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We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain…
The problem of light propagation of frequency corresponding to half of the energy difference between a metastable excited state and the ground state of atoms is examined, and solved for coherent medium by analytic means. We demonstrate that…
Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has…
Permanent gravity waves propagating in deep water, spanning amplitudes from infinitesimal to their theoretical limiting values, remain a classical yet challenging problem due to its inherent nonlinear complexities. Traditional analytical…
As an essential attribute of organic compounds, polarity has a profound influence on many molecular properties such as solubility and phase transition temperature. Thin layer chromatography (TLC) represents a commonly used technique for…
Impact craters are the primary geomorphic features on the surfaces of celestial bodies such as the Moon, and their formation has significant implications for the evolutionary history of the celestial body. The study of the impact crater…
Physics-based computational models play a key role in the study of wave propagation for structural health monitoring (SHM) and the development of improved damage detection methodologies. Due to the complex nature of guided waves, accurate…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
The primary objective of this paper is to demonstrate that problems related to stability and robust control in the harmonic context can be effectively addressed by formulating them as semidefinite optimization problems, invoking the concept…
The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…
We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…
In distributed ML applications, shared parameters are usually replicated among computing nodes to minimize network overhead. Therefore, proper consistency model must be carefully chosen to ensure algorithm's correctness and provide high…
In this study, we investigate the dispersive properties of smoothed particle magnetohydrodynamics (SPM) in a strongly magnetized medium by using linear analysis. In modern SPM, a correction term proportional to the divergence of the…
The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion-acoustic and magnetohydrodynamic waves in plasma, nonlinear transverse waves in shallow water and phonon packets…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
In this work we formulate and test a new procedure, the Multiscale Perturbation Method for Two-Phase Flows (MPM-2P), for the fast, accurate and naturally parallelizable numerical solution of two-phase, incompressible, immiscible…
A numerical method for processing the data of ground penetrating radars for a piece-wise continuous layered medium is proposed. The method combines the layer stripping technique with numerical continuation of data into the complex…
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, a challenging task is to preserve…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in…
We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…