Related papers: An FN method for the radiative transport equation …
This paper extends the recently introduced Front Face Flash Method for extraction of thermal diffusivity of thin films to samples of small optical thickness. The paper discusses the principal question whether diffusivity is uniquely defined…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over the volume of the ball in three dimensions is described. Such methods are necessary in many areas of Applied…
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…
Radiation transport plays a crucial role in star formation models, as certain questions within this field cannot be accurately addressed without taking it into account. Given the high complexity of the interstellar medium from which stars…
We present a numerical implementation of radiative transfer based on an explicitly photon-conserving advection scheme, where radiative fluxes over the cell interfaces of a structured or unstructured mesh are calculated with a second-order…
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…
We present a novel extension of the path tracing algorithm that is capable of treating highly scattering participating media in the presence of fluorescent structures. The extension is based on the formulation of the full radiative transfer…
A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
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.…
This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…
The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies…
A new approach for solving the optical inverse problem of quantitative photoacoustic tomography is introduced, which interpolates between the well-known diffusion approximation and a radiative transfer equation based model. The proposed…
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)…
There is a Computational fluid dynamics (CFD) method of incorporating the DNN inference to reduce the computational cost. The reduction is realized by replacing some calculations by DNN inference. The cost reduction depends on the…
We propose a neural network-based real-time volume rendering method for realistic and efficient rendering of volumetric media. The traditional volume rendering method uses path tracing to solve the radiation transfer equation, which…