Related papers: A structure preserving H-curl algebraic multigrid …
An algorithm for simulating self-gravitating cosmological astrophysical fluids is presented. The advantages include a large dynamic range, parallelizability, high resolution per grid element and fast execution speed. The code is based on a…
Self-stabilizing algorithms are an important because of their robustness and guaranteed convergence. Starting from any arbitrary state, a self-stabilizing algorithm is guaranteed to converge to a legitimate state.Those algorithms are not…
Hybrid beamforming architectures reduce hardware complexity but restrict access to full array observations, rendering direct implementation of classical covariance based methods such as minimum variance distortionless response (MVDR) and…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
Multigrid solvers are the standard in modern scientific computing simulations. Domain Decomposition Aggregation-Based Algebraic Multigrid, also known as the DD-$\alpha$AMG solver, is a successful realization of an algebraic multigrid solver…
We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…
Maximal ancestral graphs (MAGs) have many desirable properties; in particular they can fully describe conditional independences from directed acyclic graphs (DAGs) in the presence of latent and selection variables. However, different MAGs…
We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for the induction equation, analysing their ability to preserve the divergence free constraint of the magnetic…
Strength-of-connection algorithms play a key role in algebraic multigrid (AMG). Specifically, they determine which matrix nonzeros are classified as weak and so ignored when coarsening matrix graphs and defining interpolation sparsity…
This paper proposes a Riemannian adaptive optimization algorithm to optimize the parameters of deep neural networks. The algorithm is an extension of both AMSGrad in Euclidean space and RAMSGrad on a Riemannian manifold. The algorithm helps…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and…
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…
The partial reuse algebraic multigrid (AMG) setup cost amortization strategy is presented for the solution of non-steady state problems. The transfer operators are reused from the previous time steps, and the system matrices and the…
We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is based on the full…
Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points.…
We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with extremely high resolution. Our method utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids…
Evolutionary partial differential equations play a crucial role in many areas of science and engineering. Spatial discretization of these equations leads to a system of ordinary differential equations which can then be solved by numerical…