An expert system for setting time steps in dynamic finite element programs

An expert system, ETUDES—Expert Time integration control Using Deep and Surface Knowledge System, which addresses the determination of the timestep for time integration of linear structural dynamic equations is described. This time-step may also be applicable for a moderately nonlinear simulation of the same structure. The program also determines whether an explicit or implicit method is most efficient for the particular simulation. A production rule programming system written in OPS5 is used for the implementation of this prototype expert system. Issues relating to the expert system architecture for this application, such as knowledge representation and structure, as well as domain knowledge are discussed. The prototype is evaluated by measuring it's performance in various benchmark model problems.     

Second-order shape design sensitivity using P-version finite element analysis

Thep-version finite element analysis (FEA) approach is attractive for design sensitivity analysis (DSA) and optimization due to its high accuracy of analysis results, even with coarse mesh; insensitivity to finite element mesh distortion and aspect ratio; and tolerance for large shape design changes during design iterations. A continuum second-order shape DSA formulation is derived and implemented usingp-version FEA. The second-order shape design sensitivity can be used for reliability based analysis and design optimization by incorporating it with the second-order reliability analysis method (SORM). Both the second-order shape DSA formulations with respect to the single and mixed shape design parameters are derived for elastic solids using the material derivative concept. Both the direct differentiation and hybrid methods are presented in this paper. A shape DSA is implemented by using an establishedp-version FEA code, STRESS CHECK. Two numerical examples, a connecting rod and bracket, are presented to demonstrate the feasibility and accuracy of the proposed seond-order shape DSA approach.     

Normalized explicit finite element approximate inverse preconditioning

Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. Normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given.     

A class of explicit preconditioned conjugate gradient methods for solving large finite element systems

A class of Explicit Preconditioned Conjugate Gradient (EPCG) methods for solving large sparse linear systems of algebraic equations resulting from the Finite Element discretization of Elliptic and Parabolic PDE's is introduced. The EPCG methods are based on explicit Approximate Inverse Matrix techniques and are particularly suitable for solving numerically initial/boundary-value problems on multiprocessor systems. The application of the new methods on 2D-linear boundary-value problems is discussed and numerical results are given.     

An explicit finite element method for convection-diffusion equations using rational basis functions

An explicit Galerkin method is formulated by using rational basis functions. The characteristics of the rational difference scheme are investigated with regard to consistency, stability and numerical convergence of the method. Numerical results are also presented.     

Efficient shape matching using shape contexts

We demonstrate that shape contexts can be used to quickly prune a search for similar shapes. We present two algorithms for rapid shape retrieval: representative shape contexts, performing comparisons based on a small number of shape contexts, and shapemes, using vector quantization in the space of shape contexts to obtain prototypical shape pieces.     

Sequential approximate optimization of industrial hammer peening using finite element simulations

In this paper, the industrial hammer peening process is optimized using multi-objective, sequential approximate optimization, which is a mathematics- plus finite element- based algorithm. Since the number of design and objective variables is significant, the global optimization problem is split into two, more manageable multi-objective subproblems. The use of surrogate modelling together with an intensification and diversification strategy for solving the optimization subproblems allows for significant computational cost savings without loss of accuracy. Additionally, we propose a Bayesian inference criterion-based sensitivity approach for “filtering-out” design variables which do not significantly affect objectives variables. Finally, guidelines for selecting appropriate Pareto optima are given using \(N-1\) Pareto diagrams, where N is the number of objective variables.     

Finite element formulations for transient dynamic problems in solids using explicit time integration

This paper presents the displacement, mixed and stress formulations of the finite element method when applied to transient dynamic problems of solids. The formulations are chosen so that explicit time integration may be used. Large deformations are considered for these formulations, and infinitesimal strain assumptions are employed with the stress formulation. Displacement formulations are well-known, but the mixed formulations presented provide a viable alternative. The stress formulation has not proven successful for the large deformation problem, but when infinitesimal strains are assumed, the formulation is attractive. A problem of an internally pressurized ring is solved in order to evaluate the different proposed formulations.     

Identifying and reducing critical lag in finite element simulations

End-to-end lag time can undermine the effectiveness of interactive displays. Analyzing lag components for an FES indicated that simulation time is the critical component     

Deformable registration using patch-wise shape matching

We present a novel approach for non-rigid registration of partially overlapping surfaces acquired from a deforming object. To allow for large and general deformations our method employs a nonlinear physics-inspired deformation model, which has been designed with a particular focus on robustness and performance. We discretize the surface into a set of overlapping patches, for each of which an optimal rigid motion is found and interpolated faithfully using dual quaternion blending. Using this discretization we can formulate the two components of our objective function—a fitting and a regularization term—as a combined global shape matching problem, which can be solved through a very robust numerical approach. Interleaving the optimization with successive patch refinement results in an efficient hierarchical coarse-to-fine optimization. Compared to other approaches our as-rigid-as-possible deformation model is faster, causes less distortion, and gives more accurate fitting results.     

Non-linear explicit transient finite element analysis on the Intel Delta

Many large-scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing non-linear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.     

无条件稳定的显式降维非线性有限元

针对传统降维非线性有限元计算速度与精确度难以兼顾的问题,提出了一种无条件稳定的显式迭代算法。基于泰勒展开式得到速度、加速度的三阶精度差分表达式从而获得新的有限元显式迭代方程,并分析其单自由度系统下的传递矩阵谱半径。改进迭代方程使谱半径始终小于1从而满足无条件稳定的要求。实验表明,改进后的显式迭代算法在等效阻尼比的精度上优于中心差分法和隐式迭代法;在降维非线性有限元模型计算中的计算耗时优于隐式迭代方法,提高了降维非线性有限元的迭代计算速度。模型在降维后维度数值较高时,仍能维持良好的计算耗时和帧率,保证了模型的精确度。     

Partial shape classification using contour matching in distancetransformation

An algorithm is presented to recognize and locate partially distorted 2D shapes without regard to their orientation, location, and size. The algorithm first calculates the curvature function from the digitized image of an object. The points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary-matching procedure. The boundary-matching procedure considers two shapes at a time, one shape from the template databank, and the other from the object being classified. The procedure tries to match the control points in the unknown shape to those of a shape from the template databank, and estimates the translation, rotation, and scaling factors to be used to normalize the boundary of the unknown shape. The chamfer 3/4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes. The unknown shape is assigned to the class corresponding to the minimum distance. The algorithm has been successfully tested on partial shapes using two sets of data, one with sharp corners and the other with curve segments. This algorithm not only is computationally simple, but also works reasonably well in the presence of a moderate amount of noise     

Moving curved mesh adaptation for higher-order finite element simulations

Higher-order finite element method requires valid curved meshes in three-dimensional domains to achieve the solution accuracy. When applying adaptive higher-order finite elements in large-scale simulations, complexities that arise include moving the curved mesh adaptation along with the critical domains to achieve computational efficiency. This paper presents a procedure that combines Bézier mesh curving and size-driven mesh adaptation technologies to address those requirements. A moving mesh size field drives a curved mesh modification procedure to generate valid curved meshes that have been successfully analyzed by SLAC National Accelerator Laboratory researchers to simulate the short-range wakefields in particle accelerators. The analysis results for a 8-cavity cryomodule wakefield demonstrate that valid curvilinear meshes not only make the time-domain simulations more reliable, but also improve the computational efficiency up to 30%. The application of moving curved mesh adaptation to an accelerator cavity coupler shows a tenfold reduction in execution time and memory usage without loss in accuracy as compared to uniformly refined meshes.     

High quality real-time Image-to-Mesh conversion for finite element simulations

In this paper, we present a parallel Image-to-Mesh Conversion (I2M) algorithm with quality and fidelity guarantees achieved by dynamic point insertions and removals. Starting directly from an image, its implementation is capable of recovering the isosurface and meshing the volume with tetrahedra of good shape. Our tightly-coupled shared-memory parallel speculative execution paradigm employs carefully designed contention managers, load balancing, synchronization and optimizations schemes. These techniques are shown to boost not only the parallel but also the single-threaded efficiency of our code. Specifically, our single-threaded performance is faster than both CGAL and TetGen, the state of the art sequential open source meshing tools we are aware of. The effectiveness of our method is demonstrated on Blacklight, the Pittsburgh Supercomputing Center’s cache-coherent NUMA machine. We observe a more than 82% strong scaling efficiency for up to 64 cores, and a more than 82% weak scaling efficiency for up to 144 cores, reaching a rate of more than 14.3 million elements per second. This is the fastest 3D Delaunay mesh generation and refinement algorithm, to the best of our knowledge.     

Two dimensional shape optimization using partial control and finite element method for compressible flows

The objective of this study is to determine the two dimensional shape of a body located in a compressible viscous flow, where the applied fluid force is minimized. The formulation to obtain the optimal shape is based on an optimal control theory. An optimal state is defined as a state, in which the performance function defined as the integration of the square sum of the applied fluid forces is minimized due to a reduction in the applied fluid forces. Compressible Navier–Stokes equations are treated as constraint equations. In other words, the body is considered to have a shape that minimizes the fluid forces under the constraint of the Navier–Stokes equations. The gradient of the performance function is computed using the adjoint variables. A weighted gradient method is used as the minimization algorithm. The volume of the body is assumed to be the same as that of the initial body. In the case of the algorithm used in this study, both the creation of a structured mesh around the surface of the body and the smoothing procedure are employed for the computation of gradient. In this study, a remeshing technique based on the structured mesh around the body changing its configuration in the iteration cycle is employed. For the correction to keep the volume constant, the surface coordinates are moved along the radial direction. For the discretization of both the state and adjoint equations, the efficient bubble function interpolation presented previously by the authors [18] is employed. The algorithm, which is known as the partial control algorithm, is applied to the numerical procedure to determine the movement of the coordinates. In the case of the gradient method, in order to avoid the convergence of the final shape to the local minimum shape, the new algorithm, which is called the partial control algorithm, is presented in this study. In numerical studies, the shape determination of a body in a uniform flow field is carried out in 2D domains. The initial shape of the body is assumed to be an elliptical cylinder. The shape is modified by minimizing the applied fluid forces. Finally, the desired shape of a body, whose performance function is reduced and converged to a constant value, is obtained. By carrying out a procedure that involves the use of the partial control algorithm, the desired shape of a body, whose performance function is reduced further, is obtained. Stable shape determination of a body in a compressible viscous flow is carried out by using the presented method. It is indicated that the optimal shape can be obtained by using the partial control algorithm.     

结合轮廓与形状特征的仿射形状匹配

目的 针对仿射变换下形状匹配中存在的描述子对形状的描述能力不足,以及描述子计算耗时大的问题,改进基于所有图像点投影的方法,提出一种利用轮廓计算投影面积的仿射形状匹配算法。方法 该算法分为粗匹配和精匹配两个阶段。粗匹配阶段以CSS角点作为备选特征点,首先统计轮廓投影面积分布作为特征点描述子;然后利用动态规划蚁群算法匹配两幅图片公共特征点序列,并将匹配好的特征点序列记为对应的新特征点;最后采用该新特征点划分目标曲线,得到对应的轮廓曲线;这一阶段的目的是对形状的筛选以及寻找一致的轮廓特征点,同时完成轮廓曲线的划分。精匹配阶段,采用小波仿射不变描述子,对粗匹配阶段匹配代价最小的5%的目标进行对应曲线匹配,得到精匹配阶段的匹配代价,从而实现对仿射目标的识别;精匹配弥补了描述子对轮廓细节描述不足的问题。结果 算法的平均检索速度比传统基于形状投影分布描述子提高44.3%,在MPEG-7图像库上的检索效果为98.65%,在MPEG-7仿射图像库上的查准率与查全率综合评价指标比传统的基于形状投影分布描述子高3.1%,比形状上下文高25%。结论 本文算法匹配效果好,效率高,抗噪性强,解决了仿射描述子计算速度慢、描述能力不足的问题,能有效地应用于仿射形状匹配与检索领域。     

汽车碰撞过程的计算负载均衡并行有限元技术

为了在有限的计算资源下挖掘更高的汽车碰撞仿真计算效率,基于当前普遍采用的并行处理区域分解算法,结合一个典型碰撞案例分析可知,汽车碰撞模型计算过程中的主要时间开销与结构大变形相关.提出基于坐标递归对分（Recursive Coordinate Bisection,RCB）的计算负载均衡区域分解算法,并将此法应用于某整车碰撞仿真模型的3类典型工况.计算结果表明此法能将并行计算效率提高10%~24%.     

Space mapping optimization of waveguide filters using finite element and mode‐matching electromagnetic simulators

For the first time in design optimization of microwave circuits, the aggressive space mapping (SM) optimization technique is applied to automatically align electromagnetic (EM) models based on hybrid mode‐matching/network theory simulations with models based on finite‐element (FEM) simulations. SM optimization of an H‐plane resonator filter with rounded corners illustrates the advantages as well as the challenges of the approach. The parameter extraction phase of SM is given special attention. The impact of selecting responses and error functions on the convergence and uniqueness of parameter extraction is discussed. A statistical approach to parameter extraction involving 𝓁₁ and penalty concepts facilitates a key requirement by SM for uniqueness and consistency. A multipoint parameter extraction approach to sharpening the solution uniqueness and improving the SM convergence is also introduced. Once the mapping is established, the effects of manufacturing tolerances are rapidly estimated with the FEM accuracy. SM has also been successfully applied to optimize waveguide transformers using two hybrid mode‐matching/network theory models: a coarse model using very few modes and a fine model using many modes to represent discontinuities. ©1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 54–70, 1999.