相关论文: A Weighted Least-Squares Transport Equation Compat…
In this paper we show the extension of the Nonlinear-Diffusion Acceleration (NDA) to geometries containing small voids using a weighted least-squares (WLS) high order equation. Even though the WLS equation is well defined in voids, the…
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids, using Continuous Finite Element Methods (CFEM). The main idea is to use the Least-Squares…
In this paper, we study the least-squares finite element methods (LSFEM) for the linear hyperbolic transport equations. The linear transport equation naturally allows discontinuous solutions and discontinuous inflow conditions, while the…
In this paper, two flux-only least-squares finite element methods (LSFEM) for the linear hyperbolic transport problem are developed. The transport equation often has discontinuous solutions and discontinuous inflow boundary conditions, but…
In this work, we present a subdomain discontinuous least-squares (SDLS) scheme for neutronics problems. Least-squares (LS) methods are known to be inaccurate for problems with sharp total-cross section interfaces. In addition, the…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual equally important, the new procedure exponentially…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
In this paper, we present an accurate and robust scaling operator based on material optical thickness (OT) for the least-squares spherical harmonics (LSP$_N$) method for solving neutron transport problems. LSP$_N$ without proper scaling is…
In this paper, we study least-squares finite element methods (LSFEM) for general second-order elliptic equations with nonconforming finite element approximations. The equation may be indefinite. For the two-field potential-flux div LSFEM…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially…
In this paper, we address a data dependent modification of the moving least squares (MLS) problem. We propose a novel approach by replacing the traditional weight functions with new functions that assign smaller weights to nodes that are…
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…
In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…
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…
This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding…