Related papers: Fast Multipole Method for 3-D Linearized Poisson-B…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
It is proposed a dimensional Lattice Boltzmann Method (LBM) of wide application for simulating fluid flow and heat transfer problems. The proposed LBM consists in the numerical solution of the discrete lattice Boltzmann equation (LBE) using…
We present the pseudo-particle multipole method (P2M2), a new method to handle multipole expansion in fast multipole method and treecode. This method uses a small number of pseudo-particles to express multipole expansion. With this method,…
The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. Depending on the media and the particles to be modeled, the…
In this paper, we propose and analyze the numerical algorithms for fast solution of periodic elliptic problems in random media in $\mathbb{R}^d$, $d=2,3$. We consider the stochastic realizations using checkerboard configuration of the…
To evaluate electrostatics interactions, Molecular dynamics (MD) simulations rely on Particle Mesh Ewald (PME), an O(Nlog(N)) algorithm that uses Fast Fourier Transforms (FFTs) or, alternatively, on O(N) Fast Multipole Methods (FMM)…
We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are…
The cascaded or central-moments-based lattice Boltzmann method (CM-LBM) is a robust alternative to the more conventional BGK-LBM for the simulation of high-Reynolds number flows. Unfortunately, its original formulation makes its extension…
High-frequency issues have been remarkably challenges in numerical methods for partial differential equations. In this paper, a learning based numerical method (LbNM) is proposed for Helmholtz equation with high frequency. The main novelty…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
Flexural wave scattering plays a crucial role in optimizing and designing structures for various engineering applications. Mathematically, the flexural wave scattering problem on an infinite thin plate is described by a fourth-order…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
We propose and analyze the perfectly matched layer (PML) method for the time-harmonic acoustic waves driven by the white noise source in the presence of the uniform flow. A PML is an artificial absorbing layer commonly used to truncate…
In this paper, using the approximate particular solutions of Helmholtz equations, we solve the boundary value problems of Helmholtz equations by combining the methods of fundamental solutions (MFS) with the methods of particular solutions…
This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…
By means of the multicomponent Shan-Chen lattice Boltzmann method (LBM), we investigate the multiphase flow through porous media. Despite the excellent accuracy of the LBM, large domains result in unaffordable computational expenses. The…
We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
We develop and analyze a new approach for simultaneously computing multiple solutions to the Helmholtz equation for different frequencies and different forcing functions. The new Multi-Frequency WaveHoltz (MFWH) algorithm is an extension of…
We explore a novel simulation route for Plasma Wakefield Acceleration (PWFA) by using the computational method known as the Lattice Boltzmann Method (LBM). LBM is based on a discretization of the continuum kinetic theory while assuring the…
Perfectly matched layers (PMLs) are formulated and applied to numerically solve nonlocal Helmholtz equations in one and two dimensions. In one dimension, we present the PML modifications for the nonlocal Helmholtz equation with general…