Related papers: Numerical formulation of three-dimensional scatter…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
We investigate the scattering theory of two particles in a generic $D$-dimensional space. For the s-wave problem, by adopting an on-shell approximation for the $T$-matrix equation, we derive analytical formulas which connect the Fourier…
We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution…
We present an accurate quadrature formula on the sphere with less localized quadrature points for efficient numerical computation of the radiative transport equation (RTE) in the three dimensions. High accuracy of the present method…
Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical…
The standard unitarity-cut method is applied to several massive two-dimensional models, including the world-sheet AdS$_5\times S^5$ superstring, to compute $2\to 2$ scattering S-matrices at one loop from tree level amplitudes. Evidence is…
Discrete transformation for 3- waves problem is constructed in explicit form. Generalization of this system on the matrix case in three dimensional space together with corresponding discrete transformation is presented also.
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close…
The integro-differential formulation of the RTE and its solution by iterations on the source has been extended here to handle anisotropic scattering. The iterative part of the method is O(N ln N ), thanks to an efficient use of H-matrices.…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schr\"odinger's equation. The…
High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering…
To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex…
Three-dimensional numerical models for underwater sound propagation are popular in computational ocean acoustics. For horizontally slowly varying waveguide environments, an adiabatic mode-parabolic equation hybrid theory can be used for…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…