Abstract: Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.
Abstract: Modeling dam-break flows over non-flat beds requires
an accurate representation of the topography which is the main
source of uncertainty in the model. Therefore, developing robust
and accurate techniques for reconstructing topography in this class
of problems would reduce the uncertainty in the flow system. In
many hydraulic applications, experimental techniques have been
widely used to measure the bed topography. In practice, experimental
work in hydraulics may be very demanding in both time and cost.
Meanwhile, computational hydraulics have served as an alternative
for laboratory and field experiments. Unlike the forward problem,
the inverse problem is used to identify the bed parameters from the
given experimental data. In this case, the shallow water equations
used for modeling the hydraulics need to be rearranged in a way
that the model parameters can be evaluated from measured data.
However, this approach is not always possible and it suffers from
stability restrictions. In the present work, we propose an adaptive
optimal control technique to numerically identify the underlying bed
topography from a given set of free-surface observation data. In this
approach, a minimization function is defined to iteratively determine
the model parameters. The proposed technique can be interpreted
as a fractional-stage scheme. In the first stage, the forward problem
is solved to determine the measurable parameters from known data.
In the second stage, the adaptive control Ensemble Kalman Filter is
implemented to combine the optimality of observation data in order to
obtain the accurate estimation of the topography. The main features
of this method are on one hand, the ability to solve for different
complex geometries with no need for any rearrangements in the
original model to rewrite it in an explicit form. On the other hand, its
achievement of strong stability for simulations of flows in different
regimes containing shocks or discontinuities over any geometry.
Numerical results are presented for a dam-break flow problem over
non-flat bed using different solvers for the shallow water equations.
The robustness of the proposed method is investigated using different
numbers of loops, sensitivity parameters, initial samples and location
of observations. The obtained results demonstrate high reliability and
accuracy of the proposed techniques.
Abstract: In the case of the proposed method, the problem is
parallelized by considering multiple possible mode of operation
profiles, which determine the range in which the generators operate
in each period. For each of these profiles, the optimization is carried
out independently, and the best resulting dispatch is chosen. For each
such profile, the resulting problem is a quadratic programming (QP)
problem with a potentially negative definite Q quadratic term, and
constraints depending on the actual operation profile. In this paper we
analyze the performance of available MATLAB optimization methods
and solvers for the corresponding QP.
Abstract: The paper discusses the subinterval-based numerical
method for fractional derivative computations. It is now referred
to by its acronym – SubIval. The basis of the method is briefly
recalled. The ability of the method to be applied in time stepping
solvers is discussed. The possibility of implementing a time step size
adaptive solver is also mentioned. The solver is tested on a transient
circuit example. In order to display the accuracy of the solver –
the results have been compared with those obtained by means of a
semi-analytical method called gcdAlpha. The time step size adaptive
solver applying SubIval has been proven to be very accurate as
the results are very close to the referential solution. The solver is
currently able to solve FDE (fractional differential equations) with
various derivative orders for each equation and any type of source
time functions.
Abstract: The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.
Abstract: This paper presents an optimal duty-cycle modulation (ODCM) scheme for analog-to-digital conversion (ADC) systems. The overall ODCM-Based ADC problem is decoupled into optimal DCM and digital filtering sub-problems, while taking into account constraints of mutual design parameters between the two. Using a set of three lemmas and four morphological theorems, the ODCM sub-problem is modelled as a nonlinear cost function with nonlinear constraints. Then, a weighted least pth norm of the error between ideal and predicted frequency responses is used as a cost function for the digital filtering sub-problem. In addition, MATLAB fmincon and MATLAB iirlnorm tools are used as optimal DCM and least pth norm solvers respectively. Furthermore, the virtual simulation scheme of an overall prototyping ODCM-based ADC system is implemented and well tested with the help of Simulink tool according to relevant set of design data, i.e., 3 KHz of modulating bandwidth, 172 KHz of maximum modulation frequency and 25 MHZ of sampling frequency. Finally, the results obtained and presented show that the ODCM-based ADC achieves under 3 KHz of modulating bandwidth: 57 dBc of SINAD (signal-to-noise and distorsion), 58 dB of SFDR (Surpious free dynamic range) -80 dBc of THD (total harmonic distorsion), and 10 bits of minimum resolution. These performance levels appear to be a great challenge within the class of oversampling ADC topologies, with 2nd order IIR (infinite impulse response) decimation filter.
Abstract: The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.
Abstract: In this paper, we present the block generalized
minimal residual (BGMRES) method in order to solve the
generalized Sylvester matrix equation. However, this method may
not be converged in some problems. We construct a polynomial
preconditioner based on BGMRES which shows why polynomial
preconditioner is superior to some block solvers. Finally, numerical
experiments report the effectiveness of this method.
Abstract: Attempts to split the construct of emotional intelligence (EI) into separate components – ability to understand own and others’ emotions and ability to control own and others’ emotions may be meaningful more theoretically than practically. In real life, a personality encounters various emotional situations that require exhibition of complex EI to solve them. Emotional situation solution tests enable measurement of such undivided EI. The object of the present study is to determine sociodemographic and other factors that are important for emotional situation solutions. The study involved 1,430 participants from various regions of Lithuania. The age of participants varied from 17 years to 27 years. Emotional social and interpersonal situation scale EI-DARL-V2 was used. Each situation had two mandatory answering formats: The first format contained assignments associated with hypothetical theoretical knowledge of how the situation should be solved, while the second format included the question of how the participant would personally resolve the given situation in reality. A questionnaire that contained various sociodemographic data of subjects was also presented. Factors, statistically significant for emotional situation solution, have been determined: gender, family structure, the subject’s relation with his or her mother, mother’s occupation, subjectively assessed financial situation of the family, level of education of the subjects and his or her parents, academic achievement, etc. The best solvers of emotional situations are women with high academic achievements. According to their chosen study profile/acquired profession, they are related to the fields in social sciences and humanities. The worst solvers of emotional situations are men raised in foster homes. They are/were bad students and mostly choose blue-collar professions.
Abstract: The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.
Abstract: Singular value decomposition based optimisation of
geometric design parameters of a 5-speed gearbox is studied. During
the optimisation, a four-degree-of freedom torsional vibration model
of the pinion gear-wheel gear system is obtained and the minimum
singular value of the transfer matrix is considered as the objective
functions. The computational cost of the associated singular value
problems is quite low for the objective function, because it is only
necessary to compute the largest and smallest singular values (μmax
and μmin) that can be achieved by using selective eigenvalue solvers;
the other singular values are not needed. The design parameters are
optimised under several constraints that include bending stress,
contact stress and constant distance between gear centres. Thus, by
optimising the geometric parameters of the gearbox such as, the
module, number of teeth and face width it is possible to obtain a
light-weight-gearbox structure. It is concluded that the all optimised
geometric design parameters also satisfy all constraints.
Abstract: In order to study the aerodynamic performance of a
semi-flexible membrane wing, Fluid-Structure Interaction simulations
have been performed. The fluid problem has been modeled using
two different approaches which are the vortex panel method and the
numerical solution of the Navier-Stokes equations. Nonlinear analysis
of the structural problem is performed using the Finite Element
Method. Comparison between the two fluid solvers has been made.
Aerodynamic performance of the wing is discussed regarding its
lift and drag coefficients and they are compared with those of the
equivalent rigid wing.
Abstract: We have developed a new computer program in
Fortran 90, in order to obtain numerical solutions of a system
of Relativistic Magnetohydrodynamics partial differential equations
with predetermined gravitation (GRMHD), capable of simulating
the formation of relativistic jets from the accretion disk of matter
up to his ejection. Initially we carried out a study on numerical
methods of unidimensional Finite Volume, namely Lax-Friedrichs,
Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods
dependent on Riemann problems, applied to equations Euler in
order to verify their main features and make comparisons among
those methods. It was then implemented the method of Finite
Volume Centered of Nessyahu-Tadmor, a numerical schemes that
has a formulation free and without dimensional separation of
Riemann problem solvers, even in two or more spatial dimensions,
at this point, already applied in equations GRMHD. Finally, the
Nessyahu-Tadmor method was possible to obtain stable numerical
solutions - without spurious oscillations or excessive dissipation -
from the magnetized accretion disk process in rotation with respect
to a central black hole (BH) Schwarzschild and immersed in a
magnetosphere, for the ejection of matter in the form of jet over a
distance of fourteen times the radius of the BH, a record in terms
of astrophysical simulation of this kind. Also in our simulations,
we managed to get substructures jets. A great advantage obtained
was that, with the our code, we got simulate GRMHD equations in
a simple personal computer.
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: Transit route Network Design Problem (TrNDP) is the most important component in Transit planning, in which the overall cost of the public transportation system highly depends on it. The main purpose of this study is to develop a novel solution methodology for the TrNDP, which goes beyond pervious traditional sophisticated approaches. The novelty of the solution methodology, adopted in this paper, stands on the deterministic operators which are tackled to construct bus routes. The deterministic manner of the TrNDP solution relies on using linear and integer mathematical formulations that can be solved exactly with their standard solvers. The solution methodology has been tested through Mandl’s benchmark network problem. The test results showed that the methodology developed in this research is able to improve the given network solution in terms of number of constructed routes, direct transit service coverage, transfer directness and solution reliability. Although the set of routes resulted from the methodology would stand alone as a final efficient solution for TrNDP, it could be used as an initial solution for meta-heuristic procedures to approach global optimal. Based on the presented methodology, a more robust network optimization tool would be produced for public transportation planning purposes.
Abstract: For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach in order to make a solver quickly. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem. It is noted that our formal modeling language is not intend for providing an efficient notation for data mining application, but for facilitating a designer who develops solvers in machine learning.
Abstract: The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.
Abstract: We introduce an extended resource leveling model that abstracts real life projects that consider specific work ranges for each resource. Contrary to traditional resource leveling problems this model considers scarce resources and multiple objectives: the minimization of the project makespan and the leveling of each resource usage over time. We formulate this model as a multiobjective optimization problem and we propose a multiobjective genetic algorithm-based solver to optimize it. This solver consists in a two-stage process: a main stage where we obtain non-dominated solutions for all the objectives, and a postprocessing stage where we seek to specifically improve the resource leveling of these solutions. We propose an intelligent encoding for the solver that allows including domain specific knowledge in the solving mechanism. The chosen encoding proves to be effective to solve leveling problems with scarce resources and multiple objectives. The outcome of the proposed solvers represent optimized trade-offs (alternatives) that can be later evaluated by a decision maker, this multi-solution approach represents an advantage over the traditional single solution approach. We compare the proposed solver with state-of-art resource leveling methods and we report competitive and performing results.
Abstract: The purposes of this paper are to (1) promote
excellence in computer science by suggesting a cohesive innovative
approach to fill well documented deficiencies in current computer
science education, (2) justify (using the authors- and others anecdotal
evidence from both the classroom and the real world) why this
approach holds great potential to successfully eliminate the
deficiencies, (3) invite other professionals to join the authors in proof
of concept research. The authors- experiences, though anecdotal,
strongly suggest that a new approach involving visual modeling
technologies should allow computer science programs to retain a
greater percentage of prospective and declared majors as students
become more engaged learners, more successful problem-solvers,
and better prepared as programmers. In addition, the graduates of
such computer science programs will make greater contributions to
the profession as skilled problem-solvers. Instead of wearily
rememorizing code as they move to the next course, students will
have the problem-solving skills to think and work in more
sophisticated and creative ways.
Abstract: The MFCAV Riemann solver is practically used in many Lagrangian or ALE methods due to its merit of sharp shock profiles and rarefaction corners, though very often with numerical oscillations. By viewing it as a modification of the WWAM Riemann solver, we apply the MFCAV Riemann solver to the Lagrangian method recently developed by Maire. P. H et. al.. The numerical experiments show that the application is successful in that the shock profiles and rarefaction corners are sharpened compared with results obtained using other Riemann solvers. Though there are still numerical oscillations, they are within the range of the MFCAV applied in onther Lagrangian methods.