Related papers: Partial Reuse AMG Setup Cost Amortization Strategy…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain $\Omega$. Firstly, a fully…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
This paper introduces bootstrap multigrid methods for solving eigenvalue problems arising from the discretization of partial differential equations. Inspired by the full bootstrap algebraic multigrid (BAMG) setup algorithm that includes an…
Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process. Distributed and asynchronous variants of gradient descent have been…
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…
In this paper we develop a new technique, called \textit{state redistribution}, that allows the use of explicit time stepping when approximating solutions to hyperbolic conservation laws on embedded boundary grids. State redistribution is a…
Iterative majorize-minimize (MM) (also called optimization transfer) algorithms solve challenging numerical optimization problems by solving a series of "easier" optimization problems that are constructed to guarantee monotonic descent of…
Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric…
When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
Algebraic Multigrid (AMG) is one of the most used iterative algorithms for solving large sparse linear equations $Ax=b$. In AMG, the coarse grid is a key component that affects the efficiency of the algorithm, the construction of which…
In structurally constrained molecular optimization, state-of-the-art methods restart an expensive oracle-driven search from scratch for every new input structure, scaling poorly to settings with many starting structures or expensive…
A novel approach is presented to recover an image degraded by atmospheric turbulence. Given a sequence of frames affected by turbulence, we construct a variational model to characterize the static image. The optimization problem is solved…
Across infrastructure domains, physical damage caused by storms and other weather events often requires costly and time-sensitive repairs to restore services as quickly as possible. While recent studies have used agent-based models to…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…