基于传输线等效法的双腔体屏蔽系数快速算法

传输线等效法（TLM）是一种常用的开孔腔屏蔽系数快速计算方法,在孔缝耦合系数的计算中考虑了孔缝处的场模式,提高了TLM算法在高频段计算屏蔽系数（SE）的准确性。继而将TLM算法推广到开孔双金属腔屏蔽系数的计算,通过将外腔体中任意位置的电压等效为内孔缝处的辐射电压源,计算得到内腔体中任意位置上的屏蔽系数,解决了已有文献中方法的不足。该算法计算结果与CST仿真结果吻合较好。     

Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C

Fast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects

We present a new data structure for a set of n convex simply-shaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting—preprocess a set of n non-intersecting convex simply-shaped flat objects in 3-space, whose xy-projections are fat, for efficient vertical ray shooting queries, (ii) point enclosure—preprocess a set C of n convex simply-shaped fat objects in the plane, so that the k objects containing a query point p can be reported efficiently, (iii) bounded-size range searching— preprocess a set C of n convex fat polygons, so that the k objects intersecting a “not-too-large” query polygon can be reported efficiently, and (iv) bounded-size segment shooting—preprocess a set C as in (iii), so that the first object (if exists) hit by a “not-too-long” oriented query segment can be found efficiently. For the first three problems we construct data structures of size O(λ_s(n)log³n), where s is the maximum number of intersections between the boundaries of the (xy-projections) of any pair of objects, and λ_s(n) is the maximum length of (n, s) Davenport-Schinzel sequences. The data structure for the fourth problem is of size O(λ_s(n)log²n). The query time in the first problem is O(log⁴n), the query time in the second and third problems is O(log³n + klog²n), and the query time in the fourth problem is O(log³n).

We also present a simple algorithm for computing a depth order for a set as in (i), that is based on the solution to the vertical ray shooting problem. (A depth order for , if exists, is a linear order of , such that, if K₁, K₂ and K₁ lies vertically above K₂, then K₁ precedes K₂.) Unlike the algorithm of Agarwal et al. (1995) that might output a false order when a depth order does not exist, the new algorithm is able to determine whether such an order exists, and it is often more efficient in practical situations than the former algorithm.     

Dynamic data structures for fat objects and their applications

We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in or. Our planar structures are actually fitted for a more general class of objects – (β,δ)-covered objects – which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.     

Comparison principles applied to obstacle problems with penalties

Penalty methods form a well known technique to embed elliptic variational inequality problems into a family of variational equations (cf. [6], [13], [17]). Using the specific inverse monotonicity properties of these problems L _∞-bounds for the convergence can be derived by means of comparison solutions. Lagrange duality is applied to estimate parameters involved.

For piecewise linear finite elements applied on weakly acute triangulations in combination with mass lumping the inverse monotonicity of the obstacle problems can be transferred to its discretization. This forms the base of similar error estimations in the maximum norm for the penalty method applied to the discrete problem.

The technique of comparison solutions combined with the uniform boundedness of the Lagrange multipliers leads to decoupled convergence estimations with respect to the discretization and penalization parameters.     

Slope enclosures for functions given by two or more branches

In this paper, we consider the automatic computation of slope enclosures for continuous real functions given by two or more branches, such as piecewise defined nonsmooth functions. We show that a commonly used formula found in the literature does not always provide a slope enclosure for such functions. Furthermore, we prove a similar formula that always holds. AMS subject classification (2000)  65G20     

On a sub-supersolution method for the prescribed mean curvature problem

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub-and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub-and supersolutions are established.     

Approximate colored range and point enclosure queries

In this paper, we formulate two classes of problems, the colored range query problems and the colored point enclosure query problems to model multi-dimensional range and point enclosure queries in the presence of categorical information. Many of these problems are difficult to solve using traditional data structural techniques. Based on a new framework of combining sketching techniques and traditional data structures, we obtain two sets of results in solving the problems approximately and efficiently. In addition, the framework can be employed to attack other related problems by finding the appropriate summary structures.     

Conjugate conduction-natural convection in an enclosure with time-periodic sidewall temperature and inclination

The unsteady conjugate conduction-natural convection in enclosure is of great theoretical significance and is widely encountered in engineering applications in the areas of fluid dynamics and heat transfer. However, there are relatively few efforts to investigate the unsteady flow physics and heat transfer characteristics in the inclined enclosure of finite thickness walls. In the present work, this problem is numerically investigated by a high accuracy multidomain temporal-spatial pseudospectral method. The enclosure is filled with Boussinesq fluid and is bounded by four finite thickness and conductive walls; one of the vertical sidewall is exposed to time-periodic temperature environment while the opposite sidewall holds constant temperature; the top and bottom walls are assumed to be adiabatic. Particular efforts are focused on the effects of three types of influential factors: the wall thermophysical properties, the time-periodic temperature patterns and the inclination, and the time-periodic flow patterns and heat transfer characteristics are presented. Numerical results reveal that within the present parameter range, the heat transfer rate increases almost linearly with the thermal conductivity ratio and thermal diffusivity ratio but decreases with the inclination angle. Moreover, the heat transfer could be enhanced or weakened by selecting different temperature pulsating period in the case of finite thickness wall, while it is always enhanced if the walls are zero thickness. The back heat transfer and heat transfer resonance phenomena are observed, and their relationships with the time-periodic flow patterns and temperature distributions are analyzed. The findings are helpful to the understandings of the fluid flow and heat transfer mechanisms in the related enclosure configurations, and may be of engineering use in thermal design improvement.