Fast Simulated Algorithm Research Articles

Interpretation of borehole flexural measurements in high-angle wells using 3D spatial sensitivity functions

Undulating wells are routinely drilled to improve reservoir exposure across hydrocarbon-bearing zones. Although conventional acoustic-log interpretation methods are reliable in vertical wells, they often yield inaccurate results when applied to high-angle or horizontal wells due to azimuthal asymmetry, spatial averaging effects, and wave-mode interference. Three-dimensional finite-difference and finite-element algorithms are typically used to quantify the aforementioned effects on acoustic logs, but they are extremely demanding on the central processing unit’s (CPU) time and memory. We develop a fast algorithm to simulate flexural slownesses acquired in high-angle wells using 3D linear spatial sensitivity functions. Spatial sensitivity functions quantify the variation of phase slowness measured by the sonic tool due to spatial perturbations of elastic properties. First, we construct 3D frequency-dependent sensitivity functions of flexural modes using the product of 1D axial, radial, and azimuthal sensitivity functions obtained from first-order approximations. Then, we simulate frequency-domain flexural logs acquired with wireline tools and dipole sources in isotropic and vertical transversely isotropic (VTI) formations penetrated by high-angle wells. For the examined examples, simulated flexural logs exhibit root-mean-square errors less than [Formula: see text] when compared with those calculated with a 3D time-domain finite-difference (3D-TDFD) algorithm. We found that in isotropic formations with layers thinner than the length of the receiver array, flexural slownesses acquired separately with cross dipoles are different because of geometric asymmetry, whereas in VTI formations we observed differences between cross-dipole slownesses because of effective anisotropy. Furthermore, the flexural logs are affected by spatial averaging introduced by the acoustic wireline tool, especially in the vicinity of layer boundaries. Three-dimensional sensitivity functions reduce the computation time of the flexural logs from an average of 15 h of CPU time per depth (using 3D-TDFD methods) to less than 3 min. The fast simulation algorithm disregards wave reflections, wave-mode conversion, and wave-mode interference occurring at layer boundaries.

DVH-Based Inverse Planning Using Monte Carlo Dosimetry for LDR Prostate Brachytherapy

Inverse planning is an integral part of modern low-dose-rate brachytherapy. Current clinical planning systems do not exploit the total dose information and largely use the American Association of Physicists in Medicine TG-43 dosimetry formalism to ensure clinically acceptable planning times. Thus, suboptimal plans may be derived as a result of TG-43-related dose overestimation and nonconformity with dose distribution requirements. The purpose of this study was to propose an inverse planning approach that can improve planning quality by combining dose-volume information and precision without compromising the overall execution times. The dose map was generated by accumulating precomputed Monte Carlo (MC) dose kernels for each candidate source implantation site. The MC computational burden was reduced by using graphics processing unit acceleration, allowing accurate dosimetry calculations to be performed in the intraoperative environment. The proposed dose-volume histogram (DVH) fast simulated annealing optimization algorithm was evaluated using clinical plans that were delivered to 18 patients who underwent low-dose-rate prostate brachytherapy. Our method generated plans in 37.5±3.2seconds with similar prostate dose coverage, improved prostate dose homogeneity of up to 6.1%, and lower dose to the urethra of up to 4.0%. A DVH-based optimization algorithm using MC dosimetry was developed. The inclusion of the DVH requirements allowed for increased control over the optimization outcome. The optimal plan's quality was further improved by considering tissue heterogeneity.

3D transient electromagnetic modeling using a shift-and-invert Krylov subspace method

We present a fast and efficient algorithm for simulation of a three-dimensional (3D) transient electromagnetic (TEM) response using a modified shift-and-invert Krylov subspace method. The mimetic finite volume method with a staggered grid is carried out for spatial discretization of the time-domain Maxwell's equations. The transient electromagnetic response then can be expressed as a matrix exponential function with an analytic initial magnetic field for a step-off loop source. The shift-and-invert Krylov subspace method can be used to solve the matrix exponential function. However, it requires solving dozens of large sparse linear equations at every time point to reconstruct the Krylov subspace, which makes the conventional shift-and-invert Krylov subspace method time-consuming. By analyzing the characteristics of the optimal shift and shift-and-invert Krylov subspace dimension in detail, we proposed a fast substitute approach to obtain the optimal shift and subspace order by using single optimal shift and constant subspace order with a useful stopping criterion, and developed an efficient modified shift-and-invert Krylov subspace method. Only one LU factorization of a shift coefficient matrix and hundreds of times backward substitutions are required to obtain the results of the TEM modeling data. Time savings are considerable, and this approach makes it possible to compute the response at any time point in the given time interval within the given residual easily and accurately. This is illustrated by using synthetic examples both in layered models and in a 3D complicated model.

A fast algorithm for multifield representation and multiscale simulation of high‐quality 3D stochastic aggregate microstructures by concurrent coupling of stationary Gaussian and fractional Brownian random fields

SummaryThis study presents a multiscale computational framework for the representation and generation of concrete aggregate microstructures on the basis of the multifield theory, which couples the stationary Gaussian random field with the fractional Brownian random field. Specifically, the stationary Gaussian field is utilized to simulate the morphological shape of an aggregate on the coarse scale, whereas the surface topography of the aggregate on the fine scale is represented by the fractional Brownian field. To bridge the 2 scales, a concurrent coupling formula is proposed. This coupled technique allows for smooth transition between the coarse and fine scales and permits the rapid generation of highly realistic concrete aggregates that can be tailored to the desired quality and requirements, making the algorithm computationally appealing. In the generation of the random fields on the 2 scales, the Fourier representation of block circulant covariance matrices with circulant blocks is exploited, which yields substantial efficiency advantages over the conventional Cholesky decomposition approach in factorizing covariance matrices as well as simulating random fields. Meanwhile, a microsurface postprocessing and reconstruction procedure is also developed to convert the generated random fields into realistic 3D shapes. The numerical methodology proposed in this study offers tremendous potential for a plethora of applications in cement‐based materials.

An algorithm for fast elastic wave simulation using a vectorized finite difference operator

Modern geophysical imaging techniques exploit the full wavefield information which can be simulated numerically. These numerical simulations are computationally expensive due to several factors, such as a large number of time steps and nodes, big size of the derivative stencil and huge model size. Besides these constraints, it is also important to reformulate the numerical derivative operator for improved efficiency. In this paper, we have introduced a vectorized derivative operator over the staggered grid with shifted coordinate systems. The operator increases the efficiency of simulation by exploiting the fact that each variable can be represented in the form of a matrix. This operator allows updating all nodes of a variable defined on the staggered grid, in a manner similar to the collocated grid scheme and thereby reducing the computational run-time considerably. Here we demonstrate an application of this operator to simulate the seismic wave propagation in elastic media (Marmousi model), by discretizing the equations on a staggered grid. We have compared the performance of this operator on three programming languages, which reveals that it can increase the execution speed by a factor of at least 2–3 times for FORTRAN and MATLAB; and nearly 100 times for Python. We have further carried out various tests in MATLAB to analyze the effect of model size and the number of time steps on total simulation run-time. We find that there is an additional, though small, computational overhead for each step and it depends on total number of time steps used in the simulation. A MATLAB code package, ’FDwave’, for the proposed simulation scheme is available upon request.

Divide and conquer approach to quantum Hamiltonian simulation

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

Fast Algorithm for Rough-Surface Scene Simulation in Passive Millimeter Wave Imaging

Simulation in the passive millimeter-wave (MMW) imaging of rough surfaces is an indispensable step in the simulation in passive radiation imaging. The multi-layer brightness temperature tracing method (MBTTM) can be used to simulate the image of a rough surface, which has been proven in our previous work. However, it causes a significant decrease in efficiency of the simulation. To solve this problem, a fast MBTTM is proposed in this paper. In the new method, the uniformly emission method and multi-layer densification method are presented. To validate the correctness of the new algorithm, the comparison of the simulation and measurement results are proposed. These results are in good agreement, which indicates that the fast MBTTM can notably shorten the computing time of the simulation of the rough-surface scene.

An information and simulation framework for increased quality in welded components

The recent trend toward using simulation models with real-time data as digital twins is rapidly increasing in industry. In this paper, a digital framework supporting real-time geometrical quality control of welded components, is presented. The concept is based on a structured process model for all operations included in typical welding, strategies for selective assembly, automatic adjustment of fixtures and optimization of weld sequence. The concept utilizes recently developed algorithms for fast welding simulation and in-line scanning to be used in the optimization loop of an automated welding station—a digital twin for a welding cell.

Fast and exact simulation of univariate and bivariate Gaussian random fields

Circulant embedding is a powerful algorithm for fast simulation of stationary Gaussian random fields on a rectangular grid in , which works perfectly for compactly supported covariance functions. Cut‐off circulant embedding techniques have been developed for univariate random fields for dimensions up to and rely on the modification of a covariance function outside the simulation window, such that the modified covariance function is compactly supported. In this paper, we propose extensions of the cut‐off approach for univariate and bivariate Gaussian random fields. In particular, we provide a method for simulating bivariate fields with a powered exponential model and the Matérn model for certain sets of parameters. Copyright © 2018 John Wiley & Sons, Ltd.

A fast algorithm for simulation of periodic flows using discrete vortex particles

We present a novel fast algorithm for flow simulations using the discrete vortex method, DVM, for problems with periodic boundary conditions. In the DVM, the solution of the velocity field induced by interactions among N discrete vortex particles is governed by the Biot–Savart law and, therefore, leads to a computational cost proportional to O( $$N^2$$ ). The proposed algorithm combines exponential and power series expansions implemented using a divide and conquer strategy to accelerate the calculation of the cotangent kernel that models periodic boundary conditions. The fast multipole method, FMM, is applied for the solution of singular terms appearing in the power series expansion and also for the exponential series expansion. Error and computational cost analyses are performed for the individual steps of the algorithm for double and quadruple machine precision. The current method presents more accurate solutions when compared to those obtained by periodic domain replication using the free-field FMM kernel. The novel algorithm provides computational savings of nearly 240 times for double-precision simulations with one million particles when compared to the direct calculation of the Biot–Savart law.

A fast simulation algorithm for multiple moving bottlenecks and applications in urban freight traffic management

Moving bottlenecks are moving capacity restrictions that affect traffic flows, and they can be used to describe the effects of buses and trucks in transportation networks. The computation of solutions associated with the presence of moving bottlenecks is complex, since they both influence and are influenced by surrounding traffic. In this study, we propose a fast numerical scheme that can efficiently compute the solutions to an arbitrary number of moving (and fixed) bottlenecks, for a stretch of road modeled by the Lighthill–Whitham–Richards (LWR) model. Several different moving bottlenecks can be simulated endogenously all together by means of an algorithm based on a semi-analytic Lax–Hopf formula. Since the numerical scheme is semi-analytic and requires a very low number of operations, it can be employed for traffic estimation problems where fast and accurate solutions are required. We demonstrate the capabilities of the method by implementing two alternative traffic management strategies designed to minimize the negative impacts of trucks and buses in urban environments.

Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.

In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA) overcomes the main limitations of the standard Linear Noise Approximation (LNA) to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

A fast and high accuracy numerical simulation algorithm of the polymer spherulite at the mesoscale Level

In the multiscale numerical simulation of polymer crystallization during the processing period, flow and temperature of the polymer melt are simulated on the macroscale level, while nucleation and growth of the spherulite are simulated at the mesoscale level. As a part of the multiscale simulation, the meso-simulation requires a fast solving speed because the meso-simulation software must be run several times in every macro-element at each macro-step. Meanwhile, the accuracy of the calculation results is also very important. It is known that the simulation geometry of crystallization includes planar (2D) and three-dimensional space (3D). The 3D calculations are more accurate but more expensive because of the long CPU time consumed. On the contrary, 2D calculations are always much faster but lower in accuracy. To reach the desirable speed and high accuracy at the same time, an algorithm is presented, in which the Delesse law coupled with the Monte Carlo method and pixel method are employed to simulate the nucleation, growth, and impingement of the polymer spherulite at the mesoscale level. Based on this algorithm, a software is developed with the Visual C++ language, and its numerical examples’ results prove that the solving speed of this algorithm is as fast as the 2D classical simulation and the calculation accuracy is at the same level as the 3D simulation.

A fast image simulation algorithm for scanning transmission electron microscopy

Image simulation for scanning transmission electron microscopy at atomic resolution for samples with realistic dimensions can require very large computation times using existing simulation algorithms. We present a new algorithm named PRISM that combines features of the two most commonly used algorithms, namely the Bloch wave and multislice methods. PRISM uses a Fourier interpolation factor f that has typical values of 4–20 for atomic resolution simulations. We show that in many cases PRISM can provide a speedup that scales with f4 compared to multislice simulations, with a negligible loss of accuracy. We demonstrate the usefulness of this method with large-scale scanning transmission electron microscopy image simulations of a crystalline nanoparticle on an amorphous carbon substrate.

Fast algorithm for simulation of normal and oblique penetration into limestone targets

A fast algorithm is proposed to predict penetration trajectory in simulation of normal and oblique penetration of a rigid steel projectile into a limestone target. The algorithm is designed based on the idea of isolation between the projectile and the target. Corresponding factors of influence are considered, including analytical load model, cratering effect, free surface effect, and separation-reattachment phenomenon. Besides, a method of cavity ring is used to study the process of cavity expansion. Further, description of the projectile’s three-dimensional gesture is presented. As a result, the algorithm is coded for fast calculation, named PENE3D. A series of cases with selected normal and oblique penetrations are simulated by the algorithm. The predictions agree with the results of tests, showing that the proposed algorithm is fast and effective in simulation of the penetration process and prediction of the penetration trajectory.

Optimal sizing of a standalone photovoltaic system for remote housing electrification using numerical algorithm and improved system models

This paper presents a size optimization method of the energy sources in a standalone photovoltaic system. The proposed technique implies improved photovoltaic array model, dynamic battery model, and accurate objective function as well as a fast simulation algorithm. The loss of load probability (LLP) is used to define the availability of the system. Different system's configurations with different availability levels are generated using the proposed algorithm. These configurations are evaluated based on system availability and cost. Hourly meteorological and load demand data are utilized in this research. A design example is done to show the application of the proposed method considering the weather profile of Malaysia. The result shows that the optimal sizing ratio of the photovoltaic array (CA) is 1.184, while the sizing ratio for storage battery (CB) is 0.613. In addition, the levelized cost of energy (LCE) for the unit generated of energy by the proposed system is 0.447 $/kWh.

A fast and accurate synthetic iteration-based algorithm for numerical simulation of radiative transfer in a turbid medium

It has been shown that the regular part of the solution (RPS) which remains after separating the anisotropic part of the solution (APS) in the small-angle modification of the spherical harmonics method (SHM) is a smooth quasi-isotropic function with individual peaks in the angular distribution. The smooth part of the RPS without peaks can be determined in the two-streaming or diffuse approximation. The first iteration of the angular distribution of the radiance significantly refines the solution and allows one to restore the abovementioned angular peaks. The quasi-diffusion approximation—separation of the APS on the basis of the SHM, the determination of the RPS in the diffusion approximation, and the refinement of the solution on the basis of the first iteration—does not depend on the symmetry of the problem and, therefore, can be generalized to the case of an arbitrary geometry of the medium.

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

In this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the time-integrated variance (conditional on the SABR volatility), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alternative to Hagan’s analytic formula for short maturities that may be employed for model calibration purposes.

On a One Time-Step SABR Simulation Approach: Application to European Options

In this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the integrated variance (conditional on the SABR volatility process), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alternative to Hagan's analytic formula for short maturities that may be employed for model calibration purposes.

A fast algorithm for Direct Numerical Simulation of natural convection flows in arbitrarily-shaped periodic domains

A parallel algorithm is presented for the Direct Numerical Simulation of buoyancy- induced flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary cross-section. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. A semi-implicit scheme is employed for the diffusive terms, which are treated implicitly on the periodic plane and explicitly along the homogeneous direction, while all convective terms are explicit, via the second-order Adams-Bashfort scheme. The contemporary solution of velocity and pressure fields is achieved by means of a projection method. The numerical resolution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for the case of flow around an array of heated cylindrical rods arranged in a square lattice. Grid independence is assessed in laminar flow conditions, and DNS results in turbulent conditions are presented for two different grids and compared to available literature data, thus confirming the favorable qualities of the method.