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Showing 1 to 20 of 30 for “"reduced basis"”.
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Reduced basis method for Boltzmann equation
… of the problem. The next step is to perform the reduced basis analysis of the equation using these accurate finite element solutions. We conclude the project by verifying that the orthonormal reduced Basis method based on the greedy algorithm converges rapidly over the chosen test space.
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Reduced basis method for quantum models of crystalline solids
… We present in this thesis the application of the reduced basis method in accurate and rapid evaluations of outputs associated with some nonlinear eigenvalue problems related to electronic structure calculations. The reduced basis method provides a systematic procedure by which efficient basis sets …
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A certified reduced basis approach to PDE-constrained optimization
… surrogate models. This work builds on the reduced basis (RB) method, a model reduction method that allows efficient and reliable reduced order approximations for a large class of parametrized PDEs. Traditionally, RB models are generated during a computationally expensive offline phase for a …
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Reduced-basis output bound methods for parametrized partial differential equations
… presented. To achieve efficiency we employ the reduced-basis method: a weighted residual Galerkin-type method, where the solution is projected onto low-dimensional spaces with certain problem-specific approximation properties. Reliability is obtained by a posteriori error estimation methods - …
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Reduced basis approximation and error estimation of parametrized partial differential equations
The student, Peter Sentz, submitted this Dissertation for approval on 2022-07-11 at 14:00.
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Reduced basis output bounds for linear elasticity : application to microtruss structures
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001.
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Reduced-basis methods applied to problems in elasticity : analysis and applications
… components are: (i) rapidly convergent global reduced-basis approximations - projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space (Accuracy); (ii) a posteriori error estimation - relaxations of the error-residual …
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A reduced-basis method for input-output uncertainty propagation in stochastic PDEs
… problems. This work proposes a non-intrusive reduced-basis method for the rapid and reliable evaluation of the statistics of linear functionals of stochastic PDEs. Our approach is based on constructing a reduced-basis model for the quantity of interest that enables to solve the full problem …
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Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations
… ingredients are: (i) rapidly convergent reduced-basis approximations - Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter-time space; (ii) a posteriori error estimation - relaxations of the …
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Discrete and Continuous Nonconvex Optimization: Decision Trees, Valid Inequalities, and Reduced Basis Techniques
… through the generation of valid inequalities and reduced representations, along with the design and implementation of efficient algorithms. We first conduct a quantitative analysis for a strategic risk management problem that involves allocating certain available failure-mitigating and …
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Reduced basis method for 2nd order wave equation : application to one-dimensional seismic problem
… source x8 and the occurring time T. The reduced basis method, the offline-online computational procedures and the associated a posteriori error estimation are developed. We have shown that the reduced basis pressure distribution is an accurate approximation to the finite element pressure …
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Reduced-basis methods applied to locally non-affine and locally non-linear partial differential equations
… this issue we present and compare two new reduced basis techniques for the rapid and reliable prediction of linear functional outputs of linear elliptic partial differential equations with locally non-affine parameter dependence: the partition of unity method (PUM) and the minimax …
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Reduced basis approximation and a posteriori error estimation for non-coercive elliptic problems : applications to acoustics
… ingredients are: (i) rapidly convergent reduced basis approximations - Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter-time space; (ii) a posteriori error estimation - relaxations of the …
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Efficient reduced-basis approximation of scalar nonlinear time-dependent convection-diffusion problems, and extension to compressible flow problems
In this thesis, the reduced-basis method is applied to nonlinear time-dependent convection-diffusion parameterized partial differential equations (PDEs). A proper orthogonal decomposition (POD) procedure is used for the construction of reduced-basis approximation for the field variables. In the …
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Hessian-based model reduction with applications to initial-condition inverse problems
(cont.) Reduced-order models that are able to approximate output quantities of interest of high-fidelity computational models over a wide range of input parameters play an important role in making tractable large-scale optimal design, optimal control, and inverse problem applications. We consider …
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Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter dependent shocks
… a linear superposition of parameter-dependent basis. The sought after parametric reduced-basis arise from solutions of linear transport equations. Key to the proposed approach is the observation that the optimal transport velocities are typically smooth and continuous, despite the solution …
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Experimental determination of the thermal properties of multi-layered surfaces
… outlines a project which aims to use Certified Reduced Basis and General Empirical Interpolation Methods to conduct rapid, inexpensive, computationally simple thermal property estimation for the purpose of material identification. In this specific case, thermal conductivity and diffusivity were …
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Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations
… equations (PDEs) using techniques of reduced-order modeling. Parameterized equations of this type arise in numerous mathematical models. In some settings, e.g. sensitivity analysis, design optimization, and uncertainty quantification, it is necessary to compute discrete solutions of …
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Model-constrained optimization methods for reduction of parameterized large-scale systems
… employ a projection framework that utilizes a reduced-space basis. The basis is usually formed as the span of a set of solutions of the large-scale system, which are computed for selected values (samples) of input parameters and forcing inputs. In existing model reduction techniques, choosing …
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