Computational vascular fluid dynamics: problems,models and methods

Computing and Visualization in Science -     

Computational complexity of distributed detection problems with information constraints

For a system consisting of a set of sensors S = {S₁, S₂, …, S_m} and a set of objects O = {O₁, O₂, …, O_n}, there are information constraints given by a relation R S × O such that (S_i, O_j) R if and only if S_i is capable of detecting O_j. Each (S_i, O_j) R is assigned a confidence factor (a positive real number) which is either explicitly given or can be efficiently computed. Given that a subset of sensors have detected obstacles, the detection problem is to identify a subset H O with the maximum confidence value. The computational complexity of the detection problem, which depends on the nature of the confidence factor and the information constraints, is the main focus of this paper. This problem exhibits a myriad of complexity levels ranging from a worst-case exponential (in n) lower bound in a general case to an O(m + n) time solvability. We show that the following simple versions of a detection problem are computationally intractable: (a) deterministic formulation, where confidence factors are either 0 or 1; (b) uniform formulation where (S_i, O_j) R, for all S_i S, O_j O; (c) decomposable systems under multiplication operation. We then show that the following versions are solvable in polynomial (in n) time: (a) single object detection; (b) probabilistically independent detection; (c) decomposable systems under additive and nonfractional multiplicative measures; and (d) matroid systems.     

Computational complexity of some problems involving congruences on algebras

We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a given algebra generated by a set of pairs, and determining whether a given algebra is simple or subdirectly irreducible. We also consider the problem of determining the smallest fully invariant congruence on a given algebra containing a given set of pairs. We prove that this problem is complete for nondeterministic polynomial time.     

Visualization blackboard-visualizing bioelectric fields

A toolkit developed to visualize cardiac electrophysiology is discussed. The geometric models that play a crucial role in the analysis, manipulation, and visualization of cardiac bioelectric data and the two separate data visualization systems developed for quick, flexible viewing of spatially distributed data and for displaying selected frames of data or preparing presentation-quality images are discussed. The first data visualization system, Map 3D, is based on Silicon Graphics' GL graphics library and designed to run on SGI and IBM workstations. The second set of programs is based on ray-traced rendering and distributed computing     

Some problems of field research

For the results of ergonomic research to be of value it must be validated on the shop floor and this involves field experiments. The aim of this article is to formulate some generally applicable ideas on the problems and strategies involved in field research. The points to be made derive from experience of research in the field extending over some 20 years. It is hoped that a realistic assessment of the problems will help contribute to their solution.     

Computational complexity of the minimal committee problem and adjacent problems

The computational complexity of two important special cases of the minimal committee problem (MC), viz., the problem on the minimal committee of finite sets (MCFS) and the problem on the minimal committee of a system of linear algebraic inequalities (MCLE), is studied. Both problems are shown to be NP-hard. Separately, some adjacent problems of integer optimization are shown to be intractable. The efficient approximability threshold is estimated for the MCFS problem, the estimates being allied to the results known for the set cover problem. The intractable and polynomially solvable subclasses of the MCLE problem are given. The problem of the minimal affine separation committee (MASC) is considered in conclusion; the results obtained earlier for the MCLE problem are shown to be valid for this problem as well. Mikhail Yur’evich Khachai. Born 1970 in Krasnotur’insk, Sverdlovsk region. Graduated from the Faculty of Mathematics and Mechanics of Ural State University in Yekaterinburg in 1993 (Mathematics). Received his candidate’s degree (Mathematical Cybernetics) in 1996. Since 1994, he has been at the Institute of Mathematics and Mechanics of the Ural Division of the Russian Academy of Sciences. Since 1997, he has headed the Department of Pattern Recognition at the same institute. Scientific interests: theory and methods of pattern recognition learning, committee (perceptron) decision rules, and theory and methods of improper optimization problems. Author of more than 25 publications, including five in PRIA.     

Computational experiments with algorithms for a class of routing problems

The vehicle routing problem, a generalization of the infamous traveling salesman problem, is a well-known distribution management problem that has been the focus of much research attention. On the other hand, generalizations of arc routing problems, such as the Chinese postman problem, have been comparatively neglected. In a recent paper, we studied a class of capacitated arc routing problems from primarily a theoretical point of view. In this paper, we focus on the development and testing of algorithms for solving the capacitated Chinese postman problem. Extensive computational results are presented and analyzed.     

Computational complexity of counting problems on 3-regular planar graphs

A variety of counting problems on 3-regular planar graphs are considered in this paper. We give a sufficient condition which guarantees that the coefficients of a homogeneous polynomial can be uniquely determined by its values on a recurrence sequence. This result enables us to use the polynomial interpolation technique in high dimension to prove the #P-completeness of problems on graphs with special requirements. Using this method, we show that #3-Regular Bipartite Planar Vertex Covers is #P-complete. Furthermore, we use Valiant’s Holant Theorem to construct a holographic reduction from it to #2,3-Regular Bipartite Planar Matchings, establishing the #P-completeness of the latter. Finally, we completely classify the problems #Planar Read-twice 3SAT with different ternary symmetric relations according to their computational complexity, by giving several more applications of holographic reduction in proving the #P-completeness of the corresponding counting problems.     

Computational experience with algorithms for separable nonlinear least squares problems

Nonlinear least squares problems frequently arise in which the fitting function can be written as a linear combination of functions involving further parameters in a nonlinear manner. This paper outlines an efficient implementation of an iterative procedure originally developed by Golub and Pereyra and successively modified by various authors, which takes advantage of the linear-nonlinear structure, and investigates its performances on various test problems as compared with the standard Gauss-Newton and Gauss-Newton-Marquardt schemes. A preliminary version of this note has been presented at the CNR-GNIM meeting held in Florence, september 1976.     

基于计算思维的教学改革的若干问题

计算思维与教学改革问题成为目前教育界讨论的热点问题,争论激烈,观点很多,本文针对这个问题,阐述了基于计算思维的教学改革的若干问题,并对改革中应该面对的问题给出了自己的观点,以期与同行共同讨论,共同为我国的教育改革献计献策。     

Computational flowfield analyses of hypersonic problems with reacting boundary layer

A mathematical model able to deal with high temperature gas effects in hypersonic flow fields is presented. In order to assess this model, four typical hypersonic applications are considered. The numerical results are presented and compared with experimental data. The effects of the catalyticity of the materials on the heat fluxes are also highlighted.     

Computational experiments with heuristics for two nature reserve site selection problems

Nature reserve site selection has become critical as the human population grows and environmentalists seek ways to preserve species and their natural habitats. Simple tabu searches are developed and tested for two reserve site selection models—the maximal covering species problem and the maximal expected covering problem. The testbed is an Oregon terrestrial vertebrate data set composed of 426 species and 441 hexagonal sites. In addition, an extension to a linearized version of the maximal expected covering problem is proposed and tested.     

Applications of Computational Fluid Dynamics-based methods to problems in computational science

The objective is to describe how some of the attributes of Computational Fluid Dynamics (CFD) can be extended to solve mathematical problems in other disciplines, such as electromagnetics, that are governed by appropriate partial differential equations and boundary conditions. The concept of finite-volume schemes applied to the conservation forms of fluid dynamics equations, such as the Euler and Navier-Stokes equations, is readily extendable to other equations. For example, Maxwell's equations of electromagnetics, when cast in conservation form, can be easily solved using characteristic theory-based CFD methods allowing for a precise implementation of material interface and other boundary conditions.The possibility of extending CFD-based methods to other disciplines has a special significance because increasingly the development of advanced aerospace systems requires a total integration of multidisciplinary technologies (aerodynamics, structures, propulsion, controls, low observables, etc.). Many of the computational issues such as (1) development of implicit/explicit, higher order accurate schemes, (2) complex geometry representation and setup of structured or unstructured grid cells, (3) vector/massively parallel computer architectures and execution/memory requirements, (4) pre/post processing graphics, and (5) user interface/training requirements, are common to many disciplines.The establishment of “Computational Science” to perform interdisciplinary coupled problems addressing many of the above computational issues can certainly benefit from the CFD experience.It is briefly explained how some of the CFD-based methods are applied to study scattering problems for radar cross section (RCS) studies, and simulation of laser/material interaction accounting for melting. Also mentioned are some of the interdisciplinary computations involving CFD, aeroelasticity, and controls. Future studies will include coupling of RCS and CFD in the design process.     

Boundary element methods for magnetostatic field problems: a critical view

For the solution of magnetostatic field problems we discuss and compare several boundary integral formulations with respect to their accuracy, their efficiency, and their robustness. We provide fast boundary element methods which are able to deal with multiple connected computational domains, with large magnetic permeabilities, and with complicated structures with small gaps. The numerical comparison is based on several examples, including a controllable reactor as a real-world problem.     

Some applied problems from random field theory

Some classes of applied problems from random field theory are discussed and methods to solve them are proposed. Examples from various fields of science and technology are considered.     

Computational complexity and solution algorithms for flowshop scheduling problems with the learning effect

In this paper, we analyze the two-machine flowshop problem with the makespan minimization and the learning effect, which computational complexity was not determined yet. First, we show that an optimal solution of this problem does not have to be the ‘permutation’ schedule if the learning effect is taken into consideration. Furthermore, it is proved that the permutation and non-permutation versions of this problem are NP-hard even if the learning effect, in a form of a step learning curve, characterizes only one machine. However, if both machines have learning ability and the learning curves are stepwise then the permutation version of this problem is strongly NP-hard. Furthermore, we prove the makespan minimization problem in m-machine permutation proportional flowshop environment remains polynomially solvable with identical job processing times on each machine even if they are described by arbitrary functions (learning curves) dependent on a job position in a sequence. Finally, approximation algorithms for the general problem are proposed and analyzed.     

Finite-difference vector-potential solution of transient electromagnetic field problems

A finite-difference time–space numerical algorithm for the analysis of transient electromagnetic fields is proposed based on the expression of the field vectors in terms of vector potential functions. The method allows for both integral and finite-difference calculation of the potential functions (PF). Both approaches can be applied in combination. Since it is based on the time-domain integral-equation approach, it reduces the 3D problem to a 2D one, and only the tangential vector potential components are involved in the calculation. The consistency of the method has been proved by simulations of Gaussian pulse propagation in a homogeneous and an open-end microstripline and a thin-plate scattering problem. © 1998 John Wiley & Sons, Inc. Int J RF and Microwave CAE 8: 56–67, 1998.