Related papers: Coarsening in Algebraic Multigrid using Gaussian P…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…
Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of…
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.…
Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian…
A graph based matching is used to construct aggregation for algebraic multigrid. Effects of inexact coarse grid solve is analyzed numerically for a highly discontinuous convection diffusion coefficient matrix and problems from Florida…
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…
An efficient $hp$-multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the underlying discrete gradient and divergence operators. We…
We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…
Multiscale modeling is a systematic approach to describe the behavior of complex systems by coupling models from different scales. The approach has been demonstrated to be very effective in areas of science as diverse as materials science,…
In this paper, we develop a new parallel auxiliary grid algebraic multigrid (AMG) method to leverage the power of graphic processing units (GPUs). In the construction of the hierarchical coarse grid, we use a simple and fixed coarsening…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
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…
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…