Related papers: Reduced Order Model Enhanced Source Iteration with…
The parametric radiative transfer equation (RTE) arises in multi-query applications, such as design optimization, inverse problems, and uncertainty quantification, which require solving the RTE multiple times for various parameters.…
Parametric radiative transfer equation (RTE) occurs in multi-query applications such as uncertainty quantification, inverse problems, and sensitivity analysis, which require solving RTE multiple times for a range of parameters.…
In implicit time marching of the radiative transfer equation (RTE), the resulting linear systems are commonly solved using source iteration with diffusion synthetic acceleration (SI-DSA). Despite its widespread success, the performance of…
We propose an inexact low-rank source iteration with diffusion synthetic acceleration (SI-DSA) for solving the multidimensional steady-state radiative transfer equation (RTE) in the second-order formulation. The angular flux is represented…
Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equation (RTE). However, most existing rank-adaptive approaches…
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…
A standard approach to solving the S$_N$ transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues…
The commonly used velocity discretization for simulating the radiative transport equation (RTE) is the discrete ordinates method (DOM). One of the long-standing drawbacks of DOM is the phenomenon known as the ray effect. Due to the high…
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…
The method of discrete ordinates ($S_N$) is a popular choice for the solution of the neutron transport equation. It is however well known that it suffers from slow convergence of the scattering source in optically thick and diffusive media,…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…
In recent years, the development of diffusion models has led to significant progress in image and video generation tasks, with pre-trained models like the Stable Diffusion series playing a crucial role. Inspired by model pruning which…
We present the first algorithm to efficiently compute certifiably optimal solutions to range-aided simultaneous localization and mapping (RA-SLAM) problems. Robotic navigation systems increasingly incorporate point-to-point ranging sensors,…
Traditional range-instantaneous Doppler (RID) methods for rigid-body target imaging often suffer from low resolution due to the limitations of time-frequency analysis (TFA). To address this challenge, our primary focus is on obtaining high…
Achieving efficient and accurate simulation of the radiative transfer has long been a research challenge. Here we introduce the general synthetic iterative scheme as an easy-to-implement approach to address this issue. First, a macroscopic…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…
This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we…
The data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of the inverse scattering problems with applications to seismic and sonar imaging. One specification of this approach is that it…