Book Chapter10.1007/3-540-10694-4_37
A conjugate gradient iterative method
Prem K. Khosla,Stanley G. Rubin +1 more
32
TL;DR: In this paper, a strongly implicit pre-conditioned form of the conjugate gradient method is considered for sparse systems of difference equations arising from boundary value problems and the resulting iterative technique is used to solve two-and three-dimensional potential flows.
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About: This article is published in Computers & Fluids. The article was published on 01 Jun 1981. The article focuses on the topics: Conjugate gradient method & Conjugate residual method.
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Citations
Numerical simulation of the absolutely and convectively unstable wake
K. Hannemann,H. Oertel +1 more
TL;DR: In this paper, the authors compared the results of the Orr-Sommerfeld analysis with the results from a numerical wake simulation to determine the validity of the linear, local stability theory.
147
On the Application of the Generalized BiConjugate Gradient Method
TL;DR: In this paper, the generalized biconjugate gradient method was proposed to reduce the condition number of a non-Hermitian operator by preconditioning the distribution of the eigenvalues of the operator.
103
Natural convection in a cubical cavity heated from below at low rayleigh numbers
TL;DR: In this paper, the Boussinesq approximation has been used to model buoyancy effects on momentum transfer in a cubical cavity heated from below by means of the three-dimensional computation of the time dependent Navier-Stokes and energy transport equations in the range of Rayleigh numbers 3500 ⌽Ra ⩽ 10 000.
69
Progress in computational physics
TL;DR: In this article, recent progress in computational methods for time dependent fluid dynamics is presented with the emphasis on advances applicable to large scale systems with the connection between the numerics and the physics of the code stressed All aspects of a working code are discussed including initialization, boundary conditions, grid generation in addition to algorithmic advances.
47
Numerical solution of the steady incompressible Navier—Stokes equations for the flow past a sphere by a multigrid defect correction technique
Gh. Juncu,R. Mihail +1 more
TL;DR: A nested non-linear multigrid algorithm is developed to solve the Navier-Stokes equations which describe the steady incompressible flow past a sphere and a defect correction iteration is used as outer iteration.
46
References
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
•Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
- 01 Jun 1970
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
7.9K
A Rapidly Convergent Descent Method for Minimization
Roger Fletcher,M. J. D. Powell +1 more
TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.
A Class of Methods for Solving Nonlinear Simultaneous Equations
TL;DR: In this article, the authors discuss certain modifications to Newton's method designed to reduce the number of function evaluations required during the iterative solution process of an iterative problem solving problem, such that the most efficient process will be that which requires the smallest number of functions evaluations.
Solution of Sparse Indefinite Systems of Linear Equations
TL;DR: The method of conjugate gradients for solving systems of linear equations with a symmetric positive definite matrix A is given as a logical development of the Lanczos algorithm for tridiagonalizing...
1.8K