are of much concern. For geophysical problems, anisotropy happens commonly in many formations, e.g., shale formation. To accurately evaluate the anisotropic medium, a forward solver capable of handling arbitrary anisotropy is needed.

In this work, the formulations for EM fields in multilayered general anisotropic media are derived. Maxwell's equations in the spectral domain are written into a first-order differential (in $z$) equation concerning the transverse electric and magnetic field components in the spectral domain. The equation can be solved to obtain the EM fields in a homogeneous anisotropic medium. For fields in layered anisotropic media, the local transmission and reflection matrices, the global reflection matrices and the recursion relations of the wave amplitudes at interfaces are derived and used to express the EM fields in arbitrary layers. The electric and magnetic dipole sources can locate in arbitrary layers and the medium can possess an arbitrary anisotropy.

To transform the spectral domain solution into the spatial domain involves the inverse Fourier transform which needs integration from $-\infty$ to $+\infty$. The speed of integration calculation depends on the decaying of the integrands. The singular behavior of the fields in the close vicinity of the dipole source needs to be considered since the integrand usually converges very slowly. In this work, it is handled by subtracting the direct fields in the spectral domain, since the direct fields contribute most of the singular problem. The contributions of the subtracted part in the spatial domain are calculated and added afterwards. An example is modeled to show the convergence of the integrands with / without the singularity subtraction. The subtraction makes the integrands decaying rapidly as functions of $k_x$ and $k_y$.

To validate the algorithm, a multilayer full anisotropic medium is modeled and compared with the finite element method (FEM) results. It is also applied to the geophysical EM well logging by modeling the triaxial induction logging tool. The responses in vertical and deviated wells are computed and compared with FEM results. The good agreement between the two results further validates the algorithm and shows the capability of modeling induction logging tools in multilayered general anisotropic media.

The scattering of EM fields from anisotropic objects has been studied intensively in recent years. Most of the work studies the inhomogeneities in homogeneous isotropic background media and a few work has been done on uniaxial anisotropic media. This work extends to inhomogeneities embedded in layered general anisotropic media. The volume integral equation based on the electric dyadic Green's function is derived and solved efficiently with the fast Fourier transform (FFT) based BCGS method. The FFT technique is employed to calculate the convolution and correlation efficiently involved in the integral equation which reduces the computation cost from $O(N^2)$ to $O (N log N)$. A series of numerical examples are modeled and compared with FEM results to validate the algorithm.

Item Open Access Forward Modeling and Inversion of 3D Electromagnetic Scattering Problems in Complicated Backgrounds(2020) Wang, DezhiIn this dissertation, four topics will be presented: (1) The volume integral eqaution method with the domain decomposition method (VIE-DDM) and the inversion using VIE-DDM as forward solver; (2)The numerical mode matching method with surface current boundary condition (NMM-SCBC); (3) NMM-VIE-DDM.VIE-DDM and the inversion: In many applications, electromagnetic scattering from inhomogeneous objects embedded in multiple layers needs to be simulated numerically. The straightforward solution by the method of moments (MoM) for the volume integral equation method is computationally expensive. Due to the shift-invariance and correlation properties of the layered-medium Green's functions, the Stabilized Bi-Conjugate Gradient Fast Fourier Transform (BCGS-FFT) has been developed to greatly reduce the computational complexity of the MoM, but so far this method is limited to objects located in a homogeneous background or in the same layer of a layered medium background. For those problems with objects located in different layers, FFT cannot be applied directly in the direction normal to the layer interfaces, thus the MoM solution requires huge computer memory and CPU time. To overcome these difficulties, the BCGS-FFT method combined with the domain decomposition method (DDM) is proposed in this work. With the BCGS-FFT-DDM, the objects or different parts of an object are first treated separately in several subdomains, each of which satisfies the 3D shift-invariance and correlation properties; the couplings among the different objects/parts are then taken into account, where the coupling matrices can be built to satisfy the 2D shift-invariance property if the objects/subdomains have the same mesh size on the xy-plane. Hence, 3D FFT and 2D FFT can respectively be applied to accelerate the self- and mutual-coupling matrix-vector multiplications. By doing so, the impedance matrix is explicitly formed as one including both the self- and mutual-coupling parts, and the solver converges well for problems with considerable conductivity contrasts. The computational complexity in memory and CPU time can be significantly reduced. Using the BCGS-FFT-DDM as the forward solver, the inversion algorithm based on the Born approximation method and Born iterative method are developed to reconstructed the size, location and properties of the targets buried underground.

NMM-SCBC: The NMM method is widely employed in well-logging problems, because it can transform the original 2.5D problem to a 1D eigenvalue problem at the radial direction, which is usually treated with finite element method (FEM), and a semi-analytical problem at the z direction, which can be easily dealt with the mode matching strategy, and therefore the computational load is significantly reduced. However, more and more well-logging problems are equipped with carbon steel casing, which is extremely thin but with extremely high conductivity. With the conventional NMM method, the extremely thin casing will make the mesh for the FEM tremendously dense and the extremely high conductivity will make the matrices for the eigenvalue problem near ill-posed, both of which will make the solution of the eigenvalue problem inefficient and inaccurate. To overcome this problem, we proposed to apply the SCBC to substitute the extremely thin and highly conductive casing. To employ the NMM-SCBC, the mixed-order FEM isdeveloped to treat the 1D eigenvalue problem, in which the SCBC is deliberately applied. After the eigenvalues and the eigenvectors are solved for each horizontal layer, the mode matching strategy will be applied across the horizontal layers as the conventional NMM method.

MM-VIE-DDM: In many applications, electromagnetic scattering from inhomogeneous objects embedded in multiple layers with cylindrical geometry needs to be simulated numerically. The Numerical Mode Matching (NMM) method has long been The numerical mode matching (NMM) method has long been demonstrated to be the most efficient algorithm for the application under the axial symmetric background, compared with the full 2D methods (such as finite element, finite difference, integral equation method etc.) However, it only works well for the problems with axial symmetric background. For the problem with both cylindrical geometry and 3D objects (such as borehole with reservoirs, fractures), full 3D solvers (such as BCGS-FFT-DDM) can be applied, but will require tremendously large memory and CPU time. The combination of the NMM method and the BCGS-FFT-DDM, or NMM-BCGS-FFT-DDM, is proposed in this paper to deal with the limitations of each method alone. Following the general work flow of the conventional BCGS-FFT-DDM, we substitute the incident field and the dyadic Green's function from the objects to the receivers in the layer media with those considering the cylindrical structures, which are obtained from the NMM method, and neglect the impacts from the cylindrical structures when calculating the total fields inside the objects. Reciprocity and interpolation will be utilized to speed up the calculation when obtaining the Green's function from the objects to the receivers. With the proposed method, the problems with objects in layer media with cylindrical structure can be treated efficiently and accurately. Some numerical results are presented to show the capability of this method.

Item Open Access Memristors and Superconducting Quantum Interference Filters in RF Systems(2013) Wang, LinComplex nonlinear dynamical systems have been appeared in many fields of science and engineering. We are curious about two specific instances of those systems. Those two instances connect memristors and Josephson junctions to the electromagnetic fields. The first instance investigated microstrip patch antenna embedding dual memristors. This hybrid system produces broadband radiation in a narrow band radiation structure. The second one studies the novel ultra-sensitive magnetic field receiver implemented by superconducting quantum interference filters (SQIFs).

For the first instance, we notice that memristor has been proposed as the fourth passive element. We start with investigating the circuit model of this memristive element. Then, we embedded this circuit model into an EM radiation structure. We first report an efficient broadband electromagnetic radiation from a narrowband microstrip patch antenna. The directly modulated microstrip patch antenna system with dual memristors is calculated by using an integrated full-wave finite-difference time-domain solver and an embedded SPICE3 solver. Nonlinear transient electromagnetic responses are analyzed. The radiation frequency spectrum demonstrates the broadband radiation performance from the narrowband antenna system. We predict that the conceptual challenge of high frequency memristors will stimulate pioneering work in the fields of microwave and memristors.

For the second one, we predict that superconducting quantum interference filters (SQIFs) might play a key role in future quantum wireless communication systems. We analyze the dynamic behavior of this large-scale 2D DC SQIF (two-dimensional superconducting direct current quantum interference filter) array in a dynamic electromagnetic environment. The investigation under this framework starts from the SPICE circuit description of a RCSJ (resistively and capacitively shunted junction) model of a Josephson junction and then extends to the 2D SQIF with few device parameters. We separate the interface and the implementation of 2D DC SQIF. This approach can significantly improve circuit-level design efficiency of 2D SQIF array and ultimately allows us to accelerate the hybrid design with an electromagnetic radiation structure. Our findings on the average voltage response of this device offer compelling evidence that the bias static magnetic field plays a key role in designing an effective far-field magnetic field sensor. Since this device can function as both a robust and sensitive low noise pre-amplifier as well as a receiving antenna which only senses the magnetic field component of far-field electromagnetic wave signals, we call it magnetic-antenna or B-antenna. We believe that our research not only directly benefits the sensor design for Information Operations/Signals Intelligence (IO/SIGINT) applications in Very High Frequency/Ultra High Frequency (VHF/UHF) bands, but also opens new dimension of novel ultra-sensitive receiving antenna technology.

Item Open Access Multiscale forward and inverse problems with the DGFD method and the deep learning method(2020) Zhang, RunrenA fast electromagnetic (EM) forward solver has been developed for the subsurface detection, with application includes producing synthetic logging data and instructing large-scale field test and inversion. A deep learning based full wave inversion method has also been developed to reconstruct the underground anomaly.

Since the gas and oil industry has very high demands for the forward modeling speed when doing inversion, the inversion model is usually simpliﬁed to a 1D or 2D problem by supposing the geometry of object invariant in two or one direction. The full 3D inversion is still a hot topic for research, which requires both fast 3D forward solver and efficient inversion method. The bottleneck for the forward solver is how to solve the large-scale linear system eﬃciently; the bottleneck for the inversion is how to pick the global minimum from lots of local minimums eﬃciently for the inverse problem.

For the forward part, the domain decomposition method (DDM) inspired discontinuous Galerkin frequency domain (DGFD) method has been extended to model the vertical open borehole resistivity measurement with structured gradient meshes; besides, the DGFD method has been extended to model the logging-while-drilling (LWD) resistivity measurement in high-angle and horizontal (HA/HZ) well and curved layers with a flipped total field/scattered field (TF/SF) mixed solver. An approximated casing model has also been proposed to accelerate the large-scale curved casing modeling with borehole-to-surface measurements.

For the inversion part, a convolutional neural network based inversion has been developed to reconstruct the lateral extent and direction of the hydraulic fracture through scattered electromagnetic field data under borehole-to-surface measurements; further, the deep transfer learning is applied in the same scenario to improve the performance of the inversion. Additionally, a fully connected neural network has been developed for the Devine field data and successfully reconstruct the shape of the hydraulic fracture with good agreement to the conventional inversion.

Item Open Access Multiscale Spectral Element - Boundary Integral Method for Linear and Nonlinear Nano Optical Computation(2017) Niu, JunIn this work, a hybrid mixed order numerical framework is proposed for multiscale linear/ nonlinear nano optical computation. Starting from the principle of the spectral element boundary integral (SEBI) method, the mixed-order SEBI solver with homogeneous Green's function is first developed for the nano-scale linear and nonlinear electromagnetic scattering analyses. The SEBI realizes the exact radiation boundary condition with a set of surface integral equations (SIE's), and discretize the whole computation domain with the fast convergent Gauss-Lobatto-Legendre (GLL) basis function. The Bloch periodic boundary condition is applied for efficient simulation of structures with periodicities in one or two directions.

For nonlinear optical simulation, full-wave solver is developed self-consistently by iteratively solving the vector Helmholtz equations at each harmonic frequency. To further address the multiscale scattering analysis in nano optics, a hybrid framework is developed by combing the SEBI solver with the dyadic periodic layered medium Green's function (PLMGF) and the domain decomposition method (DDM). Formulating the SIE's with the dyadic PLMGF, all unknowns in the background layered medium are pushed to the radiation boundaries. Thus, the whole planar layered background can be truncated from the computation domain. Considering its highly singular analytical properties, the PLMGF is carefully and systematically formulated under matrix representation. A feasible and effective technique is proposed for the on-interface PLMGF singularity extractions. By extracting the primary and secondary terms' singularities separately, all PLMGF-related SIE components can be efficiently evaluated. The DDM further reduces the memory cost for electrically large problems and enhances the framework's flexibility. Finally, a scattered field perfectly matched layer - surface integral equation (PML-SIE) radiation boundary condition is proposed to enable the non-periodic modeling. With the hybrid radiation boundary condition, the periodic and non-periodic solvers are maximumly integrated together with the minimum maintenance cost.

Benefiting from the exponential convergence and flexibility of the SEBI, computationally challenging problem can be solved with considerably reduced number of samplings. As a typical application, the multilayer defects analysis in extreme ultraviolet (EUV) lithography is studied for both 2-D and 3-D models. The light absorption engineering of graphene is also investigated around the visible spectra. Benefiting from the accuracy of the full-wave nonlinear solver, couplings between the fundamental frequency (FF) field and the higher harmonic (HH) field ignored my most previous studies can also be self-consistently analyzed in nonlinear optical simulation. With this tool, the investigation is extended to the engineering of graphene's visible spectra absorption tuning and third harmonic generation (THG) enhancement. Graphene's Kerr effects are also studied under strong surface plasmonic resonance. The hybrid higher order method's efficiency and accuracy are further validated through various multiscale nano-optical cases.

Item Open Access Spectral Element Method Simulation of Linear and Nonlinear Electromagnetic Field in Semiconductor Nanostructures(2013) Luo, MaIn this dissertation, the spectral element method is developed to simulate electromagnetic field in nano-structure consisting of dielectric, metal or semiconductor. The spectral element method is a special kind of high order finite element method, which has spectral accuracy. When the order of the basis function increases, the accuracy increases exponentially. The goal of this dissertation is to implement the spectral element method to calculate the electromagnetic properties of various semiconductor nano-structures, including photonic crystal, photonic crystal slab, finite size photonic crystal block, nano dielectric sphere. The linear electromagnetic characteristics, such as band structure and scattering properties, can be calculated by this method with high accuracy. In addition, I have explored the application of the spectral element method in nonlinear and quantum optics. The effort will focus on second harmonic generation and quantum dot nonlinear dynamics.

The electromagnetic field can be simulated in both frequency domain and time domain. Each method has different application for research and engineering. In this dissertation, the first half of the dissertation discusses the frequency domain solver, and the second half of the dissertation discusses the time domain solver.

For frequency domain simulation, the basic equation is the second order vector Helmholtz equation of the electric field. This method is implemented to calculate the band structure of photonic crystals consisting of dielectric material as well as metallic materials. Because the photonic crystal is periodic, only one unit cell need to be simulated in the computational domain, and a periodic boundary condition is applied. The spectral accuracy is inspected. Adding the radiation boundary condition at top and bottom of the computational region, the scattering properties of photonic crystal slab can be calculated. For multiple layers photonic crystal slab, the block-Thomas algorithm is used to increase the efficiency of the calculation. When the simulated photonic crystals are finite size, unlike an infinitely periodic system, the periodic boundary condition does not apply. In order to increase the efficiency of the simulation, the domain decomposition method is implemented.

The second harmonic generation, which is a kind of nonlinear optical effect, is simulated by the spectral element method. The vector Helmholtz equations of multiple frequencies are solved in parallel and the consistence solution with nonlinear effect is obtained by iterative solver. The sensitivity of the second harmonic generation to the thickness of each layer can be calculated by taking the analytical differential of the equation to the thickness of each element.

The quantum dot dynamics in semiconductor are described by the Maxwell-Bloch equations. The frequency domain Maxwell-Bloch equations are deduced. The spectral element method is used to solve these equations to inspect the steady state quantum dot dynamic behaviors under the continuous wave electromagnetic excitation.

For time domain simulation, the first order curl equations in Maxwell equations are the basic equations. A spectral element method based on brick element is implemented to simulate a nano-structure consisting of woodpile photonic crystal. The resonance of a micro-cavity consisting of a point defect in the woodpile photonic crystal block is simulated. In addition, the time domain Maxwell-Bloch equations are implemented in the solver. The spontaneous emission process of quantum dot in the micro-cavity is inspected.

Another effort is to implement the Maxwell-Bloch equations in a previously implemented domain decomposition spectral element/finite element time domain solver. The solver can handle unstructured mesh, which can simulate complicated structure. The time dependent dynamics of a quantum dot in the middle of a nano-sphere are investigated by this implementation. The population inversion under continuous and pulse excitation is investigated.

In conclusion, the spectral element method is implemented for frequency domain and time domain solvers. High efficient and accurate solutions for multiple layers nano-structures are obtained. The solvers can be applied to design nano-structures, such as photonic crystal slab resonators, and nano-scale semiconductor lasers.

Item Open Access Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.(J Opt Soc Am A Opt Image Sci Vis, 2010-08-01) Luo, Ma; Liu, Qing HuoThe goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.