This paper reviews recent implementation advances and modifications in the continued development of a Concurrent Subspace Optimization (CSSO) algorithm for Multidisciplinary Design Optimization (MDO). The CSSO-MDO alg...
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This paper reviews recent implementation advances and modifications in the continued development of a Concurrent Subspace Optimization (CSSO) algorithm for Multidisciplinary Design Optimization (MDO). The CSSO-MDO algorithm implemented in this research incorporates a Coordination Procedure of System Approximation (CP-SA) for design updates. This study also details the use of a new discipline-based decomposition strategy which provides for design variable sharing across discipline design regimes (i.e., subspaces). A graphical user interface is developed which provides for menu driven execution of MDO algorithms and results display;this new programming environment highlights the modularity of the CSSO algorithm. The algorithm is implemented in a distributed computing environment using the graphical user interface, providing for truly concurrent discipline design. Implementation studies introduce two new multidisciplinary design test problems: the optimal design of a high-performance, low-cost structural system, and the preliminary sizing of a general aviation aircraft concept for optimal performance. Significant time savings are observed when using distributed computing for concurrent design across disciplines. The use of design variable sharing across disciplines does not introduce any difficulties in implementation as the design update in the CSSO-MDO algorithm is generated in the CP-SA. Application of the CSSO algorithm results in a considerable decrease in the number of system analyses required for optimization in both test problems. More importantly, for the fully coupled aircraft concept sizing problem, a significant reduction in the number of individual contributing analyses is observed.
We present a parallel GCD algorithm for sparse multivariate polynomials with integer coefficients. The algorithm combines a Kronecker substitution with a Ben-Or/Tiwari sparse interpolation modulo a smooth prime to det...
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We present a parallel GCD algorithm for sparse multivariate polynomials with integer coefficients. The algorithm combines a Kronecker substitution with a Ben-Or/Tiwari sparse interpolation modulo a smooth prime to determine the support of the GCD. We have implemented our algorithm in C for primes of various sizes and have parallelized it using Cilk C. We compare our implementation with Maple and Magma's serial implementations of Zippel's GCD algorithm. (C) 2020 Elsevier Ltd. All rights reserved.
This paper presents an efficient modular algorithm for the dynamic simulation of systems of multiple flexible robots with multiple concurrent constraints. This research represents an important extension of previous wo...
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This paper presents an efficient modular algorithm for the dynamic simulation of systems of multiple flexible robots with multiple concurrent constraints. This research represents an important extension of previous work in the modular dynamic simulation of complex rigid-body systems. In addition to a summary of the algorithm, the treatment of potentially critical nonlinear strain and kinematic effects is also discussed. The algorithm is validated through several examples, including both series and parallel robot configurations.
In this paper “abstract lifting algorithms” for polynomial equations over a commutative ring with identity element are developed. They lift solutions modulo some ideal I to solutions modulo another ideal J⊂IJ \subse...
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In this paper “abstract lifting algorithms” for polynomial equations over a commutative ring with identity element are developed. They lift solutions modulo some ideal I to solutions modulo another ideal J⊂I (e.g. J=IT). These algorithms are obtained by applying Newton’s method to the polynomial equations and include for example the Hensel-type polynomial factorization algorithms as special cases.
In a distributed network system, data collection devices (e. g., sensors) may operate on fuzzy inputs, thereby generating results that possibly deviate from the reference datum in physical world being sensed. The exte...
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ISBN:
(纸本)9781424453672
In a distributed network system, data collection devices (e. g., sensors) may operate on fuzzy inputs, thereby generating results that possibly deviate from the reference datum in physical world being sensed. The extent of deviation and the time it takes to compute an output result (i.e., inaccuracy and timeliness of event notification) depend on the number of orthogonal information elements, i.e., modes, processed from the sensed inputs. A major issue is the large dimensionality of input data and the resource-constrained system components (i.e., limited amount of processing cycles and network bandwidths). So, there is a tradeoff between the resources expended by a device algorithm to process its input data and the timeliness and accuracy of its output result. Exercising this tradeoff requires a layered construction of sensor algorithms, where each layer processes a subset of modes in the input data and the results are fused to generate a composite output event. The paper provides an information-theoretic model of such layered algorithm designs. The goal is to evaluate the tradeoff between the quality of event detection and the processing/network resources expended, so that the device algorithms can adapt their operations based on resource availability. The paper provides a case study of network topology measurements to corroborate our model.
algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomi...
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ISBN:
(纸本)9781538626269
algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomials with coefficients modulo a radical triangular set over the rational numbers. We have implemented our algorithm using Maple's RECDEN package. We compare our implementation with the procedure RegularGcd in the RegularChains package.
This thesis aims to create efficient algorithms for computing in the ring R = Q[z 1,..., z n ]/T where T is a zero-dimensional triangular set. The presence of zero-divisors in R makes it a computational challenge to u...
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This thesis aims to create efficient algorithms for computing in the ring R = Q[z 1,..., z n ]/T where T is a zero-dimensional triangular set. The presence of zero-divisors in R makes it a computational challenge to use modular algorithms. In particular, there has never been a proper modular algorithm for computing greatest common divisors of polynomials in R[x]. We present two new ways of resolving zero-divisors: Hensel lifting and fault tolerant rational reconstruction, which allows us to create a new modular gcd algorithm for R[x] as well as a new inversion algorithm for R. We have implemented our algorithms in Maple using the recden library, and we show that they outperform the methods currently implemented in Maple's RegularChains package. The method of Hensel lifting for resolving zero-divisors should give rise to other new modular algorithms for computing modulo triangular sets and our applications show that this approach is fruitful.
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