A review of error estimation and adaptivity in the boundary element method

When using the boundary element method, the accuracy of the numerical solution depends critically on the discretization of the boundary into elements (panels). The distribution of the panels is one of the most important decisions taken when analyzing a problem, but still the vast majority of users employ empirical guidelines to distribute the panels. This paper reviews the various adaptive schemes that have been proposed for boundary elements. Numerical results are obtained for infinite fluid flow problems and free surface problems and are used to assess the reliability and effectiveness of each method.     

Non‐reflecting artificial boundaries for transient scalar wave propagation in a two‐dimensional infinite homogeneous layer

This paper presents an exact non‐reflecting boundary condition for dealing with transient scalar wave propagation problems in a two‐dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x →∞ and another extends toward x→‐ ∞, the non‐reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time‐dependent partial differential equation with only one spatial variable, can be further changed into a linear first‐order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non‐reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non‐reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi‐infinite media. Copyright © 2003 John Wiley & Sons, Ltd.     

Neutron Stress Measurement of W‐Fiber Reinforced Cu Composite

Stress measurement methods using neutron and X‐ray diffraction were examined by comparing the surface stresses with internal stresses in the continuous tungsten‐fiber reinforced copper‐matrix composite. Surface stresses were measured by X‐ray stress measurement with the sin²ψ method. Furthermore, the sin²ψ method and the most common triaxal measurement method using Hooke's equation were employed for internal stress measurement by neutron diffraction. On the other hand, microstress distributions developed by the difference in the thermal expansion coefficients between these two phases were calculated by FEM. The weighted average strains and stresses were compared with the experimental results. The FEM results agreed with the experimental results qualitatively and confirmed the importance of the triaxial stress analysis in the neutron stress measurement.     

On the design of multiple key hashing files for concurrent orthogonal range retrieval between two disks

This paper concerns the following problem: given a set of multi-attribute records, a fixed number of buckets and a two-disk system, arrange the records into the buckets and then store the buckets between the disks in such a way that, over all possible orthogonal range queries (ORQs), the disk access concurrency is maximized. We shall adopt the multiple key hashing (MKH) method for arranging records into buckets and use the disk modulo (DM) allocation method for storing buckets onto disks. Since the DM allocation method has been shown to be superior to any other allocation methods for allocating an MKH file onto a two-disk system for answering ORQs, the real issue is knowing how to determine an optimal way for organizing the records into buckets based upon the MKH concept.

A performance formula that can be used to evaluate the average response time, over all possible ORQs, of an MKH file in a two-disk system using the DM allocation method is first presented. Based upon this formula, it is shown that our design problem is related to a notoriously difficult problem, namely the Prime Number Problem. Then a performance lower bound and an efficient algorithm for designing optimal MKH files in certain cases are presented. It is pointed out that in some cases the optimal MKH file for ORQs in a two-disk system using the DM allocation method is identical to the optimal MKH file for ORQs in a single-disk system and the optimal average response time in a two-disk system is slightly greater than one half of that in a single-disk system.     

Microstructure evolution during metal forming processes

Recrystallization and grain growth evolutions during metal forming processes are considered. Coupling between the thermo-mechanical and microstructure processes is realized. Die forging of a rear-axle flange is simulated numerically on the base of the finite element method. Material parameters of the models are obtained experimentally. The influence of interpass and holding times on grain size distributions in the end product is shown.     

Application of boundary element method to 3-D problems of coupled thermoelasticity

This paper deals with a new boundary element method for analysis of the quasistatic problems in coupled thermoelasticity. Through some mathematical manipulation of the Navier equation in elasticity, the heat conduction equation is transformed into a simpler form, similar to the uncoupled-type equation with the modified thermal conductivity which shows the coupling effects. This procedure enables us to treat the coupled thermoelastic problems as an uncoupled one, A few examples are computed by the proposed BEM, and the results obtained are compared with the analytical ones available in the literature, whereby the accuracy and versatility of the proposed method are demonstrated.     

Time‐dependent heat transfer coefficient of a wall

A time‐dependent coefficient of heat transfer is proposed for the computation of thermal power required, so that a room temperature reaches a desired value within a given time. A mathematical formulation of the room heating transient phenomenon is constructed in a dimensionless form. Using an integral approximate solution an analytical expression for this coefficient is provided and it is verified by diagrams adopted by DIN 4701. Copyright © 2003 John Wiley & Sons, Ltd.     

Solving regularized least squares with qualitatively controlled adaptive cross‐approximated matrices

The adaptive cross‐approximation (ACA) technique is applied to accelerating an inverse‐problem solver that estimates charge distribution on a dielectric spacer. The ACA generates an approximated system‐matrix that enables us to carry out high‐speed inverse calculation. We designed an approximation procedure based on ACA with some additional concepts, that is, (a) partitioning of matrix based on algebraic information, (b) approximation quality control based on matrix norms, and so on. The tested solver (LSQR for regularized least squares) with ACA demonstrates about 10 times faster performance than that without ACA. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(3): 10–18, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20326     

浆砌石衬砌在渠道防渗中的应用及对策

总结了浆砌石应用的历史,介绍了浆砌石的结构特性和施工工艺,从造价方面、防渗效果及施工三方面分析了浆砌石衬砌主要存在的问题,并提出了相应的解决对策,指出浆砌石衬砌在渠道防渗应用中应控制施工质量,从而更好地提高防渗效果。     

FEM model of the ohmic resistance of IP-SOFCs

In the present work, the ohmic resistance of an integrated planar-SOFC (IP-SOFC) has been evaluated by developing a model whose equations have been solved numerically through an FEM method. The model allows to estimate the distribution of voltage and current density in the cell. A comparison between simulated and experimental data of area specific resistance is reported, which shows satisfactory agreement. The mathematical model has also been used to carry out some parametric studies for optimisation purposes. Indeed, a reduction in cell pitch length and an increase in electrode thickness are predicted to lead to a reduction in ohmic losses in IP-SOFCs.