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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…

Numerical Analysis · Mathematics 2026-05-05 Marco Feder , Pasquale Claudio Africa

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

Computational Engineering, Finance, and Science · Computer Science 2024-01-26 Kasia Świrydowicz , Nicholson Koukpaizan , Maksudul Alam , Shaked Regev , Michael Saunders , Slaven Peleš

We present a scalable block preconditioning strategy for the trace system coming from the high-order hybridized discontinuous Galerkin (HDG) discretization of incompressible resistive magnetohydrodynamics (MHD). We construct the block…

Numerical Analysis · Mathematics 2020-12-15 Sriramkrishnan Muralikrishnan , Stephen Shannon , Tan Bui-Thanh , John N. Shadid

In this paper, we consider the fast numerical solution of an optimal control formulation of the Keller--Segel model for bacterial chemotaxis. Upon discretization, this problem requires the solution of huge-scale saddle point systems to…

Numerical Analysis · Mathematics 2018-06-25 Sergey Dolgov , John W. Pearson

A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…

Computational Physics · Physics 2019-10-31 Jiequn Han , Chao Ma , Zheng Ma , Weinan E

We consider the use of multipreconditioning to solve linear systems when more than one preconditioner is available but the optimal choice is not known. In particular, we consider a selective multipreconditioned GMRES algorithm where we…

Numerical Analysis · Mathematics 2021-07-08 Niall Bootland , Andrew Wathen

In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the…

Computational Physics · Physics 2019-05-14 Matteo Franciolini , Lorenzo Botti , Alessandro Colombo , Andrea Crivellini

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

Numerical Analysis · Mathematics 2021-05-18 Jennifer A. Loe , Christian A. Glusa , Ichitaro Yamazaki , Erik G. Boman , Sivasankaran Rajamanickam

This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…

Computational Engineering, Finance, and Science · Computer Science 2018-08-24 Mario Arioli , Carola Kruse , Ulrich Ruede , Nicolas Tardieu

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

Numerical Analysis · Mathematics 2016-05-18 Kookjin Lee , Howard C. Elman

This paper expands on the TRANSP description given in Computer Physics Communications 312 (2025) 109611 by describing recent progress in TRANSP's predictive functionality and emphasizing the development of the PT_SOLVER module and…

The goal of this paper is to create a fruitful bridge between the numerical methods for approximating partial differential equations (PDEs) in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear…

Numerical Analysis · Mathematics 2016-12-15 M. Dumbser , F. Fambri , I. Furci , M. Mazza , M. Tavelli , S. Serra-Capizzano

Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…

Numerical Analysis · Mathematics 2022-09-13 Maria Vasilyeva , Alexey Sadovski , D. Palaniappan

The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…

Numerical Analysis · Mathematics 2021-02-03 Xiaoqiang Yue , Shulei Zhang , Xiaowen Xu , Shi Shu , Weidong Shi

Calculations of tearing mode stability in tokamaks split conveniently into an external region, where marginally stable ideal MHD is applicable, and a resonant layer around the rational surface where sophisticated kinetic physics is needed.…

Plasma Physics · Physics 2014-08-13 C J Ham , J W Connor , S C Cowley , R J Hastie , T C Hender , Y Q Liu

The relativistic magnetohydrodynamics (RMHD) set of equations has recently seen increased use in astrophysical computations. Even so, RMHD codes remain fragile. The reconstruction can sometimes yield superluminal velocities in certain parts…

High Energy Astrophysical Phenomena · Physics 2016-03-23 Dinshaw S. Balsara , Jinho Kim

A high-order piecewise field-aligned triangular finite element method is developed and implemented for global electromagnetic gyrokinetic particle-in-cell simulations of tokamak plasmas with open field lines. The approach combines locally…

In this paper, we present a high-order finite element method based on a reconstructed approximation to the biharmonic equation. In our construction, the space is reconstructed from nodal values by solving a local least squares fitting…

Numerical Analysis · Mathematics 2024-07-08 Ruo Li , Qicheng Liu , Fanyi Yang

We study a finite Larmor radius model used to describe the ions distributions in the core of a toka-mak plasma, that consist in a gyro-kinetic transport equation, coupled with an electro-neutrality equation. Since the last equation do not…

Analysis of PDEs · Mathematics 2013-05-10 Maxime Hauray , Anne Nouri

Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic…