相关论文: Preconditioned Bi-Conjugate Gradient Method for Ra…
We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific…
Radiative backpropagation-based (RB) methods efficiently compute reverse-mode derivatives in physically-based differentiable rendering by simulating the propagation of differential radiance. A key assumption is that differential radiance is…
We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
A new method for the formal solution of the 2D radiative transfer equation in axial symmetry in the presence of arbitrary velocity fields is presented. The combination of long and short characteristics methods is used to solve the radiative…
We present a new numerical approach that is able to solve the multi-dimensional radiative transfer equations in all opacity regimes on a Lagrangian, unstructured network of characteristics based on a stochastic point process. Our method…
The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
Radiative transfer is a fundamental process in astrophysics, essential for both interpreting observations and modeling thermal and dynamical feedback in simulations via ionizing radiation and photon pressure. However, numerically solving…
A new iterative method for non-LTE multilevel polarized radiative transfer in hydrogen lines is presented. Iterative methods (such as the Jacobi method) tend to damp out high-frequency components of the error fast, but converges poorly due…
Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison…
We develop a novel preconditioning method for ridge regression, based on recent linear sketching methods. By equipping Stochastic Variance Reduced Gradient (SVRG) with this preconditioning process, we obtain a significant speed-up relative…
In this paper, curved fronts are constructed for spatially periodic bistable reaction-diffusion equations under the a priori assumption that there exist pulsating fronts in every direction. Some sufficient and some necessary conditions of…
Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
In the present study, an advection-diffusion problem has been considered for the numerical solution. The continuum equation is discretized using both upwind and centered scheme. The linear system is solved using the ILU preconditioned…
Affine frequency division multiplexing (AFDM) is a promising chirp-assisted multicarrier waveform for future high mobility communications. A significant challenge in MIMO-AFDM systems is the multi-user interference (MUI), which can be…
An algorithm for the numerical inversion of large matrices, the biconjugate gradient algorithm (BGA), is investigated in view of its use for Monte Carlo simulations of fermionic field theories. It is compared with the usual conjugate…
The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this…
We describe a novel fluctuating-surface current formulation of radiative heat transfer between bodies of arbitrary shape that exploits efficient and sophisticated techniques from the surface-integral-equation formulation of classical…