Efficient Integration Techniques Research Articles

Abundant solitary wave solutions of Gardner's equation using three effective integration techniques

<abstract><p>Gardner's equation has been discussed in the article for finding new solitary wave solutions. Three efficient integration techniques, namely, the Kudryashov's <italic>R</italic> function method, the generalized projective Ricatti method and $ \frac{G'}{G^2} $-expansion method are implemented to obtain new dark soliton, bright soliton, singular soliton, and combo soliton solutions. Moreover, some of the obtained solutions are graphically depicted by using $ 3 $D-surface plots and the corresponding $ 2 $D-contour graphs.</p></abstract>

Adaptive Stepsize Control for Extrapolation Semi-Implicit Multistep ODE Solvers

Developing new and efficient numerical integration techniques is of great importance in applied mathematics and computer science. Among the variety of available methods, multistep ODE solvers are broadly used in simulation software. Recently, semi-implicit integration proved to be an efficient compromise between implicit and explicit ODE solvers, and multiple high-performance semi-implicit methods were proposed. However, the computational efficiency of any ODE solver can be significantly increased through the introduction of an adaptive integration stepsize, but it requires the estimation of local truncation error. It is known that recently proposed extrapolation semi-implicit multistep methods (ESIMM) cannot operate with existing local truncation error (LTE) estimators, e.g., embedded methods approach, due to their specific right-hand side calculation algorithm. In this paper, we propose two different techniques for local truncation error estimation and study the performance of ESIMM methods with adaptive stepsize control. The first considered approach is based on two parallel semi-implicit solutions with different commutation orders. The second estimator, called the “double extrapolation” method, is a modification of the embedded method approach. The introduction of the double extrapolation LTE estimator allowed us to additionally increase the precision of the ESIMM solver. Using several known nonlinear systems, including stiff van der Pol oscillator, as the testbench, we explicitly show that ESIMM solvers can outperform both implicit and explicit linear multistep methods when implemented with an adaptive stepsize.

An Efficient Coupled-Perturbed Kohn-Sham Implementation of NMR Chemical Shift Computations with Local Hybrid Functionals and Gauge-Including Atomic Orbitals.

Nuclear shielding calculations for local hybrid (LH) functionals with position-dependent exact-exchange admixtures within a coupled-perturbed Kohn-Sham (CPKS) framework have been implemented into the Turbomole code using efficient seminumerical integration techniques to deal with two-electron integrals. When using gauge-including atomic orbitals, LHs generate additional terms within the "pre-loop" section of the CPKS scheme compared to global hybrid (GH) functionals, related to perturbed electron-repulsion integrals. These terms have been implemented and tested in detail, together with dependencies on grid sizes and integral screening procedures. Even with relatively small grids, a seminumerical treatment of GHs reproduces analytical GH results with high accuracy while improving scaling with system and basis-set sizes significantly. The extra terms generated by LHs in the pre-loop part increase the scaling of that contribution slightly, but the advantages compared to the analytical scheme are largely retained, in particular for the typically large basis sets used in NMR shift calculations, allowing for a very efficient computational scheme. An initial comparison of four first-generation LHs based on LDA exchange for a shielding test set of 15 small main-group molecules against high-level CCSD(T) benchmark data indicates a substantial reduction of the systematically underestimated shieldings compared to semilocal functionals or GHs for non-hydrogen nuclei when a so-called t-LMF is used to control the position dependence of the exact-exchange admixture. In contrast, proton shieldings are underestimated with this LMF, while an LH with a so-called s-LMF performs much better. These results are discussed in the context of experience for other properties, and they suggest directions for further improvements of LHs regarding nuclear shieldings.

Understanding dynamic data interaction between civil integrated management technologies: a review of use cases and enabling techniques

Civil integrated management (CIM) has emerged as an advanced paradigm to transform transportation project delivery and asset management from a paper-based to a digital data-based approach. CIM is associated with the use of computerized technologies (e.g. three-dimensional models, geographical information systems, and light detection and ranging) for data collection, organization, and utilization in across project stages from design, construction, to operation and maintenance. This change results in an increasing amount of digital data exchange between relevant tools. CIM is a new concept, and a comprehensive understanding of the data flow among CIM tools is still lacking. This article aims to investigate the data interaction between CIM technologies through an in-depth review of recently published academic articles. A critical review was conducted focusing on identifying use cases of data interaction and existing methods enabling the data communication between CIM technologies. The study found nine pairs of tools that have a strong data relationship. The study also revealed a shortcoming of efficient data extraction and integration techniques to support seamless data workflows. The research is original, being the first examination of the data interaction between CIM technologies. The findings from this research are expected to enhance awareness among researchers and professionals about the value of the data generated by each CIM technology and the state-of-the-art on supporting methods for connecting proprietary tools.

Analysis of Mathematical Techniques for the Calculation of the Electrostatic Field in a Dielectric-Loaded Waveguide

The resolution of the Green's function for obtaining the electrostatic potential generated by the charges located in the dielectric layer of a rectangular wave-guide requires efficient integration techniques. Due to the characteristics and the oscillatory nature of the function to be integrated, the use of the Filon's method together with a convergence analysis is adequate. However, the application of this numerical integration technique can lead to numerical instabilities in the result. For this reason, in this research work we have presented two different methods to deal with these numerical errors of integration: SSA/MSSA and GPR. In this way it is possible to clean the electrostatic potential avoiding subsequent errors in the calculation of the electrostatic field.

Development of a modularized two-step (M2S) chromosome integration technique for integration of multiple transcription units in Saccharomyces cerevisiae.

Background Saccharomyces cerevisiae has already been used for heterologous production of fuel chemicals and valuable natural products. The establishment of complicated heterologous biosynthetic pathways in S. cerevisiae became the research focus of Synthetic Biology and Metabolic Engineering. Thus, simple and efficient genomic integration techniques of large number of transcription units are demanded urgently.ResultsAn efficient DNA assembly and chromosomal integration method was created by combining homologous recombination (HR) in S. cerevisiae and Golden Gate DNA assembly method, designated as modularized two-step (M2S) technique. Two major assembly steps are performed consecutively to integrate multiple transcription units simultaneously. In Step 1, Modularized scaffold containing a head-to-head promoter module and a pair of terminators was assembled with two genes. Thus, two transcription units were assembled with Golden Gate method into one scaffold in one reaction. In Step 2, the two transcription units were mixed with modules of selective markers and integration sites and transformed into S. cerevisiae for assembly and integration. In both steps, universal primers were designed for identification of correct clones. Establishment of a functional β-carotene biosynthetic pathway in S. cerevisiae within 5 days demonstrated high efficiency of this method, and a 10-transcriptional-unit pathway integration illustrated the capacity of this method.ConclusionsModular design of transcription units and integration elements simplified assembly and integration procedure, and eliminated frequent designing and synthesis of DNA fragments in previous methods. Also, by assembling most parts in Step 1 in vitro, the number of DNA cassettes for homologous integration in Step 2 was significantly reduced. Thus, high assembly efficiency, high integration capacity, and low error rate were achieved.Electronic supplementary materialThe online version of this article (doi:10.1186/s13068-016-0645-4) contains supplementary material, which is available to authorized users.

Feast Eigensolver for Non-Hermitian Problems

A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue problems is presented and thoroughly discussed. It aims at broadening the class of eigenproblems that can be addressed within the framework of the FEAST algorithm. The algorithm is ideally suited for computing selected interior eigenvalues and their associated right/left biorthogonal eigenvectors located within a subset of the complex plane. It combines subspace iteration with efficient contour integration techniques that approximate the left and right spectral projectors. We discuss the various algorithmic choices that have been made to improve the stability and usability of the new non-Hermitian eigensolver. The latter retains the convergence property and multilevel parallelism of Hermitian FEAST, making it a valuable new software tool for the scientific community.

Efficient Recursive Dynamics and Real Time Simulation of Flexible Space Robots System

As space robots gain more and more importance in space operations, it was becoming imperative to understand their distinctive dynamics. The dynamics model of the space flexible robots is very complex, and the differential equation derived from dynamics was solved difficultly and slowly. In this paper the efficient recursive O(n) dynamics algorithm of space flexible robots systems with rigid base and flexible manipulators was discussed, and the fast efficient integration method was used to solve this dynamics equation for real time simulation. Simulations results show that the dynamic modeling and fast efficient numerical integration techniques of flexible space robot proposed in this paper are very useful. Keyword: space robots;efficient dynamic; recursive; real time simulation

Preface for the thematic issue

The Euromech Colloquium 524 on multibody system modeling, control and simulation for engineering design took place at the University of Twente, The Netherlands, on February 27–29, 2012. There were 41 participants from 9 European countries and 1 non-European country. The Colloquium was devoted to multibody system dynamics with regard to engineering design principles, modeling for design and simulation. A broad variety of engineering applications have been presented from nano motion systems to robotics and biomechanics as well as vehicle dynamics up to historical masonries in civil engineering. Both detailed analyses using large scaled industrial models as well as high level analyses based on simple (prototype) models with a small number of degrees of freedom were presented. The application oriented sessions clearly demonstrated that multibody system modeling techniques can effectively support the different phases of the design and optimization process, mainly because of their computational efficiency and their ability to allow models to be easily updated and extended during the design process. Obvious key aspects in this context appeared to be the development of efficient formulations and numerical integration techniques. In case of flexible multibody systems model reduction techniques are of importance. In various sessions there were presentations that demonstrated the importance of the development of contact algorithms. Based on recommendations of the members of the Scientific Committee, some selected authors have been invited to submit their contributions as peer-reviewed papers in this Thematic Issue of the journal Multibody System Dynamics. We wish you a most interesting reading.

On the analytical–numerical valuation of the Bermudan and American options

The paper further develops, both from the theoretical and numerical points of view the analytical valuation of the American options, initiated by Geske and Johnson (1984) for the American put with no dividend. We present and prove closed form formulas for the value of the Bermudan put and call, with dividend, paid continuously at a constant rate, where a general number and not necessarily equal length intervals subdivide the time. Based on the obtained formulas and recent, efficient numerical integration techniques, to obtain values of the multivariate normal c.d.f., the Bermudan put and call option values are calculated for up to twenty subdividing intervals. The sequences of option values are smoothed by sums of exponential functions and the latters are used to predict the values of the American options. Numerical results are presented and compared with those, published in the literature. It is shown that the binomial method systematically overestimates the option price, and, according to our numerical results, so do many other methods. Some properties of Richardson extrapolation are explored.

The challenge of numerically implementing numerous force–resultant models in the stability analysis of long on-bottom pipelines

Plasticity models written directly in terms of force and displacement are finding increased popularity in describing the behaviour of offshore foundations. However, when applied to the on-bottom stability analysis of pipelines under random storm loading, hundreds, if not thousands, of models must be incorporated with structural elements in a three-dimensional analysis and simultaneously solved. This necessitates extremely efficient and accurate numerical integration techniques. This paper scrutinizes constitutive integration algorithms within both explicit and implicit frameworks, and applies them to a two-surface mixed hardening model that describes the force–displacement behaviour of a pipe partially embedded in sand. Detailed solutions are provided, allowing implementation of the pipe–soil model into any standard structural finite-element program. Through use of practical examples, the efficiency and accuracy of the solution methods are assessed.

Carbon Phase Diagram fromAb InitioMolecular Dynamics

We compute the free energy of solid and liquid diamond from first-principles electronic structure theory using efficient thermodynamic integration techniques. Our calculated melting curve is in excellent agreement with the experimental estimate of the graphite-diamond-liquid triple point and is consistent with shock wave experiments. We predict the phase diagram of diamond at pressures and temperatures that are difficult to access experimentally. We confirm early speculations on the presence of a reentrant point in the diamond melting line but find no evidence for a first order liquid-liquid phase transition near the reentrant point.

A numerical formulation for grounding analysis in stratified soils

The design of safe grounding systems in electrical installations is essential to assure the security of the persons, the protection of the equipment and the continuity of the power supply. In order to achieve these goals, it is necessary to compute the equivalent electrical resistance of the system and the potential distribution on the earth surface when a fault condition occurs. In this paper we present a formulation for the analysis of grounding systems embedded in stratified soils, on the basis of the boundary element method (BEM). Suitable arrangements of the final discretized equations allow us to use the highly efficient analytical integration techniques derived by the authors for grounding systems buried in uniform soils. The feasibility of this approach is demonstrated by applying the BEM formulation to the analysis of a real grounding system with a two-layer soil model.

A Numerical Formulation for Grounding Analysis in Stratified Soils

The design of safe grounding systems in electrical installations is essential to assure the security of the persons, the protection of the equipment and the continuity of the power supply. In order to achieve these goals, it is necessary to compute the equivalent electrical resistance of the system and the potential distribution on the earth surface when a fault condition occurs. In this paper we present a formulation for the analysis of grounding systems embedded in stratified soils, on the basis of the boundary element method (BEM). Suitable arrangements of the final discretized equations allow us to use the highly efficient analytical integration techniques derived by the authors for grounding systems buried in uniform soils. The feasibility of this approach is demonstrated by applying the BEM formulation to the analysis of a real grounding system with a two-layer soil model.

Semiconductor Kadanoff-Baym Equation Results for Optically Excited Electron-Hole Plasmas in Quantum Wells

We present results from solutions of the semiconductor Kadanoff-Baym equations (full two-time semiconductor Bloch equations) with self-energies in quasistatic Born approximation, for GaAs single quantum wells. We concentrate on memory and correlation effects under fs-pulse excitation conditions. A remarkable feature is the observed kinetic energy increase which is due to the build-up of correlations among the generated carriers. We demonstrate that the two-time approach is (i) very well suited to study correlation phenomena both on short and long times, thereby avoiding well-known problems of one-time kinetic equations, and (ii) that it is becoming practical with the use of efficient integration techniques.

Integration of remotely sensed satellite images with a geographical information system

The basic data structures of a vector-based Geographical Information System (GIS) and a remotely sensed satellite image are different as the latter are in raster format. Availability of large amounts of data on both of these formats, and the potential of their combined use in environmental applications gives rise to the need for both efficient and effective data integration techniques. A new methodology is presented in this paper to integrate remotely sensed raster images with vector data in a GIS and vice versa. This methodology has been implemented successfully and demonstrated as an efficient tool for the integration of both fine and coarse resolution remotely sensed images in a GIS.

Symmetric Galerkin fracture analysis

The implementation of a symmetric Galerkin boundary integral method for crack problems is described. The symmetric Galerkin procedure requires the derivative (hypersingular) equation on the crack surface, and thus a straightforward application of the dual equation fracture method leads to a non-symmetric matrix. By employing the jump across the fracture as the variable on the crack surface, the problem can be formulated with a symmetric, and smaller dimension, coefficient matrix. An important advantage of this Galerkin approximation is that it avoids the difficulties inherent with C 1 interpolations demanded by a collocation approximation for hypersingular equations. Moreover, by incorporating previously developed efficient analytical integration techniques, the computational cost of this algorithm is shown to be competitive with collocation methods.

An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids

Analysis of large deformation of elastic-viscoplastic materials has been performed in this paper using the finite element method with the arbitrary Lagrangian-Eulerian description. An overstress type viscoplastic model using the internal variable approach in a rotated stress-strain space characterizes the material. Stable and efficient integration techniques for the viscoplastic relations are discussed. A linearized form in the ALE description is presented which is to be solved using iteration techniques. In particular the quasi-Newton methods have been used in this analysis. Several test problems which have been considered illustrate the effectiveness of the entire solution algorithm.

Determination of geopotential coefficients by efficient numerical integration techniques

An efficient, high-accuracy, double-integration method that evaluates the iterated form of the surface integral representations of the geopotential coefficients is presented.. The efficiency and high accuracy of this method is obtained by the utilization of the Romberg numerical integration scheme. Additional efficiency is obtained by computing the inner integral common to many different coefficients only once. This method was tested using a test case earth that represented the basic features of the earth's potential field.

On efficient integration techniques for oscillatory integrals in periodic system calculations

AbstractQuantum chemical calculations of polymers and solids, especially on an ab initio level, represent a large computational task and therefore necessitate efficient computing methods. This is particularly true for the oscillatory integrals appearing in such calculations. For these integrals efficient integration methods based both on the Chebyshev series and the spline representation of the nonoscillatory part of the integrand are considered; they are found far superior compared with more standard integration rules. In two‐ and three‐dimensional systems, directions with maximum oscillatory behavior can be selected along which these new efficient integration techniques can be used advantageously. The ideas are illustrated by Hückel crystal orbital (HCO) bond orders for the polyacetylene chain and the graphite layer. In the latter example, also, a method for the integration of oscillatory integrands with a singularity is given.