Simple finite-difference algorithm for calculating waveguide modes

We propose a very efficient scheme for modeling three-component seismic plane waves in vertically heterogeneous attenuative media using the finitedifference (FD) method in the time domain. The scheme is able to represent P , SV ,a ndSH waves incoming from different direction. The algorithm can also calculate the plane-wave responses of media for different incident angels. In the algorithm, neglecting lateral heterogeneity, the wave equation is rewritten for plane waves by applying a 2D Radon transform to the 3D general wave equation. QP and QS are incorporated via generalized Zener body rheological models for viscoelasticity to represent anelastic attenuation. Our FD scheme uses a 1D grid, which leads to a significant reduction in computation time and memory requirements as compared to the corresponding 3D or 2D computations. It may be an efficient tool for pre- or post-analysis of local structural effects including anelastic attenuation, before or after the large-scale seismic wave simulation. To demonstrate the ability and efficiency of the scheme, we calculate a synthetic vertical seismic profile (VSP) for a borehole with a highly heterogeneous velocity model and frequency dependent attenuation model in the Kanto area of Japan.

Utilization of a dependency-tracking language to reduce computational time during multidisciplinary design optimization

On the self-similarity of 1/fβ sequences synthesized by recursive filtering

Solving the solid-state diffusion equation in a typical pseudo-two-dimensional (P2D) battery model using conventional finite difference methods (FDM) substantially increases the model complexity (in terms of number of equations) as well as the computational time. In our previous work, we approximated the solid-state diffusion in spherical particles using Galerkin weak form method based on symmetric polynomials, which significantly improved the robustness of modeling, achieving a tenfold reduction in computational time, even for non-linear diffusion problems. However, we found that the equations represented in non-dimensional form for mathematical compactness are relatively difficult to interpret and apply in P2D and other battery models. Therefore, as a follow-up to previous work, we present the weak form formulations of solid-state diffusion in dimensional form to provide better physical interpretation and easier adaptability to battery modelling and other applications. Further, considering diverse particle morphologies in modern battery materials, we extend these formulations for cylindrical and rectangular coordinates, in addition to the spherical coordinate. We further present simulations using various experimentally reported concentration-dependent diffusivities and find that the solution convergence is strongly influenced by the degree of non-linearity in diffusion. The study enables the proposed formulation to be widely applicable facilitating accurate and fast simulations.

As the finite difference methods or other methods of discreet variables both in time andspace coordinates are used to solve the initial value problems. One of the sufficient conditionsfor computational stability is to maintain the conservation or boundness of the total energy ofthe original physical problems in the computational schemes. Those schemes, which do not exactlyguarantee the conservation or boundness of energy, have always some special computational un-stable solutions. Until recently, all published and the so-called energy-conservative finite dif-ference schemes for integrating the dynamical equations of compressible fluid or the meteoro-logical primitive equations conserve the total energy only instantaneously, i.e. when the differen-tial in time remained, but cannot exactly conserve it as the finiie difference in time is also usedinstead of the differential. In this paper, by using some transformations of independent (co-ordinates) or dependent variables, we have successfully designed some time-space finite differ-ence schemes guaranteeing the energy and mass conservations perfectly. Thus the problem ofcomputational stability is solved completely. In order to solve these finite difference equations, some split methods have been developedalso. They possess the internal consistency and reduce the original problem into successivelysolving several onedimensional initial value problems, to which the economical method of fac-torization can be applied effectively. Thus, both computational stability and economy are guar-anteed. These methods can be used in routine.

The prediction of protein-protein interactions (PPIs) is essential to understand the cellular processes from a medical perspective. Among the various machine learning techniques, kernel-based Support Vector Machine (SVM) has been commonly employed to discriminate between interacting and non-interacting protein pairs. The main drawback of employing the kernel-based SVM to datasets with many features, such as the primary sequence-based protein-protein dataset, is the significant increase in computational time of training stage. This increase in computational time is mainly due to the presence of the kernel in solving the quadratic optimisation problem (QOP) involved in nonlinear SVM. In order to fix this issue, we propose a novel and efficient computational algorithm by approximating the kernel-based SVM using a low-rank truncated Mercer series as well as desired. As a result, the QOP for the approximated kernel-based SVM will be very tractable in the sense that there is a significant reduction in computational time of training and validating stages. We illustrate the novelty of the proposed method by predicting the PPIs of “S. Cerevisiae” where the protein features extracted using the multiscale local descriptor (MLD), and then we compare the predictive performance of the proposed low-rank approximation with the existing methods. Finally, the new method results in significant reduction in computational time for predicting PPIs with almost as accuracy as kernel-based SVM.

Database sequencing applications including sequence comparison, searching, and analysis are considered among the most computation power and time consumers. Heuristic algorithms suffer from sensitivity while traditional sequencing methods, require searching the whole database to find the most matched sequences, which requires high computation power and time. This paper introduces a dynamic programming technique based-on a measure of similarity between two sequential objects in the database using two components, namely frequency and mean. Additionally, database sequences that have the lowest scores in the comparison process were excluded such that the similarity algorithm between a query sequence and other database sequences is applied to meaningful parts of the database. The proposed technique was implemented and validated using a heterogeneous HW/SW FPGA-based embedded system platform. The implementation was partitioned into (1) hardware part (running on logic gates of FPGA) and (2) software part (running on ARM processor of FPGA). The validation study showed a significant reduction in computation time by accelerating the database sequencing processes by 60% comparing to traditional known methods.

This study has focused on the UELB problem that aims at leveling the traffic load of a communication link in an information network by determining the path of a flow that minimizes the maximum load factor of the link. The UELB problem has been proved to be NP-hard, and an approximate solution method using the LP relaxation has been proposed to verify the results. This paper proposes another algorithm using the Lagrangian relaxation method in order to objectively evaluate the accuracy of the approximate solutions obtained so far. We have conducted comparison experiments with the exact solution. The results showed that the proposed algorithm gradually improves the accuracy of the solution as the number of calculations of the subgradient method is increased. In addition, it was found that when Lagrangian relaxation is performed, it is better to apply LP relaxation at the same time. Conducting the relaxation at the same time will lead to a reduction in computation time.

A quantative comparison between the boundary integral equation (BIE) method and the finite difference (FD) method is presented in which each technique is applied to an elliptic boundary‐value problem (BVP) containing a boundary singularity. Two types of singularity have previously been analysed theoretically, namely those due to a discontinuous boundary potential, which we shall refer to as S1, and those due to a sudden change from the specification of boundary potential flux, an S2 singularity. In this paper the analysis is presented for a third type of boundary singularity, namely an S3 singularity: that arising from a discontinuous boundary flux. Such a condition is frequently encountered in the field of heat transfer where, for example, a system or pipe has a change of lagging material.In general, it is found that the BIE method is superior, with regards to the computational time required to achieve a certain degree of accuracy, over standard FD methods even when there is a boundary singularity. Further, the BIE method determines the solution near the singularity much more accurately than the FD method. The FD method does, however, have advantages for a very restrictive class of problems; for example, when the boundary conditions are of the Dirichlet type and the boundary geometry is rectangular. In this case an optimum relaxation parameter can easily be obtained. A soon as Neumann conditions are prescribed, the BIE is far more efficient than the FD, whatever the boundary geometry.It is concluded that, for fast, accurate solutions of general Laplacian boundary‐value problems, the BIE is appreciably superior to the FD and this is even more pronounced when there is a boundary singularity.

In the zonal method, considerable computational resources are needed to calculate the direct exchange areas (DEA) among the isothermal zones due to integrals with up to six dimensions, while strong singularities occur in the integrands when two zones are adjacent or overlaping (self-irradiation). A special transformation of variables to reduce a double integral into several single integrals is discussed in this paper. This technique was originally presented by Erkku (1959) for calculation of DEA using a uniform zone system in a cylindrical enclosure. However, nonuniform zones are needed for applications with large thermal gradients. Thus we extended this technique to calculate the DEA for non-uniform zones in an axisymmetrical cylinder system. A six-fold reduction in computational time was observed in calculating DEA compared with cases without a variable transformation. It is shown that accuracy and efficiency of estimation of radiation heat flux is improved when using a nonuniform zone system. Reasonable accuracy of all DEA are calculated without resorting to the conservative equations. Results compared well with analytical solutions and numerical results of previous researchers. This technique can be readily extended to rectangular enclosures with similar reduction in computation time expected.

Finite-difference (FD) schemes have been used widely for solving wave equations in seismic exploration. However, the conventional FD schemes hardly guarantee high accuracy at both small and large wavenumbers. In this paper, we propose an optimal time-space domain FD scheme for acoustic vertical transversely isotropic (VTI) wave modeling. The optimal FD coefficients for the second-order spatial derivatives are derived by approaching the time-space domain dispersion relation of acoustic VTI wave equations with the combination of the Taylor-series expansion and the sampling interpolation. We perform numerical dispersion analyses and acoustic VTI modeling using the optimal time-space domain FD scheme. The numerical dispersion analyses show that the optimal FD scheme has smaller dispersion than the conventional FD scheme at large wavenumbers, and also preserves high accuracy at small wavenumbers. The acoustic VTI modeling examples also demonstrate that the optimal time-space domain FD scheme has greater accuracy compared with the conventional time-space domain FD scheme for the same modeling parameters.

The objective of this paper is to seek a generalized understanding for the influence of incorporating the gradient of the model?s physical properties (e.g., conductivity, velocity) in the forward modelling numerical algorithm. In order to take a step towards that, we examine an example from Geophysics for solving 3-D Maxwell?s equations using finite difference (FD) methods. The 3-D FD methods to obtain discrete solutions of Maxwell's equations include the staggered-grid and balance methods. The balance method 3-D algorithm exploits the conductivity gradient in order to make the FD formulation a seven-point scheme and the resulting matrix a banded septa block diagonal but not symmetric. The staggered grid algorithm is free of conductivity gradient and results in a symmetric 13- diagonal banded matrix. The objective now is to examine and understand better the influence of the conductivity gradient incorporated in the FD equations on the accuracy of the electromagnetic (EM) modelling for two 3-D benchmark models. We use three various discretizations (fine, mildly coarse, and coarse) for each model. The modelling results of each discretization have been computed separately by the balance method and staggered grid method. We have found that the staggered grid method produces accurate results for all the three discretizations investigated. However, the balance method encountered some inaccuracies for the mildly coarse and coarse discretizations. This appears to be due to the presence of the conductivity gradient in the 3-D modelling algorithm. The model studies also suggest that the thicknesses of the horizontal and vertical discretizations at the conductivity boundaries should be about 1/25 and 1/100 skin depth to maintain accurate modelling results when the conductivity derivatives exist in the 3-D modelling algorithm.

Toward flexible and persistent UAV service: Multi-period and multi-objective system design with task assignment for disaster management

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

We studied a wave control of a string near a fixed end. The equation of motion of a string is approximated as a lumped-parameter spring-and-mass system using the finite difference method. Finite difference equations (FDEs) for interior node points have the same set of coefficients, whereas the FDEs for boundary node points have a different set of coefficients. By using the control, the latter equation is modified to be as the same equation as the former one. The propagating wave is absorbed through a control actuator as if no boundary existed, and virtually, an infinite system is thus realized. Control is at the string position of the finite difference mesh spacing inside the fixed boundary that is free from supporting loads. We confirmed the effectiveness of the controller by numerical simulation for the traveling string and also did that by numerical simulation and by an experiment for the nontraveling string.