A Multiobjective Mesh Optimization Algorithm for Improving the Solution Accuracy of PDE Computations

2016 ◽  
Vol 13 (01) ◽  
pp. 1650002 ◽  
Author(s):  
Jibum Kim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimization Algorithm ◽  
Numerical Experiments ◽  
Optimization Algorithms ◽  
Mesh Optimization ◽  
Partial Differential ◽  
Solution Accuracy ◽  
Single Objective

Mesh qualities affect both the efficiency and accuracy for solving partial differential equations (PDEs). In this paper, we present a multiobjective mesh optimization algorithm, which improves the accuracy for solving PDEs. Our algorithm is designed to simultaneously improve more than two aspects of the mesh, while being able to successfully decrease errors for solving various PDEs. Numerical experiments show that our algorithm is able to significantly decrease errors compared with existing single objective mesh optimization algorithms.

Numerical and Experimental Analysis of the Nonlinear Dynamics due to Impacts of a Continuous Overhung Rotor

1997 ◽  
Author(s):  
Mohammed F. Abdul Azeez ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
The Other ◽  
Experimental Setup ◽  
Partial Differential ◽  
Qualitative Comparison ◽  
Set Up ◽  
Theory And Experiments

Abstract This work is aimed at obtaining the transient response of an overhung rotor when there are impacts occurring in the system. An overhung rotor clamped on one end, with a flywheel on the other and impacts occurring in between, due to a bearing with clearance, is considered. The system is modeled as a continuous rotor system and the governing partial differential equations are set up and solved. The method of assumed modes is used to discretize the system in order to solve the partial differential equations. Using this method numerical experiments are run and a few of the results are presented. The different numerical issues involved are also discussed. An experimental setup was built to run experiments and validate the results. Preliminary experimental observations are presented to show qualitative comparison of theory and experiments.

scholarly journals Identification of a Parameter in Fourth-Order Partial Differential Equations by an Equation Error Approach

2015 ◽  
Vol 65 (5) ◽  
Author(s):  
Nathan Bush ◽  
Baasansuren Jadamba ◽  
Akhtar A. Khan ◽  
Fabio Raciti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Short Note ◽  
Variable Parameter ◽  
Partial Differential ◽  
Convergence Results ◽  
Equation Error

AbstractThe objective of this short note is to employ an equation error approach to identify a variable parameter in fourth-order partial differential equations. Existence and convergence results are given for the optimization problem emerging from the equation error formulation. Finite element based numerical experiments show the effectiveness of the proposed framework.

scholarly journals Müntz sturm-liouville problems: Theory and numerical experiments

2021 ◽  
Vol 24 (3) ◽  
pp. 775-817
Author(s):  
Hassan Khosravian-Arab ◽  
Mohammad Reza Eslahchi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Bounds ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Recurrence Relations ◽  
Basis Functions ◽  
Partial Differential ◽  
Orthogonal Projections ◽  
Sturm Liouville

Abstract This paper presents two new classes of Müntz functions which are called Jacobi-Müntz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they have some spectral properties such as: orthogonality, completeness, three-term recurrence relations and so on. With respect to these functions two new orthogonal projections and their error bounds are derived. Also, two new Müntz type quadrature rules are introduced. As two applications of these basis functions some fractional ordinary and partial differential equations are considered and numerical results are given.

Stability for a competing system of hierarchical age-structured populations

2020 ◽  
Vol 13 (07) ◽  
pp. 2050070
Author(s):  
Ze-Rong He ◽  
Nan Zhou
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Structured Populations ◽  
Vital Rates ◽  
Partial Differential ◽  
Semigroup Method ◽  
Age Structured ◽  
The Stability

In this paper, we are concerned with the stability for a model in the form of system of integro-partial differential equations, which governs the evolution of two competing age-structured populations. The age-specified environment is incorporated in the vital rates, which displays the hierarchy of ages. By a non-zero fixed-point result, we show the existence of positive equilibria. Some conditions for the stability of steady states are derived by means of semigroup method. Furthermore, numerical experiments are also presented.

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