Related papers: The meshless method for solving radiative transfer…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
This paper deals with a numerical analysis of plastic deformation under various conditions, utilizing Radial Basis Function (RBF) approximation. The focus is on the elasto-plastic von Mises problem under plane-strain assumption. Elastic…
In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic…
Radial basis functions are typically used when discretization sche-mes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in…
A new code for evaluation of light absorption and scattering by interstellar dust grains is presented. The radiative transfer problem is solved using ray-tracing algorithm in a self-consistent and highly efficient way. The code demonstrates…
Data-driven modal decompositions are useful tools for compressing data or identifying dominant structures. Popular ones like the dynamic mode decomposition (DMD) and the proper orthogonal decomposition (POD) are defined with continuous…
A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…
In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher…
This article reports on the efficiency of a co-located diffuse approximation method coupled with a projection algorithm for the solution of two and three-dimensional incompressible flow equations. Three typical examples show the accuracy of…
We come back to the analytical solution of the standard transfer problem in a stellar atmosphere. It consists in solving the radiative transfer equation in a homogeneous and isothermal plane-parallel atmosphere, with light scattering taken…
In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…
We propose a method to obtain superresolution of turbulent statistics for three-dimensional ensemble particle tracking velocimetry (EPTV). The method is ''meshless'' because it does not require the definition of a grid for computing…
We propose a meshless method to compute pressure fields from image velocimetry data, regardless of whether this is available on a regular grid as in cross-correlation based velocimetry or on scattered points as in tracking velocimetry. The…
This article presents an on-line tool (rttools.irap.omp.eu) and its accompanying software ressources for the numerical solution of basic radiation transfer out of local thermodynamic equilibrium (LTE). State-of-the-art stationary iterative…
Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite…
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…
The Radial Point Interpolation Mixed Collocation (RPIMC) method is proposed in this paper for transient analysis of diffusion problems. RPIMC is an efficient purely meshless method where the solution of the field variable is obtained…
The study of the scattering of electromagnetic waves by a linear isotropic medium with planar symmetry can be reduced to that of their TE and TM modes. For situations where the medium consists of parallel homogeneous slabs, one may use the…