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Showing 1 to 10 of 10 for “"Reduced basis method"”.
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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 reduced-basis method for input-output uncertainty propagation in stochastic PDEs
… through random media. Monte-Carlo based sampling methods, generalized polynomial chaos and stochastic collocation methods are some of the popular approaches that have been used in the analysis of such problems. This work proposes a non-intrusive reduced-basis method for the rapid and reliable …
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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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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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Reduced-basis output bound methods for parametrized partial differential equations
An efficient and reliable method for the prediction of outputs of interest of partial differential equations with affine parameter dependence is presented. To achieve efficiency we employ the reduced-basis method: a weighted residual Galerkin-type method, where the solution is projected onto …
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Stochastic analyses of mechanical and biomedical structures with uncertainties
… matrix theory and the polynomial chaos expansion method. Hybrid techniques combining finite element analysis and Galerkin projection polynomial chaos expansion with either deterministic or stochastic model order reduction are then developed. For deterministic model order reduction, the …
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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 order reduction methods for data assimilation : state estimation and structural health monitoring
… to take advantage of MOR to design computational methods for two classes of problems in data assimilation. In the first part of the thesis, we discuss and extend the Parametrized-Background Data-Weak (PBDW) approach for state estimation. PBDW combines a parameterized best knowledge mathematical …