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In this work we present a multilayer shallow model to approximate the Navier-Stokes equations with hydrostatic pressure and the $\mu(I)$-rheology. The main advantages of this approximation are (i) the low cost associated with the numerical…

Mathematical Physics · Physics 2016-06-29 Enrique D. Fernández-Nieto , José Garres-Díaz , Anne Mangeney , Gladys Narbona-Reina

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

Numerical Analysis · Mathematics 2023-10-26 Fatemeh P. A. Beik , Michele Benzi

Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…

Numerical Analysis · Mathematics 2025-09-23 Sven Christophersen

Krylov subspace methods are widely known as efficient algebraic methods for solving large scale linear systems. However, on massively parallel hardware the performance of these methods is typically limited by communication latency rather…

Numerical Analysis · Computer Science 2018-08-22 Siegfried Cools

In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…

Numerical Analysis · Mathematics 2024-09-17 Alberto Bucci , Davide Palitta , Leonardo Robol

At physical light quark masses, efficient linear solvers are crucial for carrying out the millions of inversions of the Dirac matrix required for obtaining high statistics in quark correlation functions. Adaptive algebraic multi-grid…

High Energy Physics - Lattice · Physics 2022-01-12 Shuhei Yamamoto , Simone Bacchio , Jacob Finkenrath

This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully…

Numerical Analysis · Mathematics 2023-05-01 Amy de Castro , Hyesuk Lee , Margaret M. Wiecek

We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…

Numerical Analysis · Mathematics 2021-01-06 Daniela di Serafino , Dominique Orban

This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise…

Computational Engineering, Finance, and Science · Computer Science 2025-08-14 Joe Alexandersen , Magnus Appel

The rapid updates in error-resilient applications along with their quest for high throughput have motivated designing fast approximate functional units for Field-Programmable Gate Arrays (FPGAs). Studies that proposed imprecise functional…

Hardware Architecture · Computer Science 2022-06-29 Zahra Ebrahimi , Muhammad Zaid , Mark Wijtvliet , Akash Kumar

Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited…

We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…

Numerical Analysis · Mathematics 2025-10-30 Michael F. Herbst , Bonan Sun

We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…

Numerical Analysis · Mathematics 2023-07-19 Martina Bukac , Ivan Yotov , Rana Zakerzadeh , Paolo Zunino

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…

Numerical Analysis · Mathematics 2017-05-16 Clemens Hofreither , Stefan Takacs , Walter Zulehner

The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…

Numerical Analysis · Mathematics 2026-04-13 Shizhe Li , Li Zhao , Chen-Song Zhang

We consider the time-dependent Stokes-Darcy problem as a model case for the challenges involved in solving coupled systems. Keeping the model, its discretization, and the underlying numerics for the subproblems in the free-flow domain and…

Numerical Analysis · Mathematics 2021-08-31 Jenny Schmalfuss , Cedric Riethmüller , Mirco Altenbernd , Kilian Weishaupt , Dominik Göddeke

Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and…

Numerical Analysis · Mathematics 2022-06-13 Amy de Castro , Paul Kuberry , Irina Tezaur , Pavel Bochev

Dynamical low-rank (DLR) approximation has gained interest in recent years as a viable solution to the curse of dimensionality in the numerical solution of kinetic equations including the Boltzmann and Vlasov equations. These methods…

Numerical Analysis · Mathematics 2024-04-12 Jack Coughlin , Jingwei Hu , Uri Shumlak

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

Numerical Analysis · Mathematics 2018-05-08 Ali Karakus , Noel Chalmers , Kasia Swirydowicz , Timothy Warburton