DSpace at MIT
(35.360 recursos)
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Mostrando recursos 1 - 20 de 87
1.
Applications of Proper Orthogonal Decomposition for Inviscid Transonic Aerodynamics - Tan, Bui-Thanh; Willcox, Karen E.; Damodaran, Murali
Two extensions to the proper orthogonal decomposition (POD) technique are considered for steady transonic aerodynamic applications. The first is to couple the POD approach with a cubic spline interpolation procedure in order to develop fast, low-order models that accurately capture the variation in parameters, such as the angle of attack or inflow Mach number. The second extension is a POD technique for the reconstruction of incomplete or inaccurate aerodynamic data. First, missing flow field data is constructed with an existing POD basis constructed from complete aerodynamic data. Second, a technique is used to develop a complete snapshots from an incomplete...
2.
Bubble Simulation Using Level Set-Boundary Element Method - Tan, Kiok Lim; Khoo, Boo Cheong; White, Jacob K.
In bubble dynamics, an underwater bubble may evolve from being singly-connected to being toroidal. Furthermore, two or more individual bubbles may merge to form a single large bubble. These dynamics involve significant topological changes such as merging and breaking, which may not be handled well by front-tracking boundary element methods. In the level set method, topological changes are handled naturally through a higher-dimensional level set function. This makes it an attractive method for bubble simulation. In this paper, we present a method that combines the level set method and the boundary element method for the simulation of bubble dynamics. We...
3.
Characterizing Scattering by 3-D Arbitrarily Shaped Homogeneous Dielectric Objects Using Fast Multipole Method - Li, Jian-Ying; Li, Le-Wei
Electromagnetic scattering by 3-D arbitrarily shaped homogeneous dielectric objects is characterized. In the analysis, the method of moments is first employed to solve the combined field integral equation for scattering properties of these three-dimensional homogeneous dielectric objects of arbitrary shape. The fast multipole method, and the multi-level fast multipole algorithm are implemented into our codes for matrix-vector manipulations. Specifically, four proposals are made and discussed to increase convergence and accuracy of iterative procedures (conjugate gradient method). Numerical results are obtained using various methods and compared to each other.
4.
A Comparative Study on Optimization of Constrained Layer Damping for Vibration Control of Beams - Pau, G.S.H.; Zheng, H.; Liu, Guirong
This paper presents a comparison of optimization algorithms for constrained damping (CLD) patchesâ?? layout to minimize the maximum vibration response of the odd modes, which constitutes the dominant acoustic radiation, of a simply-supported beam excited by a harmonic transverse force. An analytical model based on Euler-Bernoulli beam assumptions is derived first to relate the displacement response of the beam with bonded CLD patches and their layout. Four different nonlinear optimization methods/algorithms are then respectively used to optimize the CLD patchesâ?? locations and lengths with aim of minimum displacement amplitude at middle of the beam. The considered methods include subproblem approximation...
5.
Computing Bounds for Linear Functionals of Exact Weak Solutions to Poissonâ??s Equation - Sauer-Budge, A.M.; Huerta, A.; Bonet, J.; Peraire, Jaime
We present a method for Poissonâ??s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization.
6.
Data Smoothing: Research 2002 - Strang, Gilbert
My research is concentrated on applications of linear algebra in engineering, including wavelet analysis and structured matrices. This paper will appear in the book Mathematical Systems Theory (J. Rosenthal and D. Gilliam, editors) IMA Volumes in Mathematics, Springer 2002.
7.
Effect of Column Inlet and Outlet Geometry on Large-scale HPLC - Tan, S.N.; Khoo, Boo Cheong
The separating characteristics of high performance liquid chromatography (HPLC) columns, measured in terms of the height equivalent of a theoretical plate (HETP) and skewness of the eluted peak, are investigated using computational fluid dynamics (CFD). Gradually expanding and contracting sections are introduced at the inlet and outlet, respectively, in columns with and without frits and their performance was compared with that of the conventional columns without expanding and contracting regions.
8.
Generalized Stationary Points and an Interior Point Method for MPEC - Liu, Xinwei; Sun, Jie
Mathematical program with equilibrium constraints (MPEC)has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC.A primal-dual interior point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or linear independence constraint qualification. Under very general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limiting point of the...
9.
Model reduction for active control design using multiple-point Arnoldi methods - Lassaux, G.; Willcox, Karen E.
A multiple-point Arnoldi method is derived for model reduction of computational fluid dynamic systems. By choosing the number of frequency interpolation points and the number of Arnoldi vectors at each frequency point, the user can select the accuracy and range of validity of the resulting reduced-order model while balancing computational expense. The multiple-point Arnoldi approach is combined with a singular value decomposition approach similar to that used in the proper orthogonal decomposition method. This additional processing of the basis allows a further reduction in the number of states to be obtained, while retaining a significant computational cost advantage over the...
10.
Multiparameter Moment Matching Model Reduction Approach for Generating Geometrically Parameterized Interconnect Performance Models - Daniel, Luca; Ong, Chin Siong; Low, Sok Chay; Lee, Kwok Hong; White, Jacob K.
In this paper we describe an approach for generating geometrically-parameterized integrated-circuit interconnect models that are efficient enough for use in interconnect synthesis. The model generation approach presented is automatic, and is based on a multi-parameter model-reduction algorithm. The effectiveness of the technique is tested using a multi-line bus example, where both wire spacing and wire width are considered as geometric parameters. Experimental results demonstrate that the generated models accurately predict both delay and cross-talk effects over a wide range of spacing and width variation.
11.
Nonsmooth Newtonâ??s Method and Semidefinite Optimization - Sun, Jie
We introduce basic ideas of a nonsmooth Newtonâ??s method and its application in solving semidefinite optimization (SDO) problems. In particular, the method can be used to solve both linear and nonlinear semidefinite complementarity problems. We also survey recent theoretical results in matrix functions and stability of SDO that are stemed from the research on the matrix form of the nonsmooth Newtonâ??s method.
12.
Optimization of Passive Constrained Layer Damping Treatments for Vibration Control of Cylindrical Shells - Zheng, H.; Pau, G.S.H.; Liu, Guirong
This paper presents the layout optimization of passive constrained layer damping (PCLD) treatment for vibration control of cylindrical shells under a broadband force excitation. The equations governing the vibration responses are derived using the energy approach and assumed-mode method. These equations provided relationship between the integrated displacement response over the whole structural volume, i.e. the structural volume displacement (SVD), of a cylindrical shell to structural parameters of base structure and multiple PCLD patches, Genetic algorithms (GAs) based penalty function method is employed to find the optimal layout of rectangular PCLD patches with minimize the maximum displacement response of PCLD-treated cylindrical...
13.
Real-Time Optimal Parametric Design of a Simple Infiltration-Evaporation Model Using the Assess-Predict-Optimize (APO) Strategy - Ali, S.; Damodaran, Murali; Patera, Anthony T.
Optimal parametric design of a system must be able to respond quickly to short term needs as well as long term conditions. To this end, we present an Assess-Predict-Optimize (APO) strategy which allows for easy modification of a systemâ??s characteristics and constraints, enabling quick design adaptation. There are three components to the APO strategy: Assess - extract necessary information from given data; Predict - predict future behavior of system; and Optimize â?? obtain optimal system configuration based on information from the other components. The APO strategy utilizes three key mathematical ingredients to yield real-time results which would certainly conform to...
14.
Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations - Oliveira, I.B.; Patera, Anthony T.
The solution of a single optimization problem often requires computationally-demanding evaluations; this is especially true in optimal design of engineering components and systems described by partial differential equations. We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of partial differential equations with affine parameter dependence. The critical ingredients of the method are: (i) reduced-basis techniques for dimension reduction in computational requirements; (ii) an "off-line/on-line" computational decomposition for the rapid calculation of outputs of interest and respective sensitivities in the limit of many queries; (iii) a posteriori error bounds for rigorous uncertainty and feasibility...
15.
Robust Discrete Optimization - Bertsimas, Dimitris J.; Sim, Melvyn
We propose an approach to address data uncertainty for discrete optimization problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. When both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows to control the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0 - 1 discrete optimization problem...
16.
Statistical Error in Particle Simulations of Fluid Flow and Heat Transfer - Hadjiconstantinou, Nicolas G.; Garcia, Alejandro L.; Bazant, Martin Z.; He, Gang
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we present predictions for the error dependence on hydrodynamic parameters and the number of samples taken. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.
17.
Structural Topology Optimization Using a Genetic Algorithm and a Morphological Representation of Geometry - Tai, Kang; Wang, Shengyin; Akhtar, Shamim; Prasad, Jitendra
This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using a genetic algorithm (GA). The geometry representation scheme works by defining a skeleton that represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any GA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a directed graph which reflects this underlying topology so that the genetic crossover and mutation operators of the GA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure...
18.
Summary Conclusions on Computational Experience and the Explanatory Value of Condition Measures for Linear Optimization* - Ordóñez, Fernando; Freund, Robert M.
The modern theory of condition measures for convex optimization problems was initially developed for convex problems in conic format, and several aspects of the theory have now been extended to handle non-conic formats as well. In this theory, the (Renegar-) condition measure C(d) for a problem instance with data d=(A,b,c) has been shown to be connected to bounds on a wide variety of behavioral and computational characteristics of the problem instance, from sizes of optimal solutions to the complexity of algorithms. Herein we test the practical relevance of the condition measure theory, as applied to linear optimization problems that one...
19.
Aerodynamic Shape Design of Transonic Airfoils Using Hybrid Optimization Techniques and CFD - Xing, X.Q.; Damodaran, Murali; Teo, Chung Piaw
This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to...
20.
Fast Methods for Bimolecular Charge Optimization - Bardhan, Jaydeep P.; Lee, J.H.; Kuo, Shihhsien; Altman, Michael D.; Tidor, Bruce; White, Jacob K.
We report a Hessian-implicit optimization method to quickly solve the charge optimization problem over protein molecules: given a ligand and its complex with a receptor, determine the ligand charge distribution that minimizes the electrostatic free energy of binding. The new optimization couples boundary element method (BEM) and primal-dual interior point method (PDIPM); initial results suggest that the method scales much better than the previous methods. The quadratic objective function is the electrostatic free energy of binding where the Hessian matrix serves as an operator that maps the charge to the potential. The unknowns are the charge values at the charge...
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