Related papers: Fast multipole method for the Laplace equation in …
In this work we formulate and test a new procedure, the Multiscale Perturbation Method for Two-Phase Flows (MPM-2P), for the fast, accurate and naturally parallelizable numerical solution of two-phase, incompressible, immiscible…
By developing the method of multipliers, we establish sufficient conditions which guarantee the total absence of eigenvalues of the Laplacian in the half-space, subject to variable complex Robin boundary conditions. As a further application…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
We present an efficient integral equation approach to solve the heat equation, $u_t (\x) - \Delta u(\x) = F(\x,t)$, in a two-dimensional, multiply connected domain, and with Dirichlet boundary conditions. Instead of using integral equations…
A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function.…
In this work, we present a semi-numerical solution of a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite…
This paper is concerned with the error estimation of the fast multipole method (FMM) for scattering problems in 2-D. The FMM error is caused by truncating Graf's addition theorem in each step of the algorithm, including two expansions and…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
In this work, we apply a fast and accurate numerical method for solving fractional reaction-diffusion equations in unbounded domains. By using the Fourier-like spectral approach in space, this method can effectively handle the fractional…
The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…
The integral equation method is widely used in numerical simulations of 2D/3D acoustic and electromagnetic scattering problems, which needs a large number of values of the Green's functions. A significant topic is the scattering problems in…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
This paper presents a new fast multipole boundary element method (FM-BEM) for solving the acoustic transmission problems in 2D periodic media. We divide the periodic media into many fundamental blocks, and then construct the boundary…
The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
Chemically-active colloids modify the concentration of chemical solutes surrounding them in order to self-propel. In doing so, they generate long-ranged hydrodynamic flows and chemical gradients that modify the trajectories of other…
Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…
The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional…
The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace…