The adaptive finite element method based on multi-scale discretizations for eigenvalue problems

In this paper, adaptive finite element methods for differential operator eigenvalue problems are discussed. For multi-scale discretization schemes based on Rayleigh quotient iteration (see Scheme 3 in [Y. Yang, H. Bi, A two-grid discretization scheme based on shifted-inverse power method, SIAM J. Numer. Anal. 49 (2011) 1602–1624]), a reliable and efficient a posteriori error indicator is given, in addition, a new adaptive algorithm based on the multi-scale discretizations is proposed, and we apply the algorithm to the Schrödinger equation for hydrogen atoms. The algorithm is performed under the package of Chen, and satisfactory numerical results are obtained.     

一种用于分布参数系统移动边界的自适应剖分数值方法

本文提出通过对具有移动边界分布参数系统中的移动边界的一步预报,自适应生成剖分 网格,然后通过系统的焓方程应用有限元方法求解,得到具有移动边界的分布参数系统的数值 解.结果表明,这种方法较好地解决了用有限元方法求解该类系统的数值解时遇到的移动边 界附近数值解精度与网格剖分过细所导致的计算量过大的矛盾.为具有移动边界的分布参数 系统的建模和仿真提供了一种有效的数值计算方法,同时也为研究系统的控制、估计、辨识等 问题的数值方法打下了基础.     

Solving PDEs in irregular geometries with multiresolution methods I: Embedded Dirichlet boundary conditions

In this work, we develop and analyze a formalism for solving boundary value problems in arbitrarily-shaped domains using the MADNESS (multiresolution adaptive numerical environment for scientific simulation) package for adaptive computation with multiresolution algorithms. We begin by implementing a previously-reported diffuse domain approximation for embedding the domain of interest into a larger domain (Li et al., 2009 [1]). Numerical and analytical tests both demonstrate that this approximation yields non-physical solutions with zero first and second derivatives at the boundary. This excessive smoothness leads to large numerical cancellation and confounds the dynamically-adaptive, multiresolution algorithms inside MADNESS. We thus generalize the diffuse domain approximation, producing a formalism that demonstrates first-order convergence in both near- and far-field errors. We finally apply our formalism to an electrostatics problem from nanoscience with characteristic length scales ranging from 0.0001 to 300 nm.     

Computer-aided design for a real-time acceleration of the convergence of adaptive control algorithms

This paper presents a technique for the computer-aided design of modified adaptive controllers for improving the transients in adaptive systems. It is based on the adaptation of well known parallel tools from numerical analysis to this problem. The software package has a modular structure. Each module has a specific task corresponding to the hardware design. In structing the modules, both the expected hardware implementation facilities, and ease of programming are taken into account. Also, a basic library of functions and routines has been designed.     

A general purpose adaptivity driver for FE software

This paper describes a tool that serves as an automatic mesh adaptivity driver program for general purpose finite element (FE) software packages. Many commercially available FE programs lack a feature to control the numerical solution's accuracy properly. Our tool implements a mesh adaptive method that, in conjunction with separate finite element software, allows one to fully automatically improve the quality of the numerical solution up to a user specified accuracy. We demonstrate the use of the package with selected computational examples performed with a commercial FE package, ANSYS, and with our FE program FEMEngine. Copyright © 2003 John Wiley & Sons, Ltd.     

Discontinuous Galerkin method on three-dimensional tetrahedral grids: Using the operator programming method

In the numerical simulation of gas-dynamic flows in domains with a complex geometry, it is necessary to use detailed unstructured grids and highly accurate numerical methods. The Galerkin method with discontinuous base functions (or the discontinuous Galerkin method) works well in dealing with such problems. This technique has several advantages inherent both in finite-element and in finite-difference approximations. At the same time, the discontinuous Galerkin method is computationally complex; therefore, the question arises about the most efficient use of the full potential of computers. In order to speed up the computations, we applied the operator programming method to develop the computational module. It allows presenting mathematical formulas in programs in compact form and helps to port programs to parallel architectures such as NVidia CUDA and Intel Xeon Phi. Earlier the operator programming method was implemented for regular three-dimensional Cartesian grids and three-dimensional locally adaptive grids. In this work, this method is applied to threedimensional tetrahedral grids. This example demonstrates that the method in question can be efficiently implemented on arbitrary three-dimensional grids. Besides, we demonstrate the use of the template metaprogramming methods of the C++ programming language in order to speed up computations.     

Finite-element analysis of a rotary oven for bread

The paper deals with a finite-element analysis of the turbulent forced-convection air flow inside a rotary oven for bread. The code ADINA-F is used for the numerical finite-element simulation. To describe the flow and the heat transfer inside the oven, a two-dimensional model has been adopted. The numerical heat-transfer convection coefficient is in good agreement with the experimental data thus providing a validation of the approximate model formulated in the numerical analysis. A structural change intended to enhance the convective heat transfer has been suggested and numerically tested. The results show a mean Nusselt number enhancement of about 30%. The finite-element analysis is, therefore, a helpful tool in estimating the performances of this kind of oven.     

Simulation of thermally induced package effects with regard to piezoresistive pressure sensors

Microsystems are on their way out of laboratories into production. One of these microsystems, a piezoresistive pressure sensor developed by Robert Bosch GmbH, is examined within this paper. Obviously, one can detect undesirable temperature effects resulting from the sensor package, which influence the electrical characteristics of the sensor. By means of finite-element modelling (FEM), a simulation of the temperature effects can be managed. It is also possible to search for alternative designs of the sensor package.     

有限元工程化的几项关键技术

本文是作者从事有限元应用开发工作的体会。从应用观点出发，作者认为：有限元数值分析及实验验证，有限元前后处理，一体化有限元软件接口，远程登录计算，是有限元方法在工程界得以普遍应用的四项关键技术；每项关键技术都在平行地发展并互相促进。     

Numerical simulation of low-Reynolds number flows past rectangular cylinders based on adaptive finite element and finite volume methods

The flow past rectangular cylinders has been investigated by two different numerical techniques, an adaptive finite-element (AFEM) and a finite-volume method (FVM). A square and a rectangular cylinder with width-to-height equal to 5 are taken into account. 2D computations have been performed for different Reynolds numbers in order to consider different flow regimes, i.e. the stationary, the periodic and the turbulent flow. The comparison between the two methods regarded both the reliability of the computed solutions and the overall resulting efficiency of the methods. Velocity profiles and integral parameters such as Strouhal number, drag coefficient and recirculation length have been compared. A good agreement between the adaptive FEM and the FVM computations, as well as with the available literature results, has been found. The computational effort has been evaluated in terms of used degrees of freedom in space and time and human resources employed to reach the mesh and timestep-length independence of the solutions. Relevant outcomes of this work are the cross validation of an adaptive FE method and a popular open source FV code.     

大气数值模式中FFT算法的设计与实现

大气数值模式中常用到的FFT软件包FFT99由于没有考虑硬件配置和FFT算法的变换参数影响,造成计算效率不高．因此,本文基于FFTw3,根据大气数值模式的特殊需求,设计实现了新的FFT99软件包SC—FFT99．数值试验表明,在FFT计算速度方面,根据新算法设计的SC～FFT99软件包比FFT99有较大的提高．理想情况下,SC—FFT99计算速度比FFT99快2．5到3．5倍．并且SC_FFT99已应用于中国科学院大气物理研究所开发的大气环流模式IAPAGCM4．0的数值模拟,测试结果显示：计算速度比原来的FFT99快0．39倍．     

High-performance finite-element simulations of seismic wave propagation in three-dimensional nonlinear inelastic geological media

We present finite-element numerical simulations of seismic wave propagation in non linear inelastic geological media. We demonstrate the feasibility of large-scale modeling based on an implicit numerical scheme and a nonlinear constitutive model. We illustrate our methodology with an application to regional scale modeling in the French Riviera, which is prone to earthquakes. The PaStiX direct solver is used to handle large matrix numerical factorizations based on hybrid parallelism to reduce memory overhead. A specific methodology is introduced for the parallel assembly in the context of soil nonlinearity. We analyse the scaling of the parallel algorithms on large-scale configurations and we discuss the physical results.     

Thermo-elastic stress of a metal-matrix composite disc under linearly-increasing temperature loading by analytical and FEM analysis

In this study, the elastic stress analysis of a composite disc with aluminium matrix subjected to a linearly-increasing temperature distribution has been carried out. The values of tangential and radial stress components that have occurred under the effect of the temperature from the inner surface of the disc towards the outer surface have been obtained by two different methods, numerical and analytical. In the analytical analysis, a computer program has been developed to get the values of thermal stresses. But in the numerical study carried out with the finite-element method, Abaqus 6.8 package program has been used. As a result of these analyses, it has been observed that the stress values obtained from both methods support each other. It has been determined under this temperature distribution that tangential stress components are always on the condition of compression in the inner surface of the disc and of tensile in the outer surface. It has also been found out that radial stress components are always in the state of tensile along the whole profile of the disc. Finally, the stress analysis of the same composite disc subjected to this temperature distribution, but with a reduced mass, has also been examined numerically.     

Accurate Assessment of Packaging Stress Effects on MEMS Sensors by Measurement and Sensor–Package Interaction Simulations

In this paper, packaging-induced stress effects are assessed for microelectromechanical systems (MEMS) sensors. A packaged MEMS sensor may experience output signal shift (offset) due to the thermomechanical stresses induced by the plastic packaging assembly processes and external loads applied during subsequent use in the field. Modeling and simulation to minimize the stress-induced offset shift are essential for high-precision accelerometers, gyroscopes, and many other MEMS devices. Improvement of plastic package modeling accuracy is accomplished by correlating finite-element analysis package models using measured material properties and package warpage. Using a refined reduced-order MEMS sensor and package interaction model, device offset is simulated, optimized, and compared with data collected from a unique three-axis accelerometer, which uses a single mass for all three axes sensing. As a result, this accelerometer has achieved very low offset in all axes over device operation temperature range of to . Device offset performance was improved by at least five times after the MEMS design optimization as compared with the one prior to the optimization.     

The Ndynamics package—Numerical analysis of dynamical systems and the fractal dimension of boundaries

A set of Maple routines is presented, fully compatible with the new releases of Maple (14 and higher). The package deals with the numerical evolution of dynamical systems and provide flexible plotting of the results. The package also brings an initial conditions generator, a numerical solver manager, and a focusing set of routines that allow for better analysis of the graphical display of the results. The novelty that the package presents an optional C interface is maintained. This allows for fast numerical integration, even for the totally inexperienced Maple user, without any C expertise being required. Finally, the package provides the routines to calculate the fractal dimension of boundaries (via box counting).New version program summaryProgram Title: NdynamicsCatalogue identifier:%Leave blank, supplied by Elsevier.Licensing provisions: no.Programming language: Maple, C.Computer: Intel(R) Core(TM) i3 CPU M330 @ 2.13 GHz.Operating system: Windows 7.RAM: 3.0 GBKeywords: Dynamical systems, Box counting, Fractal dimension, Symbolic computation, Differential equations, Maple.Classification: 4.3.Catalogue identifier of previous version: ADKH_v1_0.Journal reference of previous version: Comput. Phys. Commun. 119 (1999) 256.Does the new version supersede the previous version?: Yes.Nature of problemComputation and plotting of numerical solutions of dynamical systems and the determination of the fractal dimension of the boundaries.Solution methodThe default method of integration is a fifth-order Runge–Kutta scheme, but any method of integration present on the Maple system is available via an argument when calling the routine. A box counting [1] method is used to calculate the fractal dimension [2] of the boundaries.Reasons for the new versionThe Ndynamics package met a demand of our research community for a flexible and friendly environment for analyzing dynamical systems. All the user has to do is create his/her own Maple session, with the system to be studied, and use the commands on the package to (for instance) calculate the fractal dimension of a certain boundary, without knowing or worrying about a single line of C programming. So the package combines the flexibility and friendly aspect of Maple with the fast and robust numerical integration of the compiled (for example C) basin. The package is old, but the problems it was designed to dealt with are still there. Since Maple evolved, the package stopped working, and we felt compelled to produce this version, fully compatible with the latest version of Maple, to make it again available to the Maple user.Summary of revisionsDeprecated Maple Packages and Commands: Paraphrasing the Maple in-built help files, “Some Maple commands and packages are deprecated. A command (or package) is deprecated when its functionality has been replaced by an improved implementation. The newer command is said to supersede the older one, and use of the newer command is strongly recommended”. So, we have examined our code to see if some of these occurrences could be dangerous for it. For example, the “readlib” command is unnecessary, and we have removed its occurrences from our code. We have checked and changed all the necessary commands in order for us to be safe in respect to danger from this source.Another change we had to make was related to the tools we have implemented in order to use the interface for performing the numerical integration in C, externally, via the use of the Maple command “ssystem”. In the past, we had used, for the external C integration, the DJGPP system. But now we present the package with (free) Borland distribution. The compilation and compiling commands are now slightly changed. For example, to compile only, we had used “gcc-c”; now, we use “bcc32-c”, etc. All this installation (Borland) is explained on a “README” file we are submitting here to help the potential user.RestrictionsBesides the inherent restrictions of numerical integration methods, this version of the package only deals with systems of first-order differential equations.Unusual featuresThis package provides user-friendly software tools for analyzing the character of a dynamical system, whether it displays chaotic behaviour, and so on. Options within the package allow the user to specify characteristics that separate the trajectories into families of curves. In conjunction with the facilities for altering the user’s viewpoint, this provides a graphical interface for the speedy and easy identification of regions with interesting dynamics. An unusual characteristic of the package is its interface for performing the numerical integrations in C using a fifth-order Runge–Kutta method (default). This potentially improves the speed of the numerical integration by some orders of magnitude and, in cases where it is necessary to calculate thousands of graphs in regions of difficult integration, this feature is very desirable. Besides that tool, somewhat more experienced users can produce their own C integrator and, by using the commands available in the package, use it as the C integrator provided with the package as long as the new integrator manages the input and output in the same format as the default one does.Running timeThis depends strongly on the dynamical system. With an Intel^® Core? i3 CPU M330 @ 2.13 GHz, the integration of 50 graphs, for a system of two first-order equations, typically takes less than a second to run (with the C integration interface). Without the C interface, it takes a few seconds. In order to calculate the fractal dimension, where we typically use 10,000 points to integrate, using the C interface it takes from 20 to 30 s. Without the C interface, it becomes really impractical, taking, sometimes, for the same case, almost an hour. For some cases, it takes many hours.     

The quadratic B-spline finite-element method for the coupled Schrödinger–Boussinesq equations

In this paper, a quadratic B-spline finite-element method is proposed for solving the coupled Schrödinger–Boussinesq equations numerically. A semi-discrete finite-element scheme is constructed for this system. The existence and uniqueness of the numerical solutions and the convergence of the discrete scheme are discussed. Numerical results indicate that the proposed method is accurate and efficient.     

An Interactive Data Language software package to calculate ionospheric conductivity by using numerical models

The Inter-university Upper atmosphere Global Observation NETwork (IUGONET) project focuses on handling ground-based observational data of the upper atmosphere. To this end, the project members have been developing a data analysis software package which is based on Interactive Data Language (IDL). Filling the spatial gaps in observational data requires the use of numerical models. In this paper, we discuss an IDL software package for global ionospheric conductivity by integration of 3rd party numerical models. The model can be used to create further derived models.     

PMORSy: parallel sparse matrix ordering software for fill-in minimization†

In this paper we present PMORSy—a new parallel software package for symmetric sparse matrix ordering on shared memory systems. The NP-complete fill-in minimization problem is solved by means of multilevel nested dissection algorithm with modifications for vertex separators. Parallel processing is done in a task-based fashion with the granularity tuning. We employ threading techniques on shared memory using OpenMP 3.0 technology as opposed to the Message Passing Interface-based approach widely used for parallel sparse matrix ordering. Experimental results on symmetric matrices from the University of Florida Sparse Matrix Collection and matrices from finite-element analysis of three-dimensional strength problems show that our implementation is competitive to the ParMETIS and PT-Scotch libraries both in ordering quality and performance. The PMORSy library is publicly available from the Lobachevsky State University Supercomputing Center web-site.