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We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $\omega$ and ratio of the Lam\'e…

This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…

In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent…

Stochastic hydrodynamics provides a dynamical framework for the evolution of fluctuations in heavy-ion collisions, but poses significant challenges in numerical simulations. We present an algorithm for the simulation of non-relativistic…

In this paper, we propose a moment method to numerically solve the Vlasov equations using the framework of the NRxx method developed in [6, 8, 7] for the Boltzmann equation. Due to the same convection term of the Boltzmann equation and the…

Simulations of elastic turbulence, the chaotic flow of highly elastic and inertialess polymer solutions, are plagued by numerical difficulties: The chaotically advected polymer conformation tensor develops extremely large gradients and can…

The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…

Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of many physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case,…

Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultrafast numerical solutions of high-dimensional…

Considering a two-by-two block operator matrix system of Maxwell type, we present an elementary way of deducing exponential stability under minimal smoothness (and boundedness) requirements of the underlying domains when applications are…

We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…

The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions…

Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation…

The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…

Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…

A novel method which is called the Chebyshev inertial iteration for accelerating the convergence speed of fixed-point iterations is presented. The Chebyshev inertial iteration can be regarded as a valiant of the successive over relaxation…

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…

The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schrodinger equation in an explicitly iterative process. However, the method requires the spatial grid…

Crack microgeometries pose a paramount influence on effective elastic characteristics and sonic responses. Geophysical exploration based on seismic methods are widely used to assess and understand the presence of fractures. Numerical…

Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…