scholarly journals APPLICATION OF CALCULATION REGION DECOMPOSITION IN SOLVING MAGNETOTELLURIC SOUNDING PROBLEMS

2021 ◽  
Vol 2 (2) ◽  
pp. 218-224
Author(s):  
Valery V. Plotkin
Keyword(s):  
Numerical Experiments ◽  
Decomposition Method ◽  
Magnetotelluric Sounding ◽  
Calculation Region ◽  
Direct Problems

Using numerical experiments, possibilities of application the decomposition method of the calculation region in solving direct problems of the magnetotelluric sounding are considered.

A Reliable Treatment for Solving Nonlinear Two-Point Boundary Value Problems

2007 ◽  
Vol 62 (9) ◽  
pp. 483-489
Author(s):  
Mustafa Inc
Keyword(s):  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Shooting Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Adomian Decomposition

In this paper, we study the modified decomposition method (MDM) for solving nonlinear twopoint boundary value problems (BVPs) and show numerical experiments. The modified form of the Adomian decomposition method which is more fast and accurate than the standard decomposition method (SDM) was introduced by Wazwaz. In addition, we will compare the performance of the MDM and the new nonlinear shooting method applied to the solutions of nonlinear two-point BVPs. The comparison shows that the MDM is reliable, efficient and easy for solving the nonlinear twopoint BVPs.

Equivalence of some direct problems of magnetotelluric sounding

1994 ◽  
Vol 5 (3) ◽  
pp. 220-223
Author(s):  
V. I. Dmitriev ◽  
N. A. Mershchikova ◽  
T. G. Pavlova
Keyword(s):  
Magnetotelluric Sounding ◽  
Direct Problems

scholarly journals Coupling Parareal with Non-Overlapping Domain Decomposition Method

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Rim GUETAT
Keyword(s):  
Domain Decomposition ◽  
Convergence Analysis ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Time Dependent ◽  
Interface Problem ◽  
Time Interval ◽  
Overlapping Domain Decomposition ◽  
Time Dependent Problems

In this paper, we present a new parallel algorithm for time dependent problems based on coupling parareal with non-overlapping domain decomposition method in order to increase parallelism in time and in space. For this we focus on the iterative methods of parallization in space to solve the interface problem like Neumann-Neumann method. In the new algorithm, the coarse temporel propagator is defined on the global domain and the Neumann-Neumann method is chosen as a fine propagator with a few iterations. We present the rigorous convergence analysis of the new coupled algorithm on bounded time interval. Numerical experiments illustrate the performance of this new algorithm and confirm our analysis. RÉSUMÉ. Dans ce papier, nous présentons un nouvel algorithme parallèle pour les problèmes dé-pendant du temps basé sur le couplage du pararéel avec les méthodes de décomposition de domaine sans recouvrement afin d'augmenter le parallélisme dans le temps et l'espace. Nous nous concen-trons sur les méthodes itératives de parallélisation en espace pour résoudre le problème d'interface par la méthode de Neumann-Neumann. Dans ce nouvel algorithme, le propagateur grossier est dé-finie sur le domaine global et la méthode de Neumann-Neumann est choisi pour le propagateur fin avec quelques itérations. Nous présentons l'analyse rigoureuse de convergence du nouvel algorithme couplé sur un intervalle de temps borné. Des expèriences numériques illustrent les performances de ce nouvel algorithme et confirment notre analyse. Dans ce papier, nous présentons un nouvel algorithme parallèle pour les problèmes dépendantdu temps basé sur le couplage du pararéel avec les méthodes de décomposition de domainesans recouvrement afin d’augmenter le parallélisme dans le temps et l’espace. Nous nous concentronssur les méthodes itératives de parallélisation en espace pour résoudre le problème d’interfacepar la méthode de Neumann-Neumann. Dans ce nouvel algorithme, le propagateur grossier est définiesur le domaine global et la méthode de Neumann-Neumann est choisi pour le propagateur finavec quelques itérations. Nous présentons l’analyse rigoureuse de convergence du nouvel algorithmecouplé sur un intervalle de temps borné. Des expèriences numériques illustrent les performances dece nouvel algorithme et confirment notre analyse.

scholarly journals Approximate analytical solution for 1-D problems of thermoelasticity with dirichlet condition

2019 ◽  
Vol 23 (1) ◽  
pp. 255-269
Author(s):  
Mariam Almazmumy ◽  
Huda Bakodah ◽  
Nawal Al-Zaid ◽  
Abdelhalim Ebaid ◽  
Randolph Rach
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problem ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Approximate Analytical Solution ◽  
Inverse Operator ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dirichlet Condition ◽  
Initial Boundary Value

This paper presents the solution of the initial boundary-value problem for the system of 1-D thermoelasticity using a new modified decomposition method that takes into accounts both initial and boundary conditions. The obtained solution is based on the generalized form of the inverse operator and is given in the form of a finite series. Also, some numerical experiments were presented to the both the effectiveness and the accuracy of the presented method.

scholarly journals Adomian Decomposition Method Combined with Padé Approximation and Laplace Transform for Solving a Model of HIV Infection of CD4+T Cells

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fang Chen ◽  
Qing-Quan Liu
Keyword(s):  
T Cells ◽  
Approximate Solution ◽  
Hiv Infection ◽  
Laplace Transform ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Pade Approximation ◽  
Adomian Decomposition

The classical Adomian decomposition method (ADM) is implemented to solve a model of HIV infection of CD4+T cells. The results indicate that the approximate solution by using the ADM is the same as that by using the Laplace ADM, but it can be obtained in a more efficient way. We also use Padé approximation and Laplace transform as a posttreatment technique to obtain the result of the ADM. The advantage of the posttreatment is illustrated by numerical experiments.

scholarly journals Training v-Support Vector Classifiers: Theory and Algorithms

2001 ◽  
Vol 13 (9) ◽  
pp. 2119-2147 ◽  
Author(s):  
Chih-Chung Chang ◽  
Chih-Jen Lin
Keyword(s):  
Support Vector Machine ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Large Scale ◽  
Optimal Solution ◽  
Solution Set ◽  
Support Vector ◽  
Support Vectors ◽  
Optimal Solution Set

The ν-support vector machine (ν-SVM) for classification proposed by Schölkopf, Smola, Williamson, and Bartlett (2000) has the advantage of using a parameter ν on controlling the number of support vectors. In this article, we investigate the relation between ν-SVM and C-SVM in detail. We show that in general they are two different problems with the same optimal solution set. Hence, we may expect that many numerical aspects of solving them are similar. However, compared to regular C-SVM, the formulation of ν-SVM is more complicated, so up to now there have been no effective methods for solving large-scale ν-SVM. We propose a decomposition method for ν-SVM that is competitive with existing methods for C-SVM. We also discuss the behavior of ν-SVM by some numerical experiments.

NUMERICAL EXPERIMENTS ON THE HYPERCHAOTIC CHEN SYSTEM BY THE ADOMIAN DECOMPOSITION METHOD

2008 ◽  
Vol 05 (03) ◽  
pp. 403-412 ◽  
Author(s):  
M. MOSSA AL-SAWALHA ◽  
M. S. M. NOORANI ◽  
I. HASHIM
Keyword(s):  
Numerical Experiments ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Dimensional System ◽  
Chen System ◽  
System A ◽  
Adomian Decomposition ◽  
Rossler System ◽  
Quadratic Nonlinearities ◽  
Rössler System

The aim of this paper is to investigate the accuracy of the Adomian decomposition method (ADM) for solving the hyperchaotic Chen system, which is a four-dimensional system of ODEs with quadratic nonlinearities. Comparisons between the decomposition solutions and the fourth order Runge–Kutta (RK4) solutions are made. We look particularly at the accuracy of the ADM as the hyperchaotic Chen system has higher Lyapunov exponents than the hyperchaotic Rössler system. A comparison with the hyperchaotic Rössler system is given.

The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations

2016 ◽  
Vol 19 (2) ◽  
pp. 411-441 ◽  
Author(s):  
Zhongguo Zhou ◽  
Dong Liang
Keyword(s):  
Domain Decomposition ◽  
Parabolic Equations ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Time Step ◽  
Unconditionally Stable ◽  
One Dimensional ◽  
Splitting Technique ◽  
Theoretical Results

AbstractIn the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in L2-norm. Numerical experiments confirm theoretical results.

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