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Electromagnetic-thermal cosimulation of large antenna arrays is performed by using a supercomputing-based parallel domain decomposition method. In this letter, frequency-domain electromagnetic and thermal fields are solved self-consistently and then coupled via Joule heat and temperature-dependent material properties. The developed cosimulation solver is first validated with the commercial software COMSOL Multiphysics. Then, the parallel performance of our in-house developed code is examined in terms of scalability and efficiency. Finally, the temperature distributions over large-scale antenna arrays are obtained by our proposed solver in a highly efficient manner.

An efficient and accurate spectral-element spectral-integral method is developed for rigorously modeling arbitrary inhomogeneous objects with doubly periodicity embedded in a layered medium background. It is an improvement over the traditional finite-element boundary-integral (BI) method. In the proposed approach, the domain decomposition between the interior spectral-element domain and the outer surface BI domain enables the BI domain to be solved by a far more efficient spectral integral method using a uniform mesh; without any loss of generality, it leaves the interior spectral-element domain with flexibility to model any inhomogeneous objects. For the BI domain, with a uniform mesh and rooftop basis functions, we can exploit the Toeplitz structure of the BI matrices with the fast Fourier transform algorithm and apply the Calderon preconditioner to achieve a high iteration convergence rate that will not slow down as the problem gets larger. With the periodic layered medium Green’s functions, the layers without objects can be treated as background and the discretization is avoided. We show that this method is very promising for large-scale problems, because the CPU time and memory required with respect to the number of unknowns grow slowly. We validate this method with a commercial finite element solver and show its ability by solving a large-scale optical lithography problem.

We present a node-based discontinuous Galerkin (DG) pseudospectral time domain (PSTD) algorithm, with adaptive nonconformal unstructured meshes, for 3-D large-scale Maxwell’s equations. This algorithm is a combination of a new DG algorithm and a PSTD method, where spectral accuracy is achieved via the PSTD algorithm, while the DG serves as a stable coupling for multiple domains with unstructured hexahedra. Time marching is efficient because the mass matrix in the DG-PSTD algorithm is exactly diagonal. The scheme is low-storage and scalable because the stiffness matrix is localized into a small shared matrix. Furthermore, arbitrary nonconformal meshes can be adaptively realized, increasing the flexibility of complex media modeling. Our numerical results corroborate the long-time stability, high efficiency, and high-order accuracy of the proposed solver. Finally, an adaptive application of 5G electromagnetic signal propagation demonstrates the efficiency and capability of the proposed high-order solver.

An hp- and memory-adaptive discontinuous Galerkin time-domain algorithm is presented to efficiently model wave propagation in poroelastic media, with the incorporation of 3-D fully anisotropic intrinsic attenuation. From the perspective of physics, the attenuation from the triclinic rock frame, the loss in the pore fluid, and the friction for their interaction are all considered. From the perspective of implementation, a new frequency-domain constitutive equation is introduced, involving complex-valued poroelasticity matrix. A new $Q$ value is defined as the ratio between its real and imaginary parts for every entry. Then, a generalized Maxwell body is adopted to approximate this frequency-dependent $Q$ in the time domain. Mathematically speaking, the hyperbolicity is preserved for the new viscous poroelastic system. Our results corroborate that the intrinsic attenuation anisotropy makes tangible effects in fluid-saturated porous formations.

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-biconjugate 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 article. 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 3-D 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 2-D shift-invariance property if the objects/subdomains have the same mesh size on the $xy$ plane. Hence, 3-D FFT and 2-D 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 for self-coupling matrix-vector multiplication are $O(N_{{z}}^{q} N_{x} N_{y})$ and $O(N_{{z}} N_{x} N_{y} \log (N_{{z}} N_{x} N_{y}))$ respectively, and for mutual-coupling matrix-vector multiplication are $O(N_{{z}}^{p} N_{{z}}^{q} N_{x} N_{y})$ and $O(N_{{z}}^{p} N_{{z}}^{q} N_{x} N_{y} \log (N_{x} N_{y}))$ , respectively, for the proposed method, where $N_{x}$ and $N_{y}$ are the cell numbers of all the subdomains in the $x$ - and $y$ -directions, and $N_{{z}}^{p}$ and $N_{{z}}^{q}$ the cell numbers of different subdomains in the ${z}$ -direction. Several results of different subsurface sensing scenarios are presented to show the capabilities of this method.

Hydraulic fracturing is critical for unconventional oil and gas production. Recently, galvanic methods, including borehole-to-surface and surface-to-borehole electromagnetic methods, have been applied in hydraulic fracture evaluation. However, conventional computational electromagnetic methods require huge computational cost to simulate the common galvanic fracture model, which consists of a long cased borehole, 3-D thin fractures, and an underground stratified medium. More seriously, modeling both vertical and horizontal energized cased boreholes in layered media is exceptionally difficult. In this article, we present a hybrid numerical mode matching method with stabilized bi-conjugate gradient fast Fourier transform method (NMM-BCGS-FFT) as the forward solver to efficiently model 3-D fractures in the galvanic survey. Both vertical and horizontal energized cased boreholes are modeled in the forward solver. The numerical results show the accuracy and efficiency of the hybrid forward solver. The realistic field galvanic detection model analysis will show the practicability of the forward solver.

Microbial induced mineralization is an effective method to prepare green cementitious materials, which has the characteristics of ecological and environmental protection. In this study, preparation and targeting regulation of mineralized products by Bacillus lysine induced was investigated. Law of growth and reproduction was studied via change curves of concentration and pH value of culture solution in the culture process. Four periods, included retardation phase, logarithmic phase, stable phase and decline phase, were verified. The pH value of culture solution was on the rise throughout the culture process, which increased from 7 to 8.1. Characteristics of enzyme production were explored by the deposition of mineralized products in different systems, and the way of extracellular production enzyme was determined. The composition and microstructure of mineralized products were analyzed by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM) and X-ray spectroscopy (EDS). The mineralized products were characterized as calcite, and mineralized products in the culture solution had higher crystallinity. Finally, targeting regulation of temperature on mineralized products was conducted. At the low temperature, mineralization efficiency was higher, and the structure of mineralized products was more favorable.

In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR).

A generalized model for a nonuniform braided-shielded twisted wire pair (TWP) is formulated to investigate the effect of the nonuniformities of the braided shield on its shielding effectiveness performance. Since the apertures of the braided shield are exposed to shape deformation and also their location on the shield is irregular, they are considered to be random variables rather than deterministic values. Therefore, the effect of non uniformities of the braided shield on the induced common-mode (CM) and differential-mode (DM) currents of braided-shielded TWP and twinax cables are investigated by using the Monte Carlo method, where the probability density functions of the CM and DM currents are also generated. It is shown that TWP has a significant advantage as compared to the untwisted one in reducing the interference due to the nonuniformities of the braided-shield structure.

In this paper, a transmission line model is established to describe the electromagnetic wave coupling with transmission line cables from far and near fields. The far-field is described by a plane wave, whereas the near field is considered to be generated by a dipole antenna. Consequently, the affecting electric field due to the plane waves and electric dipole antenna are formulated analytically. In addition, a general expression for the current and voltage at both ends of the transmission line are presented. The model is used to fast calculate the induced common mode and differential mode currents at the cable terminals when the cable is exposed to electromagnetic interference from far and near fields. The results of the proposed analytical model are compared with those of commercial software FEKO, and good agreements are obtained.

Integrated modulators are key components for on-chip optical communication and information processing, which have become leading technologies in the current information-growth era. Hence, high-speed, efficient, and compact integrated modulators are in high demand. However, the current integrated midinfrared modulators meet these requirements with difficulty. Here, we present a high-speed and efficient on-chip electro-optic modulator based on midinfrared hyperbolic metamaterials using stacking of graphene and hexagonal boron nitride. The length of the modulation region is only 60 nm, which is integrated on a plasmonic waveguide composed of hyperbolic metamaterials. The maximum modulation depth is up to 30 dB, and the 3-dB modulation speed can reach up to 50 GHz, which is supported by a detailed study of a small-signal frequency-response model. Our work provides an alternative scheme for the design of modulators with the requirements of sub-100-nm integration and 50-GHz modulation speed or even beyond, which can be directly implemented into a two-dimensional-materials-based photonic integrated circuits platform.

A novel pseudospectral time-domain algorithm, combined with the discontinuous Galerkin method, is presented to simulate electromagnetic wave propagation in large-scale complex media. Compared with the edge-/curl-conforming-based finite element method, arbitrary high-order basis function is easily achieved by utilizing the nodal basis functions; compared with the conventional pseudospectral time-domain algorithm, this new algorithm is strictly long-time stable (>300 central periods) for non-orthogonal elements, in terms of both mathematical analysis and numerical experiments. In addition, both h- and p-adaptivity are supported by using the nonconformal-mesh-based domain decomposition method. Numerical examples include 3D full-waveform modeling of 5G electromagnetic pulse propagation in a bedroom (hundreds of wavelengths in each direction) and fully anisotropic heterogenous head-electromagnetics interaction.

This article presents an efficient method for calculating the scattered electromagnetic (EM) fields from anisotropic objects embedded in general anisotropic multilayers, both with arbitrary anisotropy. The electric field integral equation (EFIE) is derived based on the electric dyadic Green’s functions for general anisotropic multilayers. The volume integral equation (VIE) involves a convolution form between the dyadic Green’s function and equivalent sources. To accelerate the integral computation, the fast Fourier transform technique (FFT) is adopted which reduces the computational cost from $O(N^{2})$ to $O (N \log N)$ . The biconjugate gradient stabilized method (BiCGSTAB) is then applied to solve the EFIE efficiently to calculate the total electric fields in the computational domain. In order to validate the algorithm, several examples are modeled for anisotropic objects embedded in both isotropic and anisotropic multilayers. The modeled scattered fields are compared with the finite-element method (FEM) results. The good agreement between the two results shows the algorithm works properly.

For wave propagation problems, conventional time-domain anelastic attenuation modeling involves either Caputo fractional time derivatives for an exactly constant-[Formula: see text] model, thus leading to globally temporal memory effects; or auxiliary partial differential equations (PDEs) for a nearly constant-[Formula: see text] model, thus resulting in globally spatial operators. Therefore, memory and time consumptions increase tremendously, compared with the purely elastic counterpart. Moreover, the numerical models are usually limited to isotropic or transversely isotropic attenuation, due to the ambiguity of anisotropic attenuation parameterization. Therefore, it is indispensable to investigate an efficient method, to easily incorporate the general anisotropic attenuation effects in the time domain. To tackle these problems, we have first developed a [Formula: see text]-transformation rule, via the correspondence principle, revealing the validity range for a large enough [Formula: see text] value. Then, we construct a new constitutive equation, by extending the generalized Maxwell body, from the isotropic viscoelastic media to fully anisotropic scenario, i.e., as complex as triclinic attenuation. As a result, global memory effects are effectively localized, with several anelastic functions subject to ordinary differential equations, while preserving the original governing equations. An efficient hp-adaptive discontinuous Galerkin (DG) time-domain algorithm is implemented, where the Riemann problem is exactly solved. Consequently, the extra computation cost to incorporate [Formula: see text] effects is nearly negligible. Furthermore, we derive an analytical solution for the general anisotropic attenuation to verify this DG implementation.

A periodic perfectly matched layer (PML) is proposed for the spectral element method (SEM) for the first time, which not only simplifies the recognition process of a PML domain, but also saves degrees of freedom (DoFs) when squeezing its layer number to 1. An objective function to evaluate and optimize its performance has been theoretically derived. In the use of this objective function, the PML parameters are optimized under different conditions; the relationships between the PML's performance and the scaling factor profile, the source position, the basis functions’ order, and the PML layer number are studied, which can help guide the practical applications of PML in the SEM modeling. An estimation method is also introduced to facilitate the selection of the scaling factor.

Electromagnetic simulation of fractures has a growing importance in geophysical exploration, where the formation is usually inhomogeneous and modeled as a layered medium (LM). In this paper, we have developed the first integral-equation based solver to simulate the scattering of fractures straddling an LM. We refer to this solver as LM-thin dielectric sheet (TDS)-surface integral equation (SIE), since it is built on the TDS-based SIE and the LM Green’s function (LMGF). Compared with the traditional finite element method (FEM) and volume integral equation (VIE), LM-TDS-SIE achieves excellent efficiency by taking advantage of the multiscale feature of fracture, rather than being restricted by its volumetric mesh. Good accuracy but the lower computational cost of LM-TDS-SIE is well demonstrated by investigating several typical examples, where reference results are obtained by the commercial software COMSOL. In addition to fractures, LM-TDS-SIE can also be used to simulate the scattering from other types of TDS.

A nonconformal hybrid finite difference time domain (FDTD)/finite element time domain (FETD) method was previously introduced, which implemented the hybridization through a buffer zone. Although this method has been demonstrated to be accurate and long-time stable, further efforts are still desirable to remove the buffer zone and to implement an implicit–explicit time integration from the perspective of practical applications. In this paper, a novel hybrid method is proposed, which not only successfully eliminates the necessity of the buffer zone without compromising the featured advantage (e.g., nonconformal mesh) but also effectively applies an implicit–explicit time integration scheme to improve the computational efficiency. Furthermore, the new method extends the hybridization to a broader level by incorporating the spectral element time domain (SETD) method based on the discontinuous Galerkin and domain decomposition techniques, resulting in a more general hybrid FDTD/SETD/FETD framework. The framework employs the explicit leapfrog time integration for the FDTD region while it employs the implicit Crank–Nicolson time integration for the FETD region. For the SETD region, either the implicit or explicit time integration can be employed, depending on the mesh sizes in it. When the implicit region becomes large, it can be further split into multiple subdomains to reduce computational complexity. Numerical examples are included to demonstrate the performance of the proposed hybrid method, which is accurate, long-time stable and more efficient than the hybrid method with a buffer zone.

As one of the most important nondestructive characterization techniques, electromagnetic (EM) methods can be used in the subsurface fracture detection, especially for hydraulic fracture evaluation in unconventional petroleum exploration and development. The multiscale nature of long but extremely thin 3-D fractures is difficult for conventional EM modeling methods such as the finite element method (FEM) in numerical simulation. The problem becomes even more challenging when the effects of tilted borehole, casing, and planar stratified media need to be considered. So far, modeling a tilted borehole in layered media is still a major challenge for conventional methods. In this paper, we present the hybrid numerical mode-matching method with the stabilized biconjugate gradient fast Fourier transform method as the forward modeling algorithm that can efficiently model 3-D fractures in planar stratified media with a cased borehole environment. Numerical results validate the accuracy of the hybrid forward method and show orders of magnitude higher efficiency of this forward solver than the FEM.

In this paper, full mechanisms of dissipation and dispersion in poro-viscoelastic media are accurately simulated in time domain. Specifically, four Q values are first proposed to depict a poro-viscoelastic medium: two for the attenuation of the bulk and shear moduli in the solid skeleton, one for the bulk modulus in the pore fluid, and the other one for the solid-fluid coupling. By introducing several sets of auxiliary ordinary differential equations, the Q factors are efficiently incorporated in a high-order discontinuous Galerkin algorithm. Consequently, in the mathematical sense, the Riemann problem is exactly solved, with the same form as the inviscid poroelastic material counterpart; in the practical sense, our algorithm requires nearly negligible extra time cost, while keeping the governing equations almost unchanged. Parenthetically, an arbitrarily nonconformal-mesh technique, in terms of both h- and p-adaptivity, is implemented to realize the domain decomposition for a flexible algorithm. Furthermore, our algorithm is verified with an analytical solution for the half-space modeling. A validation with an independent numerical solver, and an application to a large-scale realistic complex topography modeling demonstrate the accuracy, efficiency, flexibility, and capability in realistic subsurface sensing.

To model the responses of electromagnetic surveys for geophysical subsurface sensing, a mixed total field/scattered field-based discontinuous Galerkin frequency-domain (TF/SF DGFD) method is proposed in this paper. The proposed TF/SF DGFD method is implemented at a subdomain level based on the domain decomposition technique. Different subdomains can employ either the TF DGFD framework or the SF DGFD framework, which are then coupled through the Riemann transmission condition. To balance the computation efficiency and accuracy for practical applications, the proposed method prefers to using the SF DGFD framework for subdomains with sources and using the TF DGFD framework for the remaining subdomains. At the interfaces between total field and scattered field subdomains, the Riemann transmission condition is slightly modified by incorporating the background fields due to the physically imposed sources in the background media. In this way, the proposed method only requires surface integrals of the background fields as extra overhead instead of elementwise integration of the scattering objects for the purely scattered field-based method, which can improve the computational efficiency. Also, it is more accurate than the purely TF DGFD method given the same mesh. Numerical examples are studied to examine the performance of the proposed method, which is proven to have better accuracy than the TF DGFD method. The TF/SF DGFD method will facilitate modeling of electromagnetic surveys under complicated geophysical environments for subsurface sensing.

In the discontinuous Galerkin framework, a generalized anisotropic wave impedance is proposed, to succinctly solve the Riemann problem for 3-D full-anisotropic poroelastic media. Consequently, the eigenvalue problem for the large hyperbolic system of poroelastic waves is effectively simplified from the rank of 13 to 4, indicating four types of waves: two P waves due to the porosity, and two S waves due to the anisotropy. Moreover, the domain decomposition is implemented by the nonconformal-mesh technique to adaptively distribute grid sizes. In addition, the perfectly matched layer is used to truncate the finite computational domain. Verifications with an independent finite-difference code and an analytical solution illustrate the accuracy and flexibility of our algorithm.

Porous materials are ubiquitous in the subsurface formations of the earth where acoustic and seismic waves are used for remote sensing. However, it is not well understood how the dissipation and the dispersion of poroelastic waves are caused by the viscoelastic and viscous properties of the constituents such as solid grains and pore fluid and by the viscoelastic dissipation of the solid frame, as well as the viscodynamic coupling of the pore fluid to the solid frame due to its global and local flows relative to the solid grains. Such attenuation mechanisms have seldom been incorporated in subsurface sensing simulations, although they can be very important to applications. In this paper, we propose a complete attenuation model, including both full stiffness and viscodynamic dissipation, for poroelastic media in seismic wave simulations. Completely based on a generalized Zener model, the effects associated with physical dissipation and frequency-dependent dispersion are accurately simulated by a finite-difference time-domain algorithm. Verifications with analytical solutions show the accuracy, efficiency, and flexibility of our method. Numerical results demonstrate that the attenuation of Biot’s model in the sediment of the seafloor has significant effects on acoustic wave scattering from complex geologic structures.

Electromagnetic modeling of triaxial induction responses in fractured formation is of growing importance in well-logging applications. Usually, fractures have a tiny thickness in a scale between micrometers and millimeters, while their length or width is several orders of magnitude larger than their thickness. Such a distinctive multiscale feature generally leads to a very dense mesh, which makes the modeling using the conventional methods, e.g., the finite element method and volume integral equation (VIE), unnecessarily expensive. With the aid of thin dielectric sheet (TDS) approximation for fractures, an efficient and accurate solution is achieved in this paper to model the triaxial induction responses by utilizing the TDS-based surface integral equation (TDS-SIE), which successfully transforms the original VIE into an SIE while guaranteeing a good accuracy. Since the TDS-SIE method only requires surface discretization, unnecessarily dense volume meshes are avoided, and a substantial amount of unknowns can be reduced in numerical simulation. By modeling the triaxial induction responses of both conductive and resistive fractures at the practical scenarios, excellent accuracy, efficiency, and flexibility of the TDS-SIE are demonstrated by comparing the result with that from the semianalytical one-dimensional solution or the VIE method. This provides a valuable solution to characterize near-borehole fractures from induction well-logging data.

Summary We formulate and implement a spectral element method (SEM) to simulate elastic wave propagation in an arbitrary anisotropic background with discrete anisotropic fractures. The approach uses a general linear-slip condition to incorporate the anisotropic fractures into SEM, which allows for discontinuities of displacement fields across the surfaces of fractures. We treat the extremely thin fractures as geometry interfaces instead of meshing them, thus reducing computational cost. The results obtained by the proposed method agree well with the reference solutions for both a single horizontal anisotropic planar fracture and a tilted fracture. Based on the numerical simulation, we analyze the effects of anisotropic fracture on the wavefields. We find that due to the presence of off-diagonal element in the anisotropic fracture stiffness matrix, the wavefields generated by the anisotropic fracture are different from the isotropic fracture. The method can also simulate the wavefields in the anisotropic background including the multiple fractures or the intersecting fractures.

In this work, an in-house developed parallel-computation simulator is employed to study the electrothermal performance of resistive random access memory (RRAM). To save computing storage, the 3D hexahedral elements are used to discretize the structures. The validity of the in-house simulator is investigated first, and then the thermal crosstalk effect of RRAM array is studied base on simulation results.

Thermal crosstalk in a high density resistive random access memory (RRAM) array due to the self-heating effect is one of the most critical issues affecting device reliability. In this paper, an improved cross-point array is proposed to optimize the thermal management of the RRAM array. An in-house simulator is employed to study the performance of the improved RRAM array. Simulation results reveal that the improved RRAM array can help to reduce thermal crosstalk in highly integrated RRAM arrays.

Fugitive dust was cemented, forming larger particles bond in the calcite-consolidation-layer by microbial method. The particular composition, the morphology, and thermal decomposition properties of the samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared (FTIR) spectroscopy, and differential scanning calorimetry-thermogravimetry (DSC-TG). The characterization data obtained showed that loose fugitive dust particles could be bonded and formed the consolidation-layer under the effect of calcite obtained by microbial method successfully. Meanwhile, the sample obtained by microbial method had superior wind-erosion resistance.

We present a discontinuous Galerkin (DG) algorithm with nonconformal meshes to simulate 3D elastic wave propagation in heterogeneous media with arbitrary discrete fractures. In our method, the fractures are not limited to be planar, single, and lossless, but can be curved, intersecting, and viscous. In contrast to the exact volumetric modeling for the extremely thin layer, explicitly treating an individual fracture as a geometry surface (i.e., an imperfect contact interface) requires the jump condition for displacement/velocity, but the continuity of traction vector on the fracture interface. A new upwind flux is proposed to weakly impose this jump boundary condition in the DG framework. This flux guarantees the stability and accuracy of the DG schemes to model arbitrary fractures. Unlike conventional Riemann solvers applied to continuous media, this solution involves an evolutionary update on the Godunov states. Besides this, no extra computational cost is added. In addition, we can extend the fracture interface into a perfectly matched layer to mimic an infinitely large fracture. Quantitative comparisons of the waveforms between our algorithm and an independent finite element code demonstrate the accuracy and efficiency of our algorithm.

We present a nonconformal mesh discontinuous Galerkin pseudospectral time domain algorithm for arbitrary anisotropic elastic/acoustic wave propagation problems. An exact Riemann solver is compactly derived to resolve the accurate coupling of multiple domains in the discontinuous Galerkin framework, including heterogeneous anisotropic solid–solid, acoustic–acoustic, and anisotropic solid–fluid interactions. We simplify the eigenvalue problem in the Riemann solution from the rank of 9 to 3, and introduce the generalized wave impedance with more physical insight. Validations and verifications with independent codes and analytical solutions illustrate the accuracy, flexibility, and stability of our algorithm.

The second-order wave equation-based discontinuous Galerkin time-domain (DGTD) methods typically employ the first-order absorbing boundary condition for modeling open problems. To improve the modeling accuracy, this paper proposes a novel coupling algorithm of the well-posed perfectly matched layer (PML) for wave equation-based DGTD methods. Based on the domain decomposition technique, the proposed coupling algorithm divides the computational domain into two regions, that is, the physical and PML regions, whose meshes can be nonconformal with each other. Instead of introducing time convolution terms, the new coupling scheme is implemented through employing different DGTD frameworks for the two regions. Specifically, the physical region employs the wave equation-based DGTD framework, while the PML region employs the first-order Maxwell’s curl equations-based DGTD framework. To facilitate modeling of electrically small problems, the implicit Newmark-beta time integration is used for the physical region. To conveniently couple with the physical region, the implicit Crank–Nicolson algorithm is used for the PML region. Numerical results are shown to examine the accuracy and efficiency of the proposed coupling algorithm for modeling electrically small problems.