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We propose a GPU-based iterative method for accelerated elastodynamic simulation with the log-barrier-based contact model. While Newton's method is a conventional choice for solving the interior-point system, the presence of ill-conditioned…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-04-14 Dewen Guo , Minchen Li , Yin Yang , Guoping Wang , Sheng Li

This paper focuses on developing a reduction-based algebraic multigrid method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a…

Numerical Analysis · Mathematics 2024-05-16 Ahsan Ali , James Brannick , Karsten Kahl , Oliver A. Krzysik , Jacob B. Schroder , Ben S. Southworth

In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proximal gradient methods, the…

Information Theory · Computer Science 2025-04-03 Xilai Fan , Bo Jiang , Ya-Feng Liu

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…

Numerical Analysis · Mathematics 2019-03-04 Ben S. Southworth , Thomas A. Manteuffel , John Ruge

We present a globally convergent method for the solution of frictionless large deformation contact problems for hyperelastic materials. The discretisation uses the mortar method which is known to be more stable than node-to-segment…

Numerical Analysis · Mathematics 2017-08-07 Jonathan Youett , Oliver Sander , Ralf Kornhuber

We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces…

Numerical Analysis · Mathematics 2020-10-15 Socratis Petrides , Leszek Demkowicz

This article is concerned with the question of constructing effcient multigrid preconditioners for the linear systems arising when applying semismooth Newton methods to large-scale linear-quadratic optimization problems constrained by…

Numerical Analysis · Mathematics 2013-11-08 Andrei Draganescu

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

Numerical Analysis · Mathematics 2025-06-18 Matteo Caldana , Paola F. Antonietti , Luca Dede'

We develop a reduction multigrid based on approximate ideal restriction (AIR) for use with asymmetric linear systems. We use fixed-order GMRES polynomials to approximate $A_\textrm{ff}^{-1}$ and we use these polynomials to build grid…

Computational Physics · Physics 2023-06-12 S. Dargaville , R. P. Smedley-Stevenson , P. N. Smith , C. C. Pain

In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…

Numerical Analysis · Mathematics 2023-01-19 Nam G. Luu , Thanh T. Banh

The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…

Numerical Analysis · Computer Science 2009-09-30 G. Haikal

Large linear systems with sparse, non-symmetric matrices arise in the modeling of Markov chains or in the discretization of convection-diffusion problems. Due to their potential to solve sparse linear systems with an effort that is linear…

Numerical Analysis · Mathematics 2023-08-17 Benjamin Seibold

In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To…

Optimization and Control · Mathematics 2020-08-11 L. Failer , T. Richter

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2020-03-19 Agniva Chowdhury , Palma London , Haim Avron , Petros Drineas

An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…

Optimization and Control · Mathematics 2016-06-21 Michal Kocvara , Sudaba Mohammed

In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. The mortar finite element method is usually employed to…

Numerical Analysis · Mathematics 2024-09-24 Xiaoyu Duan , Hengbin An , Zeyao Mo

The accuracy and efficiency of a coarse-grained (CG) force field are pivotal for high-precision molecular simulations of large systems with complex molecules. We present an automated mapping and optimization framework for molecular…

Computational Physics · Physics 2024-08-14 Zhixuan Zhong , Lifeng Xu , Jian Jiang

In this work, the matrix-free solution of quasi-static phase-field fracture problems is further investigated. More specifically, we consider a quasi-monolithic formulation in which the irreversibility constraint is imposed with a…

Numerical Analysis · Mathematics 2024-08-27 Leon Maximilian Kolditz , Thomas Wick

Problems arising in Earth's mantle convection involve finding the solution to Stokes systems with large viscosity contrasts. These systems contain localized features which, even with adaptive mesh refinement, result in linear systems that…

Numerical Analysis · Mathematics 2020-08-20 Thomas C. Clevenger , Timo Heister

Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…

Numerical Analysis · Mathematics 2026-01-01 Paola F. Antonietti , Matteo Caldana , Lorenzo Gentile , Marco Verani