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This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…

Fluid Dynamics · Physics 2026-04-17 Hangkong Wu , Yuze Zhu , Yajun Zhu , Kun Xu

The numerical modeling of fracture contact thermo-poromechanics is crucial for advancing subsurface engineering applications, including CO2 sequestration, production of geo-energy resources, energy storage and wastewater disposal…

Numerical Analysis · Mathematics 2025-10-14 Yury Zabegaev , Inga Berre , Eirik Keilegavlen

Interior point methods are widely used for different types of mathematical optimization problems. Many implementations of interior point methods in use today rely on direct linear solvers to solve systems of equations in each iteration. The…

Optimization and Control · Mathematics 2024-02-27 Felix Liu , Albin Fredriksson , Stefano Markidis

This paper presents an efficient Krylov subspace iterative solver for the three-dimensional (3D) Helmholtz equation with non-constant coefficients and absorbing boundary conditions, combining high-resolution compact schemes with low-order…

Numerical Analysis · Mathematics 2026-02-10 Yury Gryazin , Ron Gonzales , Xiaoye Sherry Li

We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…

Numerical Analysis · Mathematics 2026-01-29 Vit Dolejsi , Jakub Sistek

A Crank-Nicolson finite volume approximation for three-dimensional conservative space-fractional diffusion equation results in large and dense three-level Toeplitz discrete linear systems. Preconditioned Krylov subspace methods with sine…

Numerical Analysis · Mathematics 2026-03-19 Wei Qu , Siu-Long Lei , Sean Y. Hon , Yuan-Yuan Huang

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom…

Numerical Analysis · Mathematics 2023-07-06 Sander Rhebergen , Garth N. Wells

We introduce a robust and efficient preconditioner for a hybrid Newton-GMRES method for solving the nonlinear systems arising from incompressible Navier-Stokes equations. When the Reynolds number is relatively high, these systems often…

Computational Engineering, Finance, and Science · Computer Science 2021-08-16 Qiao Chen , Xiangmin Jiao , Oliver Yang

A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous collocation-based discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of the…

Numerical Analysis · Mathematics 2016-03-23 Sumedh M. Joshi , Greg N. Thomsen , Peter J. Diamessis

In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…

Computational Physics · Physics 2021-03-17 Tianbai Xiao , Martin Frank

A general methodology is proposed to differentiate the likelihood of energetic-particle-driven instabilities to produce frequency chirping or fixed-frequency oscillations. The method employs numerically calculated eigenstructures and…

A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…

Numerical Analysis · Mathematics 2022-05-25 Andrea Franceschini , Laura Gazzola , Massimiliano Ferronato

Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty…

Numerical Analysis · Mathematics 2021-10-07 Ben S. Southworth , Oliver Krzysik , Will Pazner , Hans De Sterck

This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the…

We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…

Numerical Analysis · Mathematics 2022-01-13 Jennifer A. Loe , Ronald B. Morgan

In this paper we study a monolithic Newton-Krylov solver with exact Jacobian for the solution of incompressible FSI problems. A main focus of this work is on the use of geometric multigrid preconditioners with modified Richardson smoothers…

Computational Physics · Physics 2017-09-19 Eugenio Aulisa , Simone Bna , Giorgio Bornia

The physical sciences require models tailored to specific nuances of different dynamics. In this work, we study outcome predictions in nuclear fusion tokamaks, where a major challenge are \textit{disruptions}, or the loss of plasma…

Plasma Physics · Physics 2024-01-02 Lucas Spangher , William Arnold , Alexander Spangher , Andrew Maris , Cristina Rea

Recent development of real-time equilibrium code Equinox [1] using a fixed-point algorithm [2] allow major plasma magnetic parameters to be identified in real-time, using rigorous analytical method. The code relies on the boundary flux code…

Plasma Physics · Physics 2007-05-23 Krzysztof Bosak , Jacques Blum , Emmanuel Joffrin

Quasilinear turbulent transport models are a successful tool for prediction of core tokamak plasma profiles in many regimes. Their success hinges on the reproduction of local nonlinear gyrokinetic fluxes. We focus on significant progress in…

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