Related papers: Preconditioning the discrete dipole approximation
DDSCAT 7.2 is a freely available open-source Fortran-90 software package applying the discrete dipole approximation (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex…
Cylindrical lattice diffusion limited aggregation (DLA), with a narrow width N, is solved for site-sticking conditions using a Markovian matrix method (which was previously developed for the bond-sticking case). This matrix contains the…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
This paper studies the spectral properties of large matrices and the preconditioning of linear systems, arising from the finite difference discretization of a time-dependent space-fractional diffusion equation with a variable coefficient…
DDSCAT.5a is a freely available software package which applies the "discrete dipole approximation" (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. The…
We investigate the wave-optical light scattering properties of deformed thin circular films of constant thickness using the discrete-dipole approximation. Effects on the intensity distribution of the scattered light due to different…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
A novel numerical method called the Thermal Discrete Dipole Approximation (T-DDA) is proposed for modeling near-field radiative heat transfer in three-dimensional arbitrary geometries. The T-DDA is conceptually similar to the Discrete…
The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations.…
It is well known that the discretization of fractional diffusion equations (FDEs) with fractional derivatives $\alpha\in(1,2)$, using the so-called weighted and shifted Gr\"unwald formula, leads to linear systems whose coefficient matrices…
Recently, the volume integral equation (VIE) approach has been proposed as an efficient simulation tool for silicon photonics applications [J. Lightw. Technol. 36, 3765 (2018)]. However, for the high-frequency and strong contrast problems…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
DDSCAT 7.3 is an open-source Fortran-90 software package applying the discrete dipole approximation to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. The…
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once diffusion-based representation of a covariance matrix…
We present a simple discretization scheme for the hypersingular integral representation of the fractional Laplace operator and solver for the corresponding fractional Laplacian problem. Through singularity subtraction, we obtain a…
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion…
In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…
Numerical climate- and weather-prediction requires the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous properties. They can be used for arbitrary domains and support a…
The $p$-step backwards difference formula (BDF) for solving the system of ODEs can result in a kind of all-at-once linear systems, which are solved via the parallel-in-time preconditioned Krylov subspace solvers (see McDonald, Pestana, and…
A novel hybrid method based on Mie theory and the Discrete Dipole Approximation (DDA) was developed to study the microscopic parameters governing the optical response of tunable photonic crystals (PC). The method is based on a two-step…