Large-Scale Parallel Wave Propagation Analysis by GeoFEM

Computational dynamic homogenization for the analysis of dispersive waves in layered rock masses with periodic fractures

This work presents a comprehensive analysis of electromagnetic wave propagation inside a two-dimensional photonic crystal in a spectral region in which the crystal behaves as an effective medium to which a negative effective index of refraction can be associated. It is obtained that the main plane wave component of the Bloch mode that propagates inside the photonic crystal has its wave vector k' out of the first Brillouin zone and it is parallel to the Poynting vector ( S' ? k'> 0 ), so light propagation in these composites is different from that reported for left-handed materials despite the fact that negative refraction can take place at the interface between air and both kinds of composites. However, wave coupling at the interfaces is well explained using the reduced wave vector ( k' ) in the first Brillouin zone, which is opposed to the energy flow, and agrees well with previous works dealing with negative refraction in photonic crystals.

ABSTRACTA computationally efficient spectral Kirchhoff plate element is presented for time‐domain analysis of wave propagation at high frequencies in thin isotropic plates. It employs a ‐continuous spectral interpolation based on the modified bi‐Hermite polynomials using the Gauss–Lobatto–Legendre (GLL) points as a basis with selective collocation of rotational and twisting degrees of freedom (DOFs) at element edge and corner nodes. The lowest order version of the proposed element reduces to the classical Bogner–Fox–Schmit (BFS) element for Kirchhoff plates. The GLL basis allows diagonalisation of the mass matrix using the nodal quadrature technique, which enhances the computational efficiency. The numerical properties of the proposed element are comprehensively evaluated, including the conditioning of the system matrices. Moreover, the effect of employing different numerical integration schemes and nodal sets is examined in both static and free vibration analyses. The effectiveness of the proposed element in wave propagation problems is evaluated by comparing its performance to the converged solutions achieved using the BFS element with a very fine mesh. Results demonstrate that the current element, without and even with mass matrix diagonalisation delivers exceptional accuracy while also exhibiting faster convergence and enhanced computational efficiency than the existing Kirchhoff plate elements.

The science and technology agency has begun an “Earth Simulator” project from the fiscal year of 1997, which enables the forecast of various earth phenomena through the simulation of virtual earth placed in a supercomputer. The “GeoFEM” is a parallel finite element software to be run on the “Earth Simulator” to solve problems involving the solid earth and is being developed at RIST. This project is expected to be a breakthrough in bridging the geoscience and information science fields. In this paper, we briefly describe the “GeoFEM” project, then capability for large-scale analysis is discussed and simple example analyses are shown. At this stage, the largest linear elastic problem solved by “GeoFEM” is more than 100M (100,000,000) degree of freedoms on 1,000 PEs Hitachi SR2201 at University of Tokyo.

Analysis of wave-induced crack propagation through a coupling algorithm of the peridynamics and isogeometric analysis

In general, FDTD and TLM are the Time Domain methods for solving the electromagnetic equations. TLM is a numerical modeling technique for analyzing wave propagation that is used extensively in EM wave propagation that is based on Huygen's model of wave propagation. Implementation of TLM is based on two steps: Incident (for output voltages of next time step) and Scattering. In this paper, analysis of wave propagation in 2D shunt node Transmission Line by using TLM method TL parameters in homogeneous and non-homogeneous medium is presented. Wave propagates from a feeding point node with the incident voltage and scatters in the dimensional space. Wave is propagated in TM mode and corresponding planes Ez, Hx, Hy are observed as output for the incident signal.

The analysis of elastic wave propagation is a critical problem in both science and engineering, with applications in structural health monitoring and seismic wave analysis. However, the efficient and accurate numerical simulation of large-scale three-dimensional structures has posed significant challenges to traditional methods, which often struggle with high computational costs and limitations. This paper presents a novel two-and-a-half-dimensional generalized finite difference method (2.5D GFDM) for efficient simulation of elastic wave propagation in longitudinally invariant structures. The proposed scheme integrates GFDM with 2.5D technology, reducing 3D problems to a series of 2D problems in the wavenumber domain via Fourier transforms. Subsequently, the solutions to the original 3D problems can be recovered by performing inverse Fourier transforms on the solutions obtained from the 2D problems. The 2.5D GFDM avoids the inherent challenge of mesh generation in traditional methods like FEM and FVM, offering a meshless solution for complex 3D problems. By employing sparse coefficient matrices, it offers significantly improved computational efficiency. The new approach achieves significant computational advantages while maintaining high accuracy, as validated through three representative examples, making it a promising tool for solving large-scale elastic wave propagation problems in longitudinally invariant structures.

Analysis of wave propagation in the lower hybrid range of frequencies (LHRF) in the past was done using ray tracing and the Wentzel-Kramers-Brillouin approximation taking advantage of the very small scale of those waves. To include the effects of wave diffraction and focusing in this regime, full-wave simulation is necessary but requires significantly more computational power. In both ray tracing and full-wave simulations in the LHRF, it is also essential to include the self-consistent evolution of the electron distribution in response to the waves. This adds a considerable computational burden in constructing the stiffness matrix for the system [Valeo , “Full-wave Simulations of LH wave propagation in toroidal plasma with non-Maxwellian electron distributions,” 18th Topical Conference on Radio Frequency Power in Plasmas, AIP Conference Proceedings (2007)]. Advances in algorithms and the availability of massively parallel computer architectures have permitted the solving of the Maxwell-Vlasov system for wave propagation directly [Wright , Phys. Plasmas (2009), 16, July]. We will discuss the various modeling advances that have led to this capability, including various memory-management approaches, physics-motivated algorithm adaptions appropriate to the LHRF, and improvements in the matrix solver to minimize communication overhead when using thousands of cores on leadership-class computer platforms. Of particular importance have been the use of verification and validation techniques and the analytic approximations to the imaginary (pole residue) contribution to the plasma dielectric response.

Concave finite elements for the cloning algorithm

A new super convergent sandwich beam finite element formulation is presented in this article. This element is a two-nodded, six degrees of freedom (dof) per node (3 dof u0, w, φ for top and bottom face sheets each), which assumes that all the axial and flexural loads are taken by face sheets, while the core takes only the shear loads. The beam element is formulated based on first-order shear deformation theory for the face sheets and the core displacements are assumed to vary linearly across the thickness. A number of numerical experiments involving static, free vibration, and wave propagation analysis examples are solved with an aim to show the super convergent property of the formulated element. The examples presented in this article consider both metallic and composite face sheets. The formulated element is verified in most cases with the results available in the published literature.

SUMMARY Modelling marine controlled-source electromagnetic (CSEM) responses in the fictitious time domain is a novel approach, which facilitates the full exploration of EM diffusive properties in the fictitious wave domain (FWD). Concepts, such as reflections, refractions, diffractions and transmissions, which are used for the analysis of elastic wave propagation can thus be adopted in FWD for interpreting CSEM data. In this paper, we use a high-order finite difference time domain (FDTD) algorithm for modelling marine CSEM responses in both the fictitious time domain and the diffusive frequency domain. A complex frequency shifted perfectly matched layer (CFS–PML) boundary condition is adopted to the FDTD modelling. We demonstrate the performance of the CFS–PML boundary condition and validate the high-order FDTD code in the FWD with the half-space sea water model and in the frequency domain with the 1-D canonical reservoir model. We investigate and analyse the propagation characteristics of electromagnetic fields in the FWD, where we apply wave propagation concepts to interpret marine CSEM data. Similarities between wave and field propagations relevant for marine CSEM data are demonstrated through several 1-D to 3-D numerical examples.

ABSTRACTIn this paper, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler–Bernoulli beam theory. The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials. A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam. Hamilton principal is used to derive governing differential equations of motion. Three behaviors of sandwich microbeam including free vibration, wave propagation, and bending analyses are studied in this paper. Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index, applied voltage, parameters of foundation, and material length scales. The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied.

SUMMARY This work presents a model to characterize the behaviour of waves propagating in non-isothermal poroelastic solids saturated by two-phase fluids. The dynamic differential equations include the poroelasticity and heat equations with the solid, fluid and thermal fields combined using coupling terms. A plane wave analysis shows that five waves can propagate, three compressional, one fast (P1) and two slow (P2, P3), a shear fast (S) and a thermal slow (T). P2, P3 and T are diffusive waves at low frequencies, while P1 and S behave as propagating waves. The T wave is coupled with the compressional waves and uncoupled with the S wave. The plane wave analysis applied to a real sandstone saturated with gas–water mixtures compares phase velocities and attenuation factors for two-phase and effective single-phase fluids, considering or neglecting the coupling terms. It is observed that P1 and P2 waves have higher velocities for coupled cases, while P3 and T waves exhibit the opposite behaviour. Furthermore the plane wave analysis is performed in the coupled case for oil–water and gas–water two-phase fluids, with compressional waves exhibiting higher velocities for gas–water than for oil–water mixtures. The propagation of waves in a 1-D thermo-poroelastic medium saturated by a gas–water mixture is presented and analysed using a finite element procedure. Considering temperature may become important in high-pressure high-temperature hydrocarbon and geothermal reservoirs.

Temperature effects on wave propagation in nanoplates

Wave propagation in sandwich panels with a poroelastic core, which is modeled by Biot's theory, is investigated using the waveguide finite element method. A waveguide poroelastic element is developed based on a displacement-pressure weak form. The dispersion curves of the sandwich panel are first identified as propagating or evanescent waves by varying the damping in the panel, and wave characteristics are analyzed by examining their motions. The energy distributions are calculated to identify the dominant motions. Simplified analytical models are also devised to show the main physics of the corresponding waves. This wave propagation analysis provides insight into the vibro-acoustic behavior of sandwich panels lined with elastic porous materials.