Fully discrete potential-based finite element methods for a transient eddy current problem

Fully discrete potential-based finite element methods called methods are used to solve a transient eddy current problem in a three-dimensional convex bounded polyhedron. Using methods, fully discrete coupled and decoupled numerical schemes are developed. The existence and uniqueness of solutions for these schemes together with the energy-norm error estimates are provided. To verify the validity of both schemes, some computer simulations are performed for the model from TEAM Workshop Problem 7. This work was supported by Postech BSRI Research Fund-2009, National Basic Research Program of China (2008CB425701), NSFC under the grant 10671025 and the Key Project of Chinese Ministry of Education (No. 107018).     

Computing the null space of finite element problems

We present a method for computing the null space of finite element models, including models with equality constraints. The method is purely algebraic; it requires access to the element matrices, but not to the geometry or material properties of the model.Theoretical considerations show that under certain conditions, both the amount of computation and the amount of memory required by our method scale linearly with model size; memory scales linearly but computation scales quadratically with the dimension of the null space. Our experiments confirm this: the method scales extremely well on 3-dimensional model problems. In general, large industrial models do not satisfy all the conditions that the theoretical results assume; however, experimentally the method performs well and outperforms an established method on industrial models, including models with many equality constraints.The accuracy of the computed null vectors is acceptable, but the method is usually less accurate than a more naive (and computationally much more expensive) method.     

Numerical approximation of incompressible flows with net flux defective boundary conditions by means of penalty techniques

We consider incompressible flow problems with defective boundary conditions prescribing only the net flux on some inflow and outflow sections of the boundary. As a paradigm for such problems, we simply refer to Stokes flow. After a brief review of the problem and of its well posedness, we discretize the corresponding variational formulation by means of finite elements and looking at the boundary conditions as constraints, we exploit a penalty method to account for them. We perform the analysis of the method in terms of consistency, boundedness and stability of the discrete bilinear form and we show that the application of the penalty method does not affect the optimal convergence properties of the finite element discretization. Since the additional terms introduced to account for the defective boundary conditions are non-local, we also analyze the spectral properties of the equivalent algebraic formulation and we exploit the analysis to set up an efficient solution strategy. In contrast to alternative discretization methods based on Lagrange multipliers accounting for the constraints on the boundary, the present scheme is particularly effective because it only mildly affects the structure and the computational cost of the numerical approximation. Indeed, it does not require neither multipliers nor sub-iterations or additional adjoint problems with respect to the reference problem at hand.     

Worst case bounds on the point-wise discretization error in boundary element method for the elasticity problem

In this work, point-wise discretization error is bounded via interval approach for the elasticity problem using interval boundary element formulation. The formulation allows for computation of the worst case bounds on the boundary values for the elasticity problem. From these bounds the worst case bounds on the true solution at any point in the domain of the system can be computed. Examples are presented to demonstrate the effectiveness of the treatment of local discretization error in elasticity problem via interval methods.     

Accelerating geoscience and engineering system simulations on graphics hardware

Many complex natural systems studied in the geosciences are characterized by simple local-scale interactions that result in complex emergent behavior. Simulations of these systems, often implemented in parallel using standard central processing unit (CPU) clusters, may be better suited to parallel processing environments with large numbers of simple processors. Such an environment is found in graphics processing units (GPUs) on graphics cards.This paper discusses GPU implementations of three example applications from computational fluid dynamics, seismic wave propagation, and rock magnetism. These candidate applications involve important numerical modeling techniques, widely employed in physical system simulations, that are themselves examples of distinct computing classes identified as fundamental to scientific and engineering computing. The presented numerical methods (and respective computing classes they belong to) are: (1) a lattice-Boltzmann code for geofluid dynamics (structured grid class); (2) a spectral-finite-element code for seismic wave propagation simulations (sparse linear algebra class); and (3) a least-squares minimization code for interpreting magnetic force microscopy data (dense linear algebra class). Significant performance increases (between 10× and 30× in most cases) are seen in all three applications, demonstrating the power of GPU implementations for these types of simulations and, more generally, their associated computing classes.     

A modified advancing layers mesh generation for thin three-dimensional objects with variable thickness

A method of generating modified advancing layers mesh is proposed. In this paper the mesh generation process of semi-unstructured prismatic/tetrahedral mesh is presented for relatively thin three-dimensional geometries with variable thickness, as in the case of injection molding analysis. Prismatic meshes are generated by offsetting initial surface triangular meshes. During the mesh generation process, mesh quality is efficiently improved with the use of a new node relocation method. Finally, tetrahedral meshes are automatically generated in the rest of the domain. The mesh generating capability of the proposed algorithm is demonstrated with the several practical test cases.     

自适应有限元常用标记策略及其在PHG中的并行实现

讨论自适应有限元计算中常用的标记策略的并行实现问题,介绍并行自适应有限元软件平台PHG中实现这些策略的统一函数接口.特别地,针对一类在分布式存储并行计算机上不易实现的策略,如GERS策略和MNS策略,介绍我们所设计的并行算法.     

基于GML的市政道路管理模型

区别于传统的道路数据模型,基于地理标记语言（GML）的市政道路模型面向市政道路组成元素管理。分析市政道路组成元素的特点以及管理部门对市政道路管理的需求,依据GML的核心模式,建立面向管理领域的市政道路设施的空间属性一体化模型,并对该道路模型的应用前景进行分析。     

面向对象的非线性有限元软件框架设计

阐述面向对象的非线性有限元软件框架设计,在前人成果的基础上,力求软件框架更灵活、更完善。采用模型分析方法与有限元模型分离的方式,明确描述各类之间的依赖关系以及相互之间的传递消息过程,建立非线性有限元软件的框架结构。增加有限元软件的模块化、代码的重用性和易扩展性,解决长期以来存在于非线性有限元开发的一个重要难题。     

低速直驱永磁同步电机的电磁场有限元分析

多极永磁同步电机在产生低速机械运动的同时提高转矩密度,并且具有较大的负载范围,从而可以直接驱动机械负载,以替代传统电机配合减速器和液力耦合器的驱动方式,摒弃了复杂冗重的减速机构.利用Ansoft/Maxwell 2D建立永磁同步电动机的有限元模型,通过拓扑形式的Modular定子结构绕线方式,对电机进行有限元分析,探究不同气隙长度对低速永磁同步电机磁通密度分布与动态转矩等其他性能的影响.