Abstract: Many problems in science and engineering field require
the solution of shifted linear systems with multiple right hand
sides and multiple shifts. To solve such systems efficiently, the
implicitly restarted global GMRES algorithm is extended in this
paper. However, the shift invariant property could no longer hold over
the augmented global Krylov subspace due to adding the harmonic
Ritz matrices. To remedy this situation, we enforce the collinearity
condition on the shifted system and propose shift implicitly restarted
global GMRES. The new method not only improves the convergence
but also has a potential to simultaneously compute approximate
solution for the shifted systems using only as many matrix vector
multiplications as the solution of the seed system requires. In
addition, some numerical experiments also confirm the effectiveness
of our method.
Abstract: In this paper, numerical solution of system of
Fredholm and Volterra integral equations by means of the Spline
collocation method is considered. This approximation reduces the
system of integral equations to an explicit system of algebraic
equations. The solution is collocated by cubic B-spline and the
integrand is approximated by the Newton-Cotes formula. The error
analysis of proposed numerical method is studied theoretically. The
results are compared with the results obtained by other methods to
illustrate the accuracy and the implementation of our method.
Abstract: An inversion-free iterative algorithm is presented for
solving nonlinear matrix equation with a stepsize parameter t. The
existence of the maximal solution is discussed in detail, and the
method for finding it is proposed. Finally, two numerical examples
are reported that show the efficiency of the method.
Abstract: Analysis of real life problems often results in linear
systems of equations for which solutions are sought. The method to
employ depends, to some extent, on the properties of the coefficient
matrix. It is not always feasible to solve linear systems of equations
by direct methods, as such the need to use an iterative method
becomes imperative. Before an iterative method can be employed
to solve a linear system of equations there must be a guaranty that
the process of solution will converge. This guaranty, which must
be determined apriori, involve the use of some criterion expressible
in terms of the entries of the coefficient matrix. It is, therefore,
logical that the convergence criterion should depend implicitly on the
algebraic structure of such a method. However, in deference to this
view is the practice of conducting convergence analysis for Gauss-
Seidel iteration on a criterion formulated based on the algebraic
structure of Jacobi iteration. To remedy this anomaly, the Gauss-
Seidel iteration was studied for its algebraic structure and contrary
to the usual assumption, it was discovered that some property of the
iteration matrix of Gauss-Seidel method is only diagonally dominant
in its first row while the other rows do not satisfy diagonal dominance.
With the aid of this structure we herein fashion out an improved
version of Gauss-Seidel iteration with the prospect of enhancing
convergence and robustness of the method. A numerical section is
included to demonstrate the validity of the theoretical results obtained
for the improved Gauss-Seidel method.
Abstract: An optimisation method using both global and local
optimisation is implemented to determine the flapping profile which
will produce the most lift for an experimental wing-actuation system.
The optimisation method is tested using a numerical quasi-steady
analysis. Results of an optimised flapping profile show a 20% increase
in lift generated as compared to flapping profiles obtained by high
speed cinematography of a Sympetrum frequens dragonfly. Initial
optimisation procedures showed 3166 objective function evaluations.
The global optimisation parameters - initial sample size and stage
one sample size, were altered to reduce the number of function
evaluations. Altering the stage one sample size had no significant
effect. It was found that reducing the initial sample size to 400
would allow a reduction in computational effort to approximately
1500 function evaluations without compromising the global solvers
ability to locate potential minima. To further reduce the optimisation
effort required, we increase the local solver’s convergence tolerance
criterion. An increase in the tolerance from 0.02N to 0.05N decreased
the number of function evaluations by another 20%. However, this
potentially reduces the maximum obtainable lift by up to 0.025N.
Abstract: This paper proposes a complementary combination scheme of affine projection algorithm (APA) filters with different order of input regressors. A convex combination provides an interesting way to keep the advantage of APA having different order of input regressors. Consequently, a novel APA which has the rapid convergence and the reduced steady-state error is derived. Experimental results show the good properties of the proposed algorithm.
Abstract: In this paper, a backward semi-Lagrangian scheme
combined with the second-order backward difference formula
is designed to calculate the numerical solutions of nonlinear
advection-diffusion equations. The primary aims of this paper are
to remove any iteration process and to get an efficient algorithm
with the convergence order of accuracy 2 in time. In order to achieve
these objects, we use the second-order central finite difference and the
B-spline approximations of degree 2 and 3 in order to approximate
the diffusion term and the spatial discretization, respectively. For the
temporal discretization, the second order backward difference formula
is applied. To calculate the numerical solution of the starting point
of the characteristic curves, we use the error correction methodology
developed by the authors recently. The proposed algorithm turns out
to be completely iteration free, which resolves the main weakness
of the conventional backward semi-Lagrangian method. Also, the
adaptability of the proposed method is indicated by numerical
simulations for Burgers’ equations. Throughout these numerical
simulations, it is shown that the numerical results is in good
agreement with the analytic solution and the present scheme offer
better accuracy in comparison with other existing numerical schemes.
Abstract: In recent years many finite elements have been
developed for plate bending analysis. The formulated elements are
based on the strain based approach. This approach leads to the
representation of the displacements by higher order polynomial terms
without the need for the introduction of additional internal and
unnecessary degrees of freedom. Good convergence can also be
obtained when the results are compared with those obtained from the
corresponding displacement based elements, having the same total
number of degrees of freedom. Furthermore, the plate bending
elements are free from any shear locking since they converge to the
Kirchhoff solution for thin plates contrarily for the corresponding
displacement based elements. In this paper the efficiency of the strain
based approach compared to well known displacement formulation is
presented. The results obtained by a new formulated plate bending
element based on the strain approach and Kirchhoff theory are
compared with some others elements. The good convergence of the
new formulated element is confirmed.
Abstract: DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so called terminal scheme to achieve finite time convergence. Lyapounov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.
Abstract: The aim of this work is to analyze a viscous flow
around the axisymmetric blunt body taken into account the mesh size
both in the free stream and into the boundary layer. The resolution of
the Navier-Stokes equations is realized by using the finite volume
method to determine the flow parameters and detached shock
position. The numerical technique uses the Flux Vector Splitting
method of Van Leer. Here, adequate time stepping parameter, CFL
coefficient and mesh size level are selected to ensure numerical
convergence. The effect of the mesh size is significant on the shear
stress and velocity profile. The best solution is obtained with using a
very fine grid. This study enabled us to confirm that the
determination of boundary layer thickness can be obtained only if the
size of the mesh is lower than a certain value limits given by our
calculations.
Abstract: In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.
Abstract: This paper describes a new efficient blind source separation method; in this method we uses a non-uniform filter bank and a new structure with different sub-bands. This method provides a reduced permutation and increased convergence speed comparing to the full-band algorithm. Recently, some structures have been suggested to deal with two problems: reducing permutation and increasing the speed of convergence of the adaptive algorithm for correlated input signals. The permutation problem is avoided with the use of adaptive filters of orders less than the full-band adaptive filter, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full-band, and can promote better rates of convergence.
Abstract: Flows developed between two parallel disks have
many engineering applications. Two types of non-swirling flows can
be generated in such a domain. One is purely source flow in disc type
domain (outward flow). Other is purely sink flow in disc type domain
(inward flow). This situation often appears in some turbo machinery
components such as air bearings, heat exchanger, radial diffuser,
vortex gyroscope, disc valves, and viscosity meters. The main goal of
this paper is to show the mesh convergence, because mesh
convergence saves time, and economical to run and increase the
efficiency of modeling for both sink and source flow. Then flow field
is resolved using a very fine mesh near-wall, using enhanced wall
treatment. After that we are going to compare this flow using
standard k-epsilon, RNG k-epsilon turbulence models. Lastly
compare some experimental data with numerical solution for sink
flow. The good agreement of numerical solution with the
experimental works validates the current modeling.
Abstract: In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.
Abstract: In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.
Abstract: By the real representation of the quaternionic matrix,
an iterative method for quaternionic linear equations Ax = b is
proposed. Then the convergence conditions are obtained. At last, a
numerical example is given to illustrate the efficiency of this method.
Abstract: This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.
Abstract: This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of 3-trailer systems in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. The effectiveness of the proposed control laws were demonstrated via simulations of two traffic scenarios.
Abstract: In this communication, we have made an attempt to design multiplier-less low-pass finite impulse response (FIR) filter with the aid of various mutation strategies of Differential Evolution (DE) algorithm. Impulse response coefficient of the designed FIR filter has been represented as sums or differences of powers of two. Performance of the proposed filter has been evaluated in terms of its frequency response and associated hardware cost. Supremacy of our approach has been substantiated by comparing our result with many of the existing multiplier-less filter design algorithms of recent interest. It has also been demonstrated that DE-optimized filter outperforms Genetic Algorithm (GA) based design by a large margin. Hardware efficiency of our algorithm has further been validated by implementing those filters on a Field Programmable Gate Array (FPGA) chip.
Abstract: Non-negative matrix factorization (NMF) is a useful computational method to find basis information of multivariate nonnegative data. A popular approach to solve the NMF problem is the multiplicative update (MU) algorithm. But, it has some defects. So the columnwisely alternating gradient (cAG) algorithm was proposed. In this paper, we analyze convergence of the cAG algorithm and show advantages over the MU algorithm. The stability of the equilibrium point is used to prove the convergence of the cAG algorithm. A classic model is used to obtain the equilibrium point and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the cAG algorithm are obtained, which help reducing the evaluation time and is confirmed in the experiments. By using the same method, the MU algorithm has zero divisor and is convergent at zero has been verified. In addition, the convergence conditions of the MU algorithm at zero are similar to that of the cAG algorithm at non-zero. However, it is meaningless to discuss the convergence at zero, which is not always the result that we want for NMF. Thus, we theoretically illustrate the advantages of the cAG algorithm.