Strategies for Preconditioning Methods of Parallel Iterative Solvers for Finite-Element Applications in Geophysics

2009 ◽  
pp. 65-106 ◽  
Author(s):  
Kengo Nakajima
Keyword(s):  
Finite Element ◽  
Iterative Solvers ◽  
Parallel Iterative

Parallel Iterative Solvers for Finite Element Analysis

2009 ◽  
Author(s):  
R. Valkenberg ◽  
G. Warzee ◽  
P. Saint-Georges ◽  
R. Beauwens ◽  
Y. Notay
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Iterative Solvers ◽  
Element Analysis ◽  
Parallel Iterative

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

Communication-Computation Overlapping for Preconditioned Parallel Iterative Solvers with Dynamic Loop Scheduling

2022 ◽  
Author(s):  
Kengo Nakajima ◽  
Balazs Gerofi ◽  
Masashi Horikoshi ◽  
Yutaka Ishikawa
Keyword(s):  
Iterative Solvers ◽  
Loop Scheduling ◽  
Parallel Iterative

Parallel iterative solvers for sparse linear systems in circuit simulation

2005 ◽  
Vol 21 (8) ◽  
pp. 1275-1284 ◽  
Author(s):  
A. Basermann ◽  
U. Jaekel ◽  
M. Nordhausen ◽  
K. Hachiya
Keyword(s):  
Linear Systems ◽  
Circuit Simulation ◽  
Iterative Solvers ◽  
Sparse Linear Systems ◽  
Parallel Iterative
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