CPU Time Savings Research Articles

Method of Moments Based on Equivalent Periodic Problem and FFT with NURBS Surfaces for Analysis of Multilayer Periodic Structures

In this paper, an efficient technique of computation of method of moments (MM) matrix entries for multilayer periodic structures with NURBS surface and Bézier patches modelling is proposed. An approximation in terms of constant pulses of generalized rooftop basis functions (BFs) defined on Bézier patches is proposed. This approximation leads discrete convolutions instead of usual continuous convolution between Green’s functions and BFs obtained by the direct mixed potential integral equation (MPIE) approach. An equivalent periodic problem (EPP) which contains the original problem is proposed to transform the discrete convolutions in discrete cyclic convolutions. The resultant discrete cyclic convolutions are computed by efficiently using the Fast Fourier Transform (FFT) procedure. The performance of the proposed method and direct computation of the MM entries are compared for phases of reflection coefficient. The proposed method is between 9 and 50 times faster than the direct computation for phase errors less than 1 deg. The proposed method exhibits a behaviour of CPU time consumption of O(NbLog10Nb) as the number Nb of BFs increases. This behaviour provides significant CPU time savings with respect to the expected behaviour of O(Nb2) provided by the direct computation of the MM matrix entries.

A new high accuracy cubic spline method based on half-step discretization for the system of 1D non-linear wave equations

PurposeThis paper aims to develop a new 3-level implicit numerical method of order 2 in time and 4 in space based on half-step cubic polynomial approximations for the solution of 1D quasi-linear hyperbolic partial differential equations. The method is derived directly from the consistency condition of spline function which is fourth-order accurate. The method is directly applied to hyperbolic equations, irrespective of coordinate system, and fourth-order nonlinear hyperbolic equation, which is main advantage of the work.Design/methodology/approachIn this method, three grid points for the unknown function w(x,t) and two half-step points for the known variable x in spatial direction are used. The methodology followed in this paper is construction of a cubic spline polynomial and using its continuity properties to obtain fourth-order consistency condition. The proposed method, when applied to a linear equation is shown to be unconditionally stable. The technique is extended to solve system of quasi-linear hyperbolic equations. To assess the validity and accuracy, the method is applied to solve several benchmark problems, and numerical results are provided to demonstrate the usefulness of the method.FindingsThe paper provides a fourth-order numerical scheme obtained directly from fourth-order consistency condition. In earlier methods, consistency conditions were only second-order accurate. This brings an edge over other past methods. In addition, the method is directly applicable to physical problems involving singular coefficients. Therefore, no modification in the method is required at singular points. This saves CPU time, as well as computational costs.Research limitations/implicationsThere are no limitations. Obtaining a fourth-order method directly from consistency condition is a new work. In addition, being an implicit method, this method is unconditionally stable for a linear test equation.Practical implicationsPhysical problems with singular and nonsingular coefficients are directly solved by this method.Originality/valueThe paper develops a new fourth-order implicit method which is original and has substantial value because many benchmark problems of physical significance are solved in this method.

Efficient Algorithm for Scattering by a Large Cluster of Moving Objects

A highly efficient algorithm for analysis of electromagnetic scattering by a large cluster of independently moving objects is proposed in this paper. A double octree structure is introduced, which consists of a main octree stationary to the cluster as a whole, and many sub-octrees moving with individual objects. Based on the new double octree structure, the computation of interactions between two elements is divided into four categories: the two elements are on the same object and are near; the two elements are on the same object but are far; the two elements are on different objects but the two objects are adjacent; the two elements are on different objects and the two objects are non-adjacent. For different interacting categories, different approaches are adopted to maximize the computing efficiency. The new algorithm enables possible fast simulations of scattering by hundreds of independently moving objects. Compared with the conventional Multilevel Fast Multipole Algorithm (MLFMA) and the recently developed Multi-Moving-Object (MMO)-MLFMA, the present scheme has substantial improvement in saving CPU time, providing a viable solution for engineering applications. Numerical validations for accuracy and efficiency are performed.

Skyway

Managed languages such as Java and Scala are prevalently used in development of large-scale distributed systems. Under the managed runtime, when performing data transfer across machines, a task frequently conducted in a Big Data system, the system needs to serialize a sea of objects into a byte sequence before sending them over the network. The remote node receiving the bytes then deserializes them back into objects. This process is both performance-inefficient and labor-intensive: (1) object serialization/deserialization makes heavy use of reflection, an expensive runtime operation and/or (2) serialization/deserialization functions need to be hand-written and are error-prone. This paper presents Skyway, a JVM-based technique that can directly connect managed heaps of different (local or remote) JVM processes. Under Skyway, objects in the source heap can be directly written into a remote heap without changing their formats. Skyway provides performance benefits to any JVM-based system by completely eliminating the need (1) of invoking serialization/deserialization functions, thus saving CPU time, and (2) of requiring developers to hand-write serialization functions.

Wang–Landau sampling: Saving CPU time

In this work we propose an improvement to the Wang–Landau (WL) method that allows an economy in CPU time of about 60% leading to the same results with the same accuracy. We used the 2D Ising model to show that one can initiate all WL simulations using the outputs of an advanced WL level from a previous simulation. We showed that up to the seventh WL level (f6) the simulations are not biased yet and can proceed to any value that the simulation from the very beginning would reach. As a result the initial WL levels can be simulated just once. It was also observed that the saving in CPU time is larger for larger lattice sizes, exactly where the computational cost is considerable. We carried out high-resolution simulations beginning initially from the first WL level (f0) and another beginning from the eighth WL level (f7) using all the data at the end of the previous level and showed that the results for the critical temperature Tc and the critical static exponents β and γ coincide within the error bars. Finally we applied the same procedure to the 1/2-spin Baxter–Wu model and the economy in CPU time was of about 64%.

Propeller/rudder interaction with direct and coupled CFD/potential flow propeller approaches, and application to a zigzag manoeuvre

ABSTRACTThis paper investigates a coupled computational fluid dynamics (CFD)/potential propeller code approach to simulate maneuvers of ships. While this approach is successful in submarines, the concept has not been evaluated before for cases where an object (the rudder) is immersed in the wake. The study uses the CFD code REX and the propeller code PUF-14 applied to propeller/rudder interactions in open water configuration and to a 15/1 zigzag maneuver for the KCS container ship. Self-propulsion results, and motions, forces, moments and mean flow field during the maneuver agree well with experiments and discretized propeller simulations. The approach is an effective and economical way to perform direct simulation of surface ship maneuvers, providing CPU time savings approaching an order of magnitude. Massively separated rudder flows may not perform as well, since the propeller turbulence reaching the rudder is under-predicted in the coupled approach.

Reduced shift operator alternating direction implicit FDTD applied to plasma

ABSTRACTIn order to analyze the electromagnetic characteristics of plasma more efficiently, a novel FDTD called R-SO-ADI FDTD is proposed. The proposed method which is based on the shift operator technique has clear conceptions and simple formulae, and it saves CPU time and reduces the storage of the field components through combining the reduced formulation technique and the ADI scheme. Calculation results of the RCS of a perfectly conducting cylinder coated by plasma confirm the validity of the proposed method.

Moving particle semi-implicit method with improved pressures stability properties

AbstractMoving particle semi-implicit (MPS) method is one of the Lagrangian methods widely used in engineering issues. This method, however, suffers from unphysical oscillations in its original form. In the present study, a modified incompressible MPS method is proposed to suppress these oscillations and is used for simulating free surface problems. To demonstrate the stability of the presented method, different kernel functions are used in the case of numerical dam break modeling as a benchmark simulation. A simple form of definition of curved wall boundaries is suggested which eliminates dummy particles and subsequently saves CPU time. Flow over an ogee spillway is simulated for the first time with the I-MPS method and as a new test case which has several curved lines in its geometry. The comparisons between theoretical solutions/experimental data and simulation results in terms of free surface and pressure show the accuracy of the method.

Tabulation of combustion chemistry via Artificial Neural Networks (ANNs): Methodology and application to LES-PDF simulation of Sydney flame L

In this work, a methodology for the tabulation of combustion mechanisms via Artificial Neural Networks (ANNs) is presented. The objective of the methodology is to train the ANN using samples generated via an abstract problem, such that they span the composition space of a family of combustion problems. The abstract problem in this case is an ensemble of laminar flamelets with an artificial pilot in mixture fraction space to emulate ignition, of varying strain rate up to well into the extinction range. The composition space thus covered anticipates the regions visited in a typical simulation of a non-premixed flame. The ANN training consists of two-stage process: clustering of the composition space into subdomains using the Self-Organising Map (SOM) and regression within each subdomain via the multilayer Perceptron (MLP). The approach is then employed to tabulate a mechanism of CH4–air combustion, based on GRI 1.2 and reduced via Rate-Controlled Constrained Equilibrium (RCCE) and Computational Singular Perturbation (CSP). The mechanism is then applied to simulate the Sydney flame L, a turbulent non-premixed flame that features significant levels of local extinction and re-ignition. The flow field is resolved through Large Eddy Simulation (LES), while the transported probability density function (PDF) approach is employed for modelling the turbulence–chemistry interaction and solved numerically via the stochastic fields method. Results demonstrate reasonable agreement with experiments, indicating that the SOM-MLP approach provides a good representation of the composition space, while the great savings in CPU time allow for a simulation to be performed with a comprehensive combustion model, such as the LES-PDF, with modest CPU resources such as a workstation.

A simplified parametrised model for lung microstructures capable of mimicking realistic geometrical and mechanical properties

The respiratory zone of mammalian lungs contains several millions of so-called alveoli. The geometrical and mechanical properties of this microstructure are crucial for respiration and influence the macroscopic behaviour of the entire organ in health and disease. Hence, if computational models are sought to gain more insight into lung behaviour, predict lung states in certain scenarios or suggest better treatment options in early stages of respiratory dysfunction, an adequate representation of this microstructure is essential. However, investigating the real alveolar architecture requires complex medical-imaging methods and would be computationally extremely expensive. Even worse, there is currently no way of obtaining the real patient-specific microstructure in vivo. Hence, we present a fast and easy to compute parametrised model of lung microstructures based on tetrakaidecahedra which can represent both geometrical and mechanical properties of the parenchyma. We show that gas transport pathways and stress and strain distributions are comparable to real alveolar microstructures and even capable of capturing variations present in biology. The created parametrised lung microstructure models can be utilized in finite element simulations to study, e.g., alveolar flow phenomena, particle deposition, or alveolar stresses and strains during mechanical ventilation. Due to the simpler geometry of the parametrised microgeometries compared to imaging-based microstructures, remarkable savings in CPU time can be achieved. We show that our model requires a minimum of 10% of the computational time for computing the same strain state in structural mechanics simulations compared to imaging-based alveolar microstructures.

Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem

We consider the solution of block-coupled large-scale linear systems of equations, arising from the finite element approximation of the linear elasticity problem. Due to the large scale of the problems we use properly preconditioned iterative methods, where the preconditioners utilize the underlying block matrix structures, involving inner block solvers and, when suited, broadly established tools such as the algebraic Multigrid method (AMG).For the considered problem, despite of its optimal rate of convergence, AMG, as implemented in some publicly available scientific libraries, imposes unacceptably high demands for computer resources. In this paper we propose and analyze an efficient multilevel preconditioner, based on the Generalized Locally Toeplitz framework, with a specialized transfer operator. We prove and numerically illustrate the optimal convergence rate of the proposed preconditioner, and experimentally report memory and CPU time savings. We also provide comparisons with respect to another aggregation-based algebraic multigrid algorithm.

A hierarchical uniformly high order DG-IMEX scheme for the 1D BGK equation

A class of high order nodal discontinuous Galerkin implicit–explicit (DG-IMEX) schemes with asymptotic preserving (AP) property has been developed for the one-dimensional (1D) BGK equation in Xiong et al. (2015) [40], based on a micro–macro reformulation. The schemes are globally stiffly accurate and asymptotically consistent, and as the Knudsen number becomes small or goes to zero, they recover first the compressible Navier–Stokes (CNS) and then the Euler limit. Motivated by the recent work of Filbet and Rey (2015) [27] and the references therein, in this paper, we propose a hierarchical high order AP method, namely kinetic, CNS and Euler solvers are automatically applied in regions where their corresponding models are appropriate. The numerical solvers for different regimes are coupled naturally by interface conditions. To the best of our knowledge, the resulting scheme is the very first hierarchical one being proposed in the literature, that enjoys AP property as well as uniform high order accuracy. Numerical experiments demonstrate the efficiency and effectiveness of the proposed approach. As time evolves, three different regimes are dynamically identified and naturally coupled, leading to significant CPU time savings (more than 80% for some of our test problems).

Narrowing Support Searching Range in Maintaining Arc Consistency for Solving Constraint Satisfaction Problems

Arc consistency is the most popular filtering technique for solving constraint satisfaction problems. Constraint check plays a central role in establishing arc consistency. In this paper, we propose a method to save constraint checks in maintaining coarse-grained arc consistency during backtracking search for solving the constraint satisfaction problems. We reduce the support searching range by utilizing the information generated by an AC3.1 algorithm at preprocessing step. Compared with the existing maintaining arc consistency (MAC) algorithms, the proposed MAC3 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">be</sub> algorithm saves constraint checks without maintaining additional data structures at each search tree node. Our experimental results show that MAC3 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">be</sub> saves both constraint checks and CPU time while solving some benchmark problems.

Decomposition model for naval hydrodynamic applications, Part I: Computational method

The present paper and its companion present a solution and domain decomposition model for general two-phase, incompressible and turbulent flows encountered in naval hydrodynamics. The mathematical and numerical model are derived within the framework of polyhedral finite volume method. Interface capturing is obtained with implicitly redistanced level set method derived from the phase field equation. This approach removes the need to redistance the level set field, thus saving CPU time and increasing numerical stability. A modified, Spectral Wave Explicit Navier–Stokes Equations method is introduced and used for wave modelling, where the solution is decomposed into incident and perturbation fields. The incident field is readily available from potential flow theories, and only the perturbation component is solved within the non-linear equation set of the free surface flow model. The domain is decomposed with implicit relaxation zones used to prevent wave reflection by forcing the perturbation fields to vanish in the far-field. A second-order, collocated finite volume method is used to discretise the equations. All equations are solved implicitly, which enables the use of higher Courant–Friedrichs–Lewy numbers compared to explicit scheme. The algorithm is implemented in foam-extend-3.1, a community driven fork of the OpenFOAM CFD software. Verification and validation of the model is presented in the accompanying paper.

On the space separated representation when addressing the solution of PDE in complex domains

Separated representations allow impressive computational CPU time savings when applied in different fields of computational mechanics. They have been extensively used for solving models defined in multidimensional spaces coming from (i) its proper physics, (ii) model parameters that were introduced as extra-coordinates and (iii) 3D models when the solution can be separated as a finite sum of functional products involving lower dimensional spaces. The last route is especially suitable when models are defined in hexahedral domains. When it is not the case, different possibilities exist and were considered in our former works. In the present work, we are analyzing two alternative routes. The first one consists of immersing the real non-separable domain into a fully separable hexahedral domain. The second procedure consists in applying a geometrical transformation able to transform the real domain into a hexahedra in which the model is solved by using a fully separated representation of the unknown field.

Predictive Elastoplastic Damage Constitutive Law: Establishment of Equivalence Relation between Intrinsic and Extrinsic Material Parameters

The purpose of the current work is the development and application of a new identification method of material parameters of elastoplastic damage constitutive model under large strains. A relationship relating the intrinsic and extrinsic parameters of a reference material is built and transformed in equivalence relation. Extrinsic parameters concern the shape of their experimental tensile force/elongation curve, however, intrinsic parameters deal with Swift hardening law coupled with an isotropic damage variable. The relationship is carried out from a statistical characterization of a material reference (standard-steel E24). It based on multiple linear regression of a data set obtained according to a full factor design of numerical simulations of mechanical tensile tests. All materials satisfying this equivalence relation belong to the same equivalence class. This is motivated by observing that gathered materials must behave somewhat like the reference material. The material parameters can be immediately identified by only one task by running the found relationship. The current method facilitates the identification procedure and offers a substantial savings in CPU time. However it just needs only one simulation for the identification of similar behavior instead of the few hundred required when using other methods.

An Improved Approach for Estimating the Hyperparameters of the Kriging Model for High-Dimensional Problems through the Partial Least Squares Method

During the last years, kriging has become one of the most popular methods in computer simulation and machine learning. Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models. When many input variables are used, kriging is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (100+), one method is recently proposed that combines kriging with the Partial Least Squares technique, the so-called KPLS model. This method has shown interesting results in terms of saving CPU time required to build model while maintaining sufficient accuracy, on both academic and industrial problems. However, KPLS has provided a poor accuracy compared to conventional kriging on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging. The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging.

A Backward Euler Method Based Thévenin Equivalent Integral Model for Full-bridge Modular Multi-level Converters

–The Thévenin equivalent electromagnetic transient model of the full-bridge modular multi-level converter adopts Dommel's Algorithm to discretize individual capacitor to maintain the identity of each switching level and achieves significant CPU time savings. This article presents an enhanced integral full-bridge modular multi-level converter model with built-in efficient sorting algorithms. Basically it achieves further speedup from the traditional equivalent algorithm by assuming the switch's “OFF” condition as an ideal open circuit, by using the A-stable backward Euler integration method instead of the trapezoidal rule to discretize the individual capacitor in each sub-module and by using the proposed efficient capacitor voltage sorting algorithm. Then the blocking implementation method and the way to simulate the open and short-circuit faults of the internal full-bridge modular multi-level converter devices are also provided to make the full-bridge modular multi-level converter model complete and effective. The validity and scalabilities of the presented model are demonstrated using closed-loop simulation of a back-to-back high-voltage DC system and open-loop simulations of full-bridge modular multi-level converters. The results obtained from both demonstrations have shown that the presented integral model is able to accurately simulate the typical behaviors of the full-bridge modular multi-level converter during normal operation and AC/DC network transients.

A conservative finite volume scheme with time-accurate local time stepping for scalar transport on unstructured grids

In this article we propose a new conservative high resolution TVD (total variation diminishing) finite volume scheme with time-accurate local time stepping (LTS) on unstructured grids for the solution of scalar transport problems, which are typical in the context of water quality simulations. To keep the presentation of the new method as simple as possible, the algorithm is only derived in two space dimensions and for purely convective transport problems, hence neglecting diffusion and reaction terms. The new numerical method for the solution of the scalar transport is directly coupled to the hydrodynamic model of Casulli and Walters (2000) that provides the dynamics of the free surface and the velocity vector field based on a semi-implicit discretization of the shallow water equations. Wetting and drying is handled rigorously by the nonlinear algorithm proposed by Casulli (2009). The new time-accurate LTS algorithm allows a different time step size for each element of the unstructured grid, based on an element-local Courant-Friedrichs-Lewy (CFL) stability condition. The proposed method does not need any synchronization between different time steps of different elements and is by construction locally and globally conservative. The LTS scheme is based on a piecewise linear polynomial reconstruction in space–time using the MUSCL–Hancock method, to obtain second order of accuracy in both space and time.The new algorithm is first validated on some classical test cases for pure advection problems, for which exact solutions are known. In all cases we obtain a very good level of accuracy, showing also numerical convergence results; we furthermore confirm mass conservation up to machine precision and observe an improved computational efficiency compared to a standard second order TVD scheme for scalar transport with global time stepping (GTS). Then, the new LTS method is applied to some more complex problems, where the new scalar transport scheme has also been coupled to a semi-implicit model for the simulation of the free surface hydrodynamics, including nonlinear wetting and drying. The last application shown in this paper is carried out on a real geometry, for which we have taken available DTM data of the lake Guaiba in Brazil. Comparisons have been made in all cases with a second order TVD scheme based on GTS. For the new LTS algorithm we report a significant reduction in computational effort, with a savings of CPU time of the order of up to 95%.

A multiple-resolution strategy for Direct Numerical Simulation of scalar turbulence

In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolution than that of the momentum. The latter usually requires a less refined mesh and integrating both fields on a single grid tailored to the most demanding variable produces an unnecessary computational overhead. A multiple resolution approach is used also in the time integration in order to maintain the stability of the scalars on the finer grid. The method is the more advantageous the less diffusive the scalar is with respect to momentum, therefore it is particularly well suited for large Prandtl or Schmidt number flows. However, even in the case of equal diffusivities the present procedure gives CPU time and memory occupation savings, due to the increased gradients and more intermittent behaviour of the scalars when compared to momentum.