Hybrid asymptotic-numerical approach for estimating first-passage-time densities of the two-dimensional narrow capture problem
AE Lindsay, RT Spoonmore, JC Tzou - Physical Review E, 2016 - APS
A hybrid asymptotic-numerical method is presented for obtaining an asymptotic estimate for
the full probability distribution of capture times of a random walker by multiple small traps …
the full probability distribution of capture times of a random walker by multiple small traps …
The stability and dynamics of localized spot patterns in the two-dimensional Gray–Scott model
W Chen, MJ Ward - SIAM Journal on Applied Dynamical Systems, 2011 - SIAM
The dynamics and stability of multispot patterns to the Gray–Scott (GS) reaction-diffusion
model in a two-dimensional domain is studied in the singularly perturbed limit of small …
model in a two-dimensional domain is studied in the singularly perturbed limit of small …
A tuned and scalable fast multipole method as a preeminent algorithm for exascale systems
Among the algorithms that are likely to play a major role in future exascale computing, the
fast multipole method (fmm) appears as a rising star. Our previous recent work showed …
fast multipole method (fmm) appears as a rising star. Our previous recent work showed …
Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations
AT Layton, ML Minion - BIT Numerical Mathematics, 2005 - Springer
This paper concerns a class of deferred correction methods recently developed for initial
value ordinary differential equations; such methods are based on a Picard integral form of …
value ordinary differential equations; such methods are based on a Picard integral form of …
A fast integral equation method for the two-dimensional Navier-Stokes equations
The integral equation approach to partial differential equations (PDEs) provides significant
advantages in the numerical solution of the incompressible Navier-Stokes equations. In …
advantages in the numerical solution of the incompressible Navier-Stokes equations. In …
[HTML][HTML] Numerical simulation of two-dimensional modified Helmholtz problems for anisotropic functionally graded materials
In this paper we consider the modified Helmholtz type equation governing 2D-boundary
value problems for anisotropic functionally graded materials (FGMs) with Dirichlet and …
value problems for anisotropic functionally graded materials (FGMs) with Dirichlet and …
Fourier truncation regularization method for a three-dimensional Cauchy problem of the modified Helmholtz equation with perturbed wave number
F Yang, P Fan, XX Li - Mathematics, 2019 - mdpi.com
In this paper, the Cauchy problem of the modified Helmholtz equation (CPMHE) with
perturbed wave number is considered. In the sense of Hadamard, this problem is severely ill …
perturbed wave number is considered. In the sense of Hadamard, this problem is severely ill …
A free-space adaptive FMM-based PDE solver in three dimensions
H Langston, L Greengard, D Zorin - Communications in Applied …, 2011 - msp.org
We present a kernel-independent, adaptive fast multipole method (FMM) of arbitrary order
accuracy for solving elliptic PDEs in three dimensions with radiation and periodic boundary …
accuracy for solving elliptic PDEs in three dimensions with radiation and periodic boundary …
A fast method for imposing periodic boundary conditions on arbitrarily-shaped lattices in two dimensions
A new scheme is presented for imposing periodic boundary conditions on unit cells with
arbitrary source distributions. We restrict our attention here to the Poisson, modified …
arbitrary source distributions. We restrict our attention here to the Poisson, modified …
A fourth-order kernel-free boundary integral method for the modified Helmholtz equation
Y Xie, W Ying - Journal of Scientific Computing, 2019 - Springer
Based on the kernel-free boundary integral method proposed by Ying and Henriquez (J
Comput Phys 227 (2): 1046–1074, 2007), which is a second-order accurate method for …
Comput Phys 227 (2): 1046–1074, 2007), which is a second-order accurate method for …