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作者： Blaheta, R. Byczanski, P. Kohut, R. Department of Applied Mathematics Institute of Geonics Academy of Sciences of the Czech Republic Studentská 1768 Ostrava 708 00 Czech Republic

This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits of the described methods. We also discuss the case of inexact subproblems, which can frequently arise in the course of hierarchical modelling. © 2002 Mathematical Institute, Academy of Sciences of Czech Republic.

关键词： composite grids computer implementation finite element method inexact subproblems iterative solution numerical experiments

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FUZZY PROJECT SCHEDULING SYSTEM FOR SOFTWARE-DEVELOPMENT

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FUZZY SETS AND SYSTEMS 1994年第1期67卷 101-117页

作者： HAPKE, M JASZKIEWICZ, A SLOWINSKI, R Institute of Computing Science Technical University of Poznan ul. Piotrowo 3a 60-965 Poznan Poland

This paper presents an FPS (Fuzzy Project Scheduling) decision support system applied to software project scheduling. The purpose of the FPS system is to allocate resources (software engineers) among dependent activities (system design, user interface design, modules implementation, modules integration and tests), taking into account one of two criteria: project completion time and maximum lateness, under uncertain time parameters of activities. By time parameters we understand durations, ready times and due dates of particular activities. Uncertainty of these parameters is modelled by means of L-R fuzzy numbers. A general procedure for transforming the fuzzy scheduling problem into a set of associate deterministic problems is based on the use of alpha-cuts. Optimistic and pessimistic schedules are heuristically generated for given alpha-levels. Aggregation of optimistic and pessimistic values of a minimized criterion for all alpha-levels gives a fuzzy result. Comparison of fuzzy result is based on a compensation of areas determined by the membership functions. The FPS system is described and its application to software project management is presented on a real example.

关键词： PROJECT SCHEDULING FUZZY TIME PARAMETERS RENEWABLE RESOURCES DECISION SUPPORT SYSTEM computer implementation SOFTWARE PROJECT MANAGEMENT

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OPTIMAL-DESIGN OF EFFICIENT ACOUSTIC ANTENNA-ARRAYS

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MATHEMATICAL PROGRAMMING 1987年第2期39卷 131-155页

作者： LASDON, LS PLUMMER, J BUEHLER, B WAREN, AD USN CTR UNDERWATER SYSTCODE 3292NEW LONDONCT 06320 CLEVELAND STATE UNIV DEPT COMP & INFORMAT SCICLEVELANDOH 44115

Minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with many convex quadratic constraints and a nonconvex quadratic efficiency constraint. The variables of this problem are a sc... 详细信息

关键词： Acoustic arrays optimal design Lagrangian relaxation nonlinear programming computer implementation

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A FEM approximation of a two-phase obstacle problem and its a posteriori error estimate

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computerS & MATHEMATICS WITH APPLICATIONS 2017年第3期73卷 419-432页

作者： Bozorgnia, Farid Valdman, Jan Inst Super Tecn Dept Math Av Rovisco Pais P-1049001 Lisbon Portugal Univ South Bohemia Fac Sci Inst Math & Biomath Branisovska 31 CR-37005 Ceske Budejovice Czech Republic CAS Inst Informat Theory & Automat Pod Vodarenskou Vezi 4 CZ-18208 Prague 8 Czech Republic

This paper is concerned with the two-phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A solution algorithm is proposed for the construction of the finite element approximation to the two-phase obstacle problem. The algorithm is not based on the primal (convex and nondifferentiable) energy minimization problem but on a dual maximization problem formulated for Lagrange multipliers. The dual problem is equivalent to a quadratic programming problem with box constraints. The quality of approximations is measured by a functional a posteriori error estimate which provides a guaranteed upper bound of the difference of approximated and exact energies of the primal minimization problem. The majorant functional in the upper bound contains auxiliary variables and it is optimized with respect to them to provide a sharp upper bound. A space density of the nonlinear related part of the majorant functional serves as an indicator of the free boundary. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： A free boundary problem A posteriori error analysis Finite element method Dual problem Discretization computer implementation

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IPACS: Integrated Phase-Field Advanced Crack Propagation Simulator. An adaptive, parallel, physics-based-discretization phase-field framework for fracture propagation in porous media

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computer METHODS IN APPLIED MECHANICS AND ENGINEERING 2020年 367卷 113124-113124页

作者： Wheeler, Mary F. Wick, Thomas Lee, Sanghyun Univ Texas Austin Inst Computat Engn & Sci Ctr Subsurface Modeling Austin TX 78712 USA Leibniz Univ Hannover Inst Angew Math AG Wissenschaftl Rechnen Welfengarten 1 D-30167 Hannover Germany Florida State Univ Dept Math 1017 Acad Way Tallahassee FL 32306 USA

In this work, we review and describe our computational framework for solving multiphysics phase-field fracture problems in porous media. Therein, the following five coupled nonlinear physical models are addressed: displacements (geo-mechanics), a phase-field variable to indicate the fracture position, a pressure equation (to describe flow), a proppant concentration equation, and/or a saturation equation for two-phase fracture flow, and finally a finite element crack width problem. The overall coupled problem is solved with a staggered solution approach, known in subsurface modeling as the fixed-stress iteration. A main focus is on physics-based discretizations. Galerkin finite elements are employed for the displacement-phase-field system and the crack width problem. Enriched Galerkin formulations are used for the pressure equation. Further enrichments using entropy-vanishing viscosity are employed for the proppant and/or saturation equations. A robust and efficient quasi-monolithic semi-smooth Newton solver, local mesh adaptivity, and parallel implementations allow for competitive timings in terms of the computational cost. Our framework can treat two-and three-dimensional realistic field and laboratory examples. The resulting program is an in-house code named IPACS (Integrated Phase-field Advanced Crack Propagation Simulator) and is based on the finite element library ***. Representative numerical examples are included in this document. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Phase-field fracture Porous media computer implementation Numerical simulations Handbook IPACS

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Optimal single ordering policy with multiple delivery modes and Bayesian information updates

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computerS & OPERATIONS RESEARCH 2004年第12期31卷 1965-1984页

作者： Choi, TM Li, D Yan, HM Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

We investigate in this paper a retailer's optimal single ordering policy with multiple delivery modes. Due to the existence of different delivery modes, the unit delivery cost (and hence the product cost) is formulated as a decreasing function of the lead-time. Market information can be collected in the earlier stages and used to update the demand forecast by using a Bayesian approach. The trade-off between ordering earlier or later is evident. The former enjoys a lower product cost but suffers a less accurate demand forecast. The latter pays a higher product cost, but benefits from a lower uncertainty in the demand forecast. In this paper, a multi-stage dynamic optimization problem is formulated and the optimal ordering policy is derived using dynamic programming. The characteristics of the ordering policy are investigated and the variance of profit associated with the ordering decision is discussed. Numerical analyses through simulation experiments are carried out to gain managerial insights. implementation tips are also proposed. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： inventory management optimal stopping problem Bayesian normal conjugate family dynamic programming computer implementation

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Optimization of 2D image reconstruction for positron emission mammography using IDL

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computerS IN BIOLOGY AND MEDICINE 2009年第2期39卷 119-129页

作者： Oliveira, N. Matela, N. Bugalho, P. Ferreira, N. Almeida, P. Univ Lisbon Fac Ciencias IBEB Lisbon Portugal Univ Coimbra IBILI P-3000 Coimbra Portugal

The Clear-PEM system is a prototype machine for Positron Emission Mammography (PEM) under development within the Portuguese PET-Mammography consortium. We have embedded 2D image reconstruction algorithms implemented in IDL within the prototype's image analysis package. The IDL implementation of these algorithms proved to be accurate and computationally efficient. In this paper, we present the implementation of the MLEM, OSEM and ART 2D iterative image reconstruction algorithms for PEM using IDL C and IDL implementations are compared using realistic Monte Carlo simulated data. We show that IDL can be used for the easy implementation of image reconstruction algorithms for emission tomography. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Image reconstruction Iterative algorithms Emission tomography Positron emission mammography IDL ART OSEM MLEM computer implementation

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Fortran subroutines for computing approximate solutions of weighted MAX-SAT problems using GRASP

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DISCRETE APPLIED MATHEMATICS 2000年第1-2期100卷 95-113页

作者： Resende, MGC Pitsoulis, LS Pardalos, PM AT&T Labs Res Informat Sci Res Florham Park NJ 07932 USA Univ Florida Dept Ind & Syst Engn Ctr Appl Optimizat Gainesville FL 32611 USA

This paper describes Fortran subroutines for computing approximate solutions to the weighted MAX-SAT problem using a greedy randomized adaptive search procedure (GRASP). The algorithm (Resende, Pitsoulis, and Pardalos, in: D.Z. Du et al. (Ed.), Satisfiability problem: Theory and Applications, Vol. 35 DIMACS Series on Discrete Mathametics and Theoretical computer Science, American Mathematical Society, Providence, RI, 1997, pp. 393-405) is briefly outlined and its implementation is discussed. Usage of the subroutines is considered in detail. The subroutines are tested on a set of test problems, illustrating the tradeoff between running lime and solution quality. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： MAX-SAT problem satisfiability approximate solution heuristic GRASP computer implementation Fortran subroutines

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Shape computations with NURB curves

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AI EDAM-ARTIFICIAL INTELLIGENCE FOR ENGINEERING DESIGN ANALYSIS AND MANUFACTURING 2018年第3期32卷 282-294页

作者： Ensari, Elif Ozkar, Mine Istanbul Tech Univ Fac Architecture TR-34437 Istanbul Turkey

Freeform curves are commonly used in contemporary design practices, especially with digital modeling tools. We investigate facilitating shape subtraction and addition with two-dimensional (planar) non-uniform rational basis-spline (NURB) curves with the codes and conventions of modeling while preserving the visual continuity of curved shapes. Our proposed tool, developed in a common digital modeling environment, automates the adjustment of parameters for tangential continuity of curves in shape rule applications. When the user designates a curve range to subtract from an initial shape and provides a new curved shape to add to it, the tool splits the initial shape, scales and aligns the curve to be added to fit into this range, introduces additional control points at the joining ends of the new curve to preserve continuity and redraws the new curve. We present a sample set of design variations produced using this practical approach which can be utilized as a method or become part of an automated NURB curve manipulation tool for designers.

关键词： computer implementation curve implementation NURB curve grammars shape grammars

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GREEDY RANDOMIZED ADAPTIVE SEARCH PROCEDURES

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JOURNAL OF GLOBAL OPTIMIZATION 1995年第2期6卷 109-133页

作者： FEO, TA RESENDE, MGC UNIV TEXAS DEPT MECH ENGN OPERAT RES GRP AUSTIN TX 78712 USA AT&T BELL LABS MATH SCI RES CTR MURRAY HILL NJ 07974 USA

Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function;the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

关键词： COMBINATORIAL OPTIMIZATION SEARCH HEURISTIC GRASP computer implementation

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