Related papers: A Fast Multipole Method based on Band-limited Appr…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…
Peridynamic (PD) theory is significant and promising in engineering and materials science; however, it imposes challenges owing to the enormous computational cost caused by its nonlocality. Our main contribution, which overcomes the…
In this paper, we propose a meshfree method based on the Gaussian radial basis function (RBF) to solve both classical and fractional PDEs. The proposed method takes advantage of the analytical Laplacian of Gaussian functions so as to…
Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
This paper presents the first parallel implementation of the novel "Interpolated Factored Green Function" (IFGF) method introduced recently for the accelerated evaluation of discrete integral operators arising in wave scattering and other…
We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the reconstruction of the optical wavefront from measurements provided by a wavefront sensor. As our application is adaptive optics on extremely large telescopes, our…
This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
This study presents a meshless-based local reanalysis (MLR) method. The purpose of this study is to extend reanalysis methods to the Kriging interpolation meshless method due to its high efficiency. In this study, two reanalysis methods:…
Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…
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…
One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD)…
In this paper, we present a spherical Fast Multipole Method (sFMM) for ray tracing simulation of gravitational lensing (GL) on a curved sky. The sFMM is a non-trivial extension of the Fast Multiple Method (FMM) to sphere $\mathbb S^2$, and…
In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even…
Transmission matrix (TM) linearly maps the incident and transmitted complex fields, and has been used widely due to its ability to characterize scattering media. It is computationally demanding to reconstruct the TM from intensity images…
It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \in \mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\tilde{O}(n)$ exact field operations in…
The boundary knot method (BKM) [1] is a meshless boundary-type radial basis function (RBF) collocation scheme, where the nonsingular general solution is used instead of fundamental solution to evaluate the homogeneous solution, while the…
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…