Related papers: Wave propagation in a fractional viscoelastic Andr…
Controlling systems governed by partial differential equations is an inherently hard problem. Specifically, control of wave dynamics is challenging due to additional physical constraints and intrinsic properties of wave phenomena such as…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is…
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
This article studies a direct numerical approach for fractional advection-diffusion equations (ADEs). Using a set of cubic trigonometric B-splines as test functions, a differential quadrature (DQ) method is firstly proposed for the 1D and…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
Mathematical models and computer algorithms are developed to calculate dynamic stress concentration and fracture wave propagation in a reinforced composite sheet. The composite consists of a regular system alternating extensible fibers and…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
We study waves in a rod of finite length with a viscoelastic constitutive equation of fractional distributed-order type for the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain case…
The numerical simulation of acoustic waves in complex 3D media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this…
In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…
In this paper we develop a finite element method for acoustic wave propagation in Drude-type metamaterials. The governing equation is written as a symmetrizable hyperbolic system with auxiliary variables. The standard mixed finite elements…
This work is devoted to the asymptotic analysis of high frequency wave propagation in random media with long-range dependence. We are interested in two asymptotic regimes, that we investigate simultaneously: the paraxial approximation,…
A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of function values at past times. In order to lessen the computational load while maintaining the…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions,…
The frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency independent…
We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fluctuations in…