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A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space Dimensions

Anastasia-Dimitra Lipitakis
2016 Applied Mathematics  
A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising  ...  The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied.  ...  These adaptive exact and approximate inverse algorithmic techniques can be used for solving efficiently highly nonlinear large sparse systems arising in the numerical solution of complex computational  ... 
doi:10.4236/am.2016.711108 fatcat:vqf3zrfcebasbcsxc427h4e5lu

Page 2684 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
Gravvanis, A class of explicit precondi- tioned conjugate gradient methods for solving large finite element systems (255-272); Emanuele Galligani and Valeria Ruggiero, The arithmetic mean preconditioner  ...  Griewank, Approximate inverse preconditionings for sparse linear systems (141-160). G. Zilli, Iterative methods for solving sparse linear systems with a parallel preconditioner (161-169); Y.  ... 

Iterative solvers for BEM algebraic systems of equations

F.P. Valente, H.L.G. Pina
1998 Engineering analysis with boundary elements  
For tridimensional problems, with large scale systems (several thousand of equations) direct methods like Gauss elimination become too expensive and iterative methods may be preferable.  ...  A key issue in the Boundary Element Method is the solution of the associated system of algebraic equations. The matrices of this systems are dense and sometimes ill conditioned.  ...  Starting from (8) it is possible to augment this algorithm in order to get the Bi-Conjugate Gradient method for solving the system Ax_ -6, for general unsymmetric A. We have: For k=0,l,2,...  ... 
doi:10.1016/s0955-7997(98)00044-7 fatcat:2brlx4l65jamhomtwlj25elzii

Page 5570 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
A class of isomorphic it- erative schemes is presented which in conjunction with explicit preconditioned iterative methods can be efficiently used for solv- ing large sparse unsymmetric systems of algebraic  ...  (GR-ASEC-IF; Athens) Solving non-linear elliptic and parabolic difference equations by explicit preconditioned iterative methods based on sparse approximate inverses.  ... 

Page 5173 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
Summary: “This paper contains the main ideas for an AMGe (algebraic multigrid for finite elements) method based on element agglomeration.  ...  Summary: “The CGNR algorithm is a robust algorithm solving large nonsymmetric linear systems.  ... 

Page 443 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
The solution is approximated 65F Numerical linear algebra 96a:65052 by conforming finite elements. We design and analyze some multi- level methods for solving the resulting linear system.  ...  When the ad- ditive algorithms are used, an equivalent/preconditioned equation is solved by an iterative method such as the conjugate gradient method.  ... 

Page 3726 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
Summary: “The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsym- metric nonsingular matrix.  ...  Therefore the conjugate gradient method converges linearly when applied to solving the circulant preconditioned systems.  ... 

AMPS: A Real-time Mesh Cutting Algorithm for Surgical Simulations [article]

Yu-Hong Yeung, Alex Pothen, Jessica Crouch
2018 arXiv   pre-print
of finite element meshes.  ...  We present the AMPS algorithm, a finite element solution method that combines principal submatrix updates and Schur complement techniques, well-suited for interactive simulations of deformation and cutting  ...  Thus the scope of this paper does not include algorithms for simulation tasks other than solving the finite element system of equations.  ... 
arXiv:1811.00328v1 fatcat:q7fhmyl6ercjtlrhnuwnydfffe

Page 257 of American Society of Civil Engineers. Collected Journals Vol. 119, Issue 3 [page]

1993 American Society of Civil Engineers. Collected Journals  
The assembled system of equations were solved in parallel using a conjugate gradient algorithm for unsymmetric, nonpositive definite systems. Numer- ical studies were done on connection machine 2.  ...  For linear and nonlinear static anal- ysis, Newton-like methods with iterative and direct solvers and explicit dynamic relaxation algorithms were implemented on Intel’s iPSC 128, Cray- 2, and the connection  ... 

A three-dimensional explicit preconditioned solver

G.A. Gravvanis, E.A. Lipitakis
1996 Computers and Mathematics with Applications  
A class of explicit preconditioned conjugate gradient methods for solving large finite element systems, I. J. of Computer Mathematics 44, 189-206 (1992). 4. E.A. Lipitakis and D.J.  ...  The Explicit Preconditioned Generalized Conjugate Gradient Solver (EPGCGS) algorithm, a modified form of Sonneveld preconditioned CGS, cf. [3,8], for solving unsymmetric linear systems, Explicit Preconditioned  ... 
doi:10.1016/0898-1221(96)00108-3 fatcat:cqmx3jzfefcepkymbwymlz54vy

Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements

Sanna Mönkölä
2010 Journal of Computational and Applied Mathematics  
This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods.  ...  The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences.  ...  Timo Männikkö for useful advice and Dr. Janne Martikainen and MSc. Anssi Pennanen for providing the AMG solver.  ... 
doi:10.1016/j.cam.2009.08.040 fatcat:nb45dlm6uzaszgsazpvt3er7uq

Page 1172 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
Explicit preconditioned iterative methods, in conjunction with modified forms of the GAIM techniques, are presented for solving numeri- cally boundary value problems in three dimensions.  ...  The authors apply a Galerkin finite-element method for the spatial variable, a backward Euler-Galerkin difference quo- tient for the time variable and a certain iteration to propose a contractive recursive  ... 

On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning [article]

M. A. Sbai, A. Larabi
2020 arXiv   pre-print
Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems.  ...  The new solver was compared with traditional preconditioned iterative methods and direct sparse solvers on several two- and three-dimensional benchmark problems spanning homogeneous and heterogeneous formations  ...  A similar issue occurs for the conforming finite element method when applied to solute advection-dispersion transport problems.  ... 
arXiv:2001.05798v2 fatcat:tdjgydw2bvh5jf4wliogia5reu

Conjugate gradient type methods and preconditioning

Henk A. Van der Vorst, Kees Dekker
1988 Journal of Computational and Applied Mathematics  
In this paper we consider various iterative methods for the numerical solution of very large, sparse linear systems of equations, which arise in the discretization of partial differential equations.  ...  As the performance of the methods generally depends on the characteristics of the problems to be solved, a judicious choice between the methods will require knowledge about the system.  ...  Introduction In many situations iterative methods for the solution of large sparse linear systems may be preferred over direct methods, for one or more reasons: _ usually less memory requirements, _ often  ... 
doi:10.1016/0377-0427(88)90344-5 fatcat:wujdqj5dvnfg5jjtg3chscv4ge

A partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computers

Ahmed K. Noor, Jeanne M. Peters
1989 Computers & structures  
The top left sketch in figure 1 shows the original unsymmetric finite element model. On the other hand, for unsymmetric structures, the equations are coupled.  ...  vii Abstract A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems.  ...  A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems.  ... 
doi:10.1016/0045-7949(89)90214-9 fatcat:gfwiw53q6nhj7i3arq6s43wd2y
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