Stability and Convergence of Iterative Solvers

2016 ◽  
pp. 169-218
Author(s):  
Sandip Mazumder
Keyword(s):  
Iterative Solvers ◽  
Stability And Convergence

An Out-of-Core Dataflow Middleware to Reduce the Cost of Large Scale Iterative Solvers

2012 ◽  
Author(s):  
Zheng Zhou ◽  
Erik Saule ◽  
Hasan Metin Aktulga ◽  
Chao Yang ◽  
Esmond G. Ng ◽  
...  
Keyword(s):  
Large Scale ◽  
Iterative Solvers ◽  
The Cost

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.

scholarly journals An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed Al-Smadi ◽  
Nadir Djeddi ◽  
Shaher Momani ◽  
Shrideh Al-Omari ◽  
Serkan Araci
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Reproducing Kernel ◽  
Numerical Approach ◽  
Accurate Solution ◽  
Stability And Convergence ◽  
Type Model ◽  
Schmidt Orthogonalization ◽  
And Performance ◽  
Abel Differential Equation

AbstractOur aim in this paper is presenting an attractive numerical approach giving an accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed with a Caputo–Fabrizio fractional derivative. By means of such an approach, we utilize the Gram–Schmidt orthogonalization process to create an orthonormal set of bases that leads to an appropriate solution in the Hilbert space $\mathcal{H}^{2}[a,b]$ H 2 [ a , b ] . We investigate and discuss stability and convergence of the proposed method. The n-term series solution converges uniformly to the analytic solution. We present several numerical examples of potential interests to illustrate the reliability, efficacy, and performance of the method under the influence of the Caputo–Fabrizio derivative. The gained results have shown superiority of the reproducing kernel algorithm and its infinite accuracy with a least time and efforts in solving the fractional Abel-type model. Therefore, in this direction, the proposed algorithm is an alternative and systematic tool for analyzing the behavior of many nonlinear temporal fractional differential equations emerging in the fields of engineering, physics, and sciences.

scholarly journals Entropy Generation Analysis and Radiated Heat Transfer in MHD (Al2O3-Cu/Water) Hybrid Nanofluid Flow

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 887
Author(s):  
Nabeela Parveen ◽  
Muhammad Awais ◽  
Saeed Ehsan Awan ◽  
Wasim Ullah Khan ◽  
Yigang He ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Entropy Generation ◽  
Magnetic Induction ◽  
Axisymmetric Flow ◽  
Computational Method ◽  
Stability And Convergence ◽  
Hybrid Nanofluid ◽  
Physical Factors ◽  
Induction Effect ◽  
Entropy Generation Number

This research concerns the heat transfer and entropy generation analysis in the MHD axisymmetric flow of Al2O3-Cu/H2O hybrid nanofluid. The magnetic induction effect is considered for large magnetic Reynolds number. The influences of thermal radiations, viscous dissipation and convective temperature conditions over flow are studied. The problem is modeled using boundary layer theory, Maxwell’s equations and Fourier’s conduction law along with defined physical factors. Similarity transformations are utilized for model simplification which is analytically solved with the homotopy analysis method. The h-curves upto 20th order for solutions establishes the stability and convergence of the adopted computational method. Rheological impacts of involved parameters on flow variables and entropy generation number are demonstrated via graphs and tables. The study reveals that entropy in system of hybrid nanofluid affected by magnetic induction declines for [...]

scholarly journals High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations

2021 ◽  
Author(s):  
Giacomo Albi ◽  
Lorenzo Pareschi
Keyword(s):  
Multistep Methods ◽  
General Setting ◽  
Reaction Diffusion ◽  
Strong Stability ◽  
High Order ◽  
Iterative Solvers ◽  
Time Dependent ◽  
Linear Multistep Methods ◽  
Advection Diffusion Equation ◽  
Separation Of Scales

AbstractWe consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino et al. (J. Sci. Comput. 68: 975–1001, 2016) for Runge-Kutta methods, these semi-implicit techniques give a great flexibility, and allow, in many cases, the construction of simple linearly implicit schemes with no need of iterative solvers. In this work, we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype linear advection-diffusion equation and in the setting of strong stability preserving (SSP) methods. Our findings are demonstrated on several examples, including nonlinear reaction-diffusion and convection-diffusion problems.

scholarly journals A Hybridization of Dragonfly Algorithm Optimization and Angle Modulation Mechanism for 0-1 Knapsack Problems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 598
Author(s):  
Lin Wang ◽  
Ronghua Shi ◽  
Jian Dong
Keyword(s):  
Vertical Displacement ◽  
Continuous Functions ◽  
Convergence Speed ◽  
Knapsack Problems ◽  
Stability And Convergence ◽  
Algorithm Optimization ◽  
Solution Quality ◽  
Dragonfly Algorithm ◽  
Algorithm Stability ◽  
Angle Modulation

The dragonfly algorithm (DA) is a new intelligent algorithm based on the theory of dragonfly foraging and evading predators. DA exhibits excellent performance in solving multimodal continuous functions and engineering problems. To make this algorithm work in the binary space, this paper introduces an angle modulation mechanism on DA (called AMDA) to generate bit strings, that is, to give alternative solutions to binary problems, and uses DA to optimize the coefficients of the trigonometric function. Further, to improve the algorithm stability and convergence speed, an improved AMDA, called IAMDA, is proposed by adding one more coefficient to adjust the vertical displacement of the cosine part of the original generating function. To test the performance of IAMDA and AMDA, 12 zero-one knapsack problems are considered along with 13 classic benchmark functions. Experimental results prove that IAMDA has a superior convergence speed and solution quality as compared to other algorithms.

scholarly journals Randomized Runge–Kutta method — Stability and convergence under inexact information

2021 ◽  
pp. 101554
Author(s):  
Tomasz Bochacik ◽  
Maciej Goćwin ◽  
Paweł M. Morkisz ◽  
Paweł Przybyłowicz
Keyword(s):  
Stability And Convergence ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Inexact Information ◽  
Runge Kutta

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

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