Related papers: The Integral Equation Method for a Steady Kinemati…
This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…
In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I. Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G. Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM…
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
Solving large-scale eigenvalue problems poses a significant challenge due to the computational complexity and limitations on the parallel scalability of the orthogonalization operation, when many eigenpairs are required. In this paper, we…
In this paper, we propose a numerical method to solve isotropic elliptic equations on point cloud by generalizing the point integral method. The idea of the point integral method is to approximate the differential operators by integral…
In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves,…
The asymmetrically mounted flat plasma actuator is studied using a self-consistent 2-DIM fluid model at atmospheric pressure. The computational model use the drift-diffusion approximation and a simple plasma phenomenological kinetic model.…
In this paper, we propose a horizontal type method of lines numerical scheme for the unsteady Euler-Bernoulli beam equation. The problem is initially reformulated as a first order system of initial value problems and a suitable one-step…
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…
A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by smoothing steps on a series of multilevel finite…
In this article, non-linear Equal Width-Wave (EW) equation will be numerically solved . For this aim, the non-linear term in the equation is firstly linearized by Rubin-Graves type approach. After that, to reduce the equation into a…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The…
The magnetohydrodynamic dynamo equation is derived within general relativity, using the covariant 1+3 approach, for a plasma with finite electric conductivity. This formalism allows for a clear division and interpretation of plasma and…
The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that…
A novel dielectric scheme is proposed for strongly coupled electron liquids that handles quantum mechanical effects beyond the random phase approximation level and treats electronic correlations within the integral equation theory of…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both…