Results 41 to 50 of about 481 (184)

Chebyshev Smoothing With Adaptive Block‐FSAI Preconditioners for the Multilevel Solution of Higher‐Order Problems With the Partition of Unity Method

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT In this paper, we assess the performance of adaptive and nested factorized sparse approximate inverses as smoothers in multilevel V‐cycles, when smoothing is performed following the Chebyshev iteration of the fourth kind, for the efficient solution of linear systems arising from a conforming discretization of higher‐order partial differential ...
Pablo Jiménez Recio, Marc Alexander Schweitzer   +1 more
wiley   +1 more source

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

International Journal of Applied Mechanics and Engineering, 2018
The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order ...
F. De Oliveira, S.R. Franco, M.A. Villela Pinto   +2 more
doaj   +1 more source

An Augmented Lagrangian Preconditioner for Navier–Stokes Equations With Runge–Kutta in Time

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT We consider an implicit Runge–Kutta method for the numerical time integration of the nonstationary incompressible Navier–Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge–Kutta method. The resulting nonlinear system of differential equations is discretized using a finite element method.
Santolo Leveque, Yunhui He, Maxim Olshanskii   +2 more
wiley   +1 more source

Algebraic multigrid for the nonlinear powerflow equations

Numerical Linear Algebra with Applications, 2020
AbstractIn a recent article, one of the authors developed a multigrid technique for coarse‐graining dynamic powergrid models. A key component in this technique is a relaxation‐based coarsening of the graph Laplacian given by the powergrid network and its weighted graph, which is represented by the admittance matrix.
Barry Lee, Enrique Pereira Batista
openaire   +2 more sources

Monolithic Multi‐Level Overlapping Schwarz Preconditioners for Fluid Problems

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT Additive overlapping Schwarz methods are iterative methods of the domain decomposition type for the solution of partial differential equations. Numerical and parallel scalability of these methods can be achieved by adding coarse levels. A successful coarse space, inspired by iterative substructuring, is the generalized Dryja–Smith–Widlund ...
Stephan Köhler, Oliver Rheinbach
wiley   +1 more source

Algebraic analysis of aggregation-based multigrid [PDF]

Numerical Linear Algebra with Applications, 2010
Numerical solution of a system \(Ax=b\) is considered, where \(A\) is large, sparse, symmetric and positive definite. A two-grid scheme using an agglomeration of unknowns into pairwise disjoint sets is studied. In spite of the classical multigrid theory, the numbers of pre- and post-smoothing steps can be different.
Napov, Artem, Notay, Yvan
openaire   +2 more sources

A fast constrained image segmentation algorithm

Results in Applied Mathematics, 2020
Normalized cut or Ncut has been one of the most widely used models for image processing. A constraint can also be included in the framework of Ncut to represent a priori information for an effective image segmentation.
Iván Ojeda-Ruiz, Young-Ju Lee
doaj   +1 more source

A Hybrid a–φ Cell Method for Solving Eddy–Current Problems in 3–D Multiply–Connected Domains

IEEE Access, 2021
A hybrid $a - \varphi $ Cell Method formulation for solving eddy–current problems in 3–D multiply–connected regions is presented.
Federico Moro, Artem Napov, Lorenzo Codecasa   +2 more
doaj   +1 more source

Algebraic Multigrid Based Preconditioning Approaches for Generalized Continuum Models and Indirect Displacement Control Techniques

International Journal for Numerical Methods in Engineering, Volume 127, Issue 6, 30 March 2026.
ABSTRACT The contribution deals with algebraic multigrid (AMG) based preconditioning methods for the iterative solution of a coupled linear system of equations arising in numerical simulations of failure of quasi‐brittle materials using generalized continuum approaches.
Nasser Alkmim, Peter Gamnitzer, Alexander Dummer, Matthias Neuner, Günter Hofstetter   +4 more
wiley   +1 more source

Accelerating Conjugate Gradient Solvers for Homogenization Problems With Unitary Neural Operators

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous microstructures.
Julius Herb, Felix Fritzen
wiley   +1 more source