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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…
Stochastic Dual Coordinate Descent (SDCD) has become one of the most efficient ways to solve the family of $\ell_2$-regularized empirical risk minimization problems, including linear SVM, logistic regression, and many others. The vanilla…
In this work we propose an efficient black-box solver for two-dimensional stationary diffusion equations, which is based on a new robust discretization scheme. The idea is to formulate an equation in a certain form without derivatives with…
This paper introduces a parallel-in-time algorithm for efficient steady-state solution of the eddy current problem. Its main idea is based on the application of the well-known multi-harmonic (or harmonic balance) approach as the coarse…
An iterative scheme can be used to find a steady-state solution to the Boltzmann equation, however, it is very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the…
In this article we introduce a novel coupled algorithm for massively parallel direct numerical simulations of electrophoresis in microfluidic flows. This multiphysics algorithm employs an Eulerian description of fluid and ions, combined…
In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on…
We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving…
We study the multi-dimensional properties of neutrino transfer inside supernova cores by solving the Boltzmann equations for neutrino distribution functions in genuinely six dimensional (6D) phase space. Adopting representative snapshots of…
We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses Pn and filtered Pn expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
In this paper, we propose an efficient method for solving multi-dimensional Riesz space fractional diffusion equations with variable coefficients. The Crank-Nicolson (CN) method is used for temporal discretization, while the fourth-order…
Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature. Existing solver-based acceleration methods often face significant image quality…
The linear Boltzmann model for proton beams is a six-dimensional partial differential equation (PDE). We propose a deterministic solver for the linear Boltzmann model based on scattering decomposition and depth-splitting methods. The main…
A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…
Modern supercomputers are increasingly requiring the presence of accelerators and co-processors. However, it has not been easy to achieve good performance on such heterogeneous clusters. The key challenge has been to ensure good load…
The problem of a spatially discontinuous diffusion coefficient ($D(\boldsymbol x)$) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow…