Abstract: In a previous work, we presented the numerical
solution of the two dimensional second order telegraph partial
differential equation discretized by the centred and rotated five-point
finite difference discretizations, namely the explicit group (EG) and
explicit decoupled group (EDG) iterative methods, respectively. In
this paper, we utilize a domain decomposition algorithm on these
group schemes to divide the tasks involved in solving the same
equation. The objective of this study is to describe the development
of the parallel group iterative schemes under OpenMP programming
environment as a way to reduce the computational costs of the
solution processes using multicore technologies. A detailed
performance analysis of the parallel implementations of points and
group iterative schemes will be reported and discussed.
Abstract: Modeling of a heterogeneous industrial fixed bed
reactor for selective dehydrogenation of heavy paraffin with Pt-Sn-
Al2O3 catalyst has been the subject of current study. By applying
mass balance, momentum balance for appropriate element of reactor
and using pressure drop, rate and deactivation equations, a detailed
model of the reactor has been obtained. Mass balance equations have
been written for five different components. In order to estimate
reactor production by the passage of time, the reactor model which is
a set of partial differential equations, ordinary differential equations
and algebraic equations has been solved numerically.
Paraffins, olefins, dienes, aromatics and hydrogen mole percent as
a function of time and reactor radius have been found by numerical
solution of the model. Results of model have been compared with
industrial reactor data at different operation times. The comparison
successfully confirms validity of proposed model.
Abstract: Based on the standard finite element method, a new
finite element method which is known as nonlocal finite element
method (NL-FEM) is numerically implemented in this article to
study the nonlocal effects for solving 1D nonlocal elastic problem.
An Eringen-type nonlocal elastic model is considered. In this model,
the constitutive stress-strain law is expressed interms of integral
equation which governs the nonlocal material behavior. The new
NL-FEM is adopted in such a way that the postulated nonlocal elastic
behavior of material is captured by a finite element endowed with a
set of (cross-stiffness) element itself by the other elements in mesh.
An example with their analytical solutions and the relevant numerical
findings for various load and boundary conditions are presented and
discussed in details. It is observed from the numerical solutions that
the torsional deformation angle decreases with increasing nonlocal
nanoscale parameter. It is also noted that the analytical solution fails
to capture the nonlocal effect in some cases where numerical
solutions handle those situation effectively which prove the
reliability and effectiveness of numerical techniques.
Abstract: As is known, one of the priority directions of research
works of natural sciences is introduction of applied section of
contemporary mathematics as approximate and numerical methods to
solving integral equation into practice. We fare with the solving of
integral equation while studying many phenomena of nature to whose
numerically solving by the methods of quadrature are mainly applied.
Taking into account some deficiency of methods of quadrature for
finding the solution of integral equation some sciences suggested of
the multistep methods with constant coefficients. Unlike these papers,
here we consider application of hybrid methods to the numerical
solution of Volterra integral equation. The efficiency of the suggested
method is proved and a concrete method with accuracy order p = 4
is constructed. This method in more precise than the corresponding
known methods.
Abstract: In this paper, different approaches to solve the
forward kinematics of a three DOF actuator redundant hydraulic
parallel manipulator are presented. On the contrary to series
manipulators, the forward kinematic map of parallel manipulators
involves highly coupled nonlinear equations, which are almost
impossible to solve analytically. The proposed methods are using
neural networks identification with different structures to solve the
problem. The accuracy of the results of each method is analyzed in
detail and the advantages and the disadvantages of them in
computing the forward kinematic map of the given mechanism is
discussed in detail. It is concluded that ANFIS presents the best
performance compared to MLP, RBF and PNN networks in this
particular application.