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Morse and Ingard give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas sensors. Like other wave propagation problems, the…
Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric…
We discuss Green's-function solutions of the equation for a geometrically thin, axisymmetric Keplerian accretion disc with a viscosity prescription "\nu ~ R^n". The mathematical problem was solved by Lynden-Bell & Pringle (1974) for the…
Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
Accurately predicting nonlinear transient thermal fields in two-dimensional domains is a significant challenge in various engineering fields, where conventional analytical and numerical methods struggle to balance physical fidelity with…
A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the…
We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…
We present a time-domain scheme for computing Casimir forces within the Maxwell stress tensor formalism, together with a specific realization using the finite-element-based discontinuous Galerkin time-domain method. The approach enables…
In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a…
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
The "flexible boundary condition" method, introduced by Sinclair and coworkers in the 1970s, remains among the most popular methods for simulating isolated two-dimensional crystalline defects, embedded in an effectively infinite atomistic…
We show that the boundary behaviour of solutions to nonlocal fractional equations posed in bounded domains strongly differs from the one of solutions to elliptic problems modelled upon the Laplace-Poisson equation with zero boundary data.…
We show how the linearized equations of motion of any dissipative current are determined by the analytical structure of the associated retarded Green's function. If the singularity of the Green's function, which is nearest to the origin in…
At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as…
In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete…
Recently, an exact Green's function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was derived. Here, we use the obtained Green's function to calculate…
This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…