Related papers: An integral equation based numerical method for th…
In this paper, we present a robust and fully discretized method for solving the time fractional diffusion equation with high-contrast multiscale coefficients. We establish the homogenized equation using a multicontinuum approach and employ…
Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the…
A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The…
An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate Neumann-Neumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
In this note we describe a space-time boundary element discretization of the heat equation and an efficient and robust preconditioning strategy which is based on the use of boundary integral operators of opposite orders, but which requires…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it provides the reader with error estimates that are uniform in…
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
In this paper we study the variational method and integral equation methods for a conical diffraction problem for imperfectly conducting gratings modeled by the impedance boundary value problem of the Helmholtz equation in periodic…
We give large-time asymptotic estimates, both in uniform and $L^1$ norms, for solutions of the Dirichlet heat equation in the complement of a bounded open set of $\mathbb{R}^d$ satisfying certain technical assumptions. We always assume that…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Recently, the numerical solution of multi-frequency, highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. When the problem derives from the space semi-…
By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$…
Inspired by the Galerkin and particular method, a new approximation approach is recalled in the Cartesian case. In this paper, we are interested specially by constructing this method, when the domain of consideration is a two dimensional…