Related papers: On the use of Multigrid Preconditioners for Topolo…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
While Retrieval Augmented Generation (RAG) has emerged as a popular technique for improving Large Language Model (LLM) systems, it introduces a large number of choices, parameters and hyperparameters that must be made or tuned. This…
Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models…
Prefix adders are widely used in compute-intensive applications for their high speed. However, designing optimized prefix adders is challenging due to strict design rules and an exponentially large design space. We introduce PrefixGPT, a…
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
A well-known strategy for building effective preconditioners for higher-order discretizations of some PDEs, such as Poisson's equation, is to leverage effective preconditioners for their low-order analogs. In this work, we show that…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
Trimming is a ubiquitous operation in computer-aided-design whereby parts of a geometry are merged, intersected, or simply discarded. While it grants virtually unlimited flexibility in geometric design, it introduces a plethora of other…
Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most common methods of…
The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a Finite Element approximation to diffusion-dominated convection-diffusion equations. We consider a model setting in which the…
It is tested whether machine learning methods can be used for preconditioning to increase the performance of the linear solver -- the backbone of the semi-implicit, grid-point model approach for weather and climate models. Embedding the…
This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
As Grid computing is becoming an inevitable future, managing, scheduling and monitoring dynamic, heterogeneous resources will present new challenges. Solutions will have to be agile and adaptive, support self-organization and autonomous…
Despite tremendous progress in developing deep-learning-based weather forecasting systems, their design space, including the impact of different design choices, is yet to be well understood. This paper aims to fill this knowledge gap by…
This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of…
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…
We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial…
Lattice metamaterials enable lightweight, multifunctional structures, yet homogenization-based evaluation of their effective properties remains computationally expensive. Neural surrogates offer speed but often lack the accuracy and…
This paper provides a unified and detailed presentation of root-node style algebraic multigrid (AMG). Algebraic multigrid is a popular and effective iterative method for solving large, sparse linear systems that arise from discretizing…