1,720,976 research outputs found
An Empirical Interpolation and Model-Variance Reduction Method for Computing Statistical Outputs of Parametrized Stochastic Partial Differential Equations
Full text linkWe present an empirical interpolation and model-variance reduction method for the fast and reliable computation of statistical outputs of parametrized stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the real-time computation of reduced basis (RB) outputs approximating high-fidelity outputs computed with the hybridizable discontinuous Galerkin (HDG) discretization; (2) the empirical interpolation for an efficient offline-online decoupling of the parametric and stochastic inuence; and (3) a multilevel variance reduction method that exploits the statistical correlation between the low-fidelity approximations and the high-fidelity HDG dis- cretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the RB approximations. Fur- thermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the RB approximations and the size of Monte Carlo samples to achieve a given error tolerance. In addition, we extend the method to compute estimates for the gradients of the statistical out- puts. The proposed method is particularly useful for stochastic optimization problems where many evaluations of the objective function and its gradient are required
A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations
Full text linkWe present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method
Simulation methods for plasmonic structures
No full textThesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017.Cataloged from PDF version of thesis.Includes bibliographical references (pages 129-148).In the recent years there has been a growing interest in studying electromagnetic wave propagation at the nanoscale. The interaction of light with metallic nanostructures produces a collective excitation of conduction electrons at the metal surface, also known as surface plasmons. These plasmonic resonances enable an unprecedented control of light by confining the electromagnetic field to regions well beyond the diffraction limit, thereby leading to nearfield enhancements of the incident wave of several orders of magnitude. These remarkable properties have motivated the application of plasmonic devices in sensing, nano-resolution imaging, energy harvesting, nanoscale electronics and cancer treatment. Despite state-of-the-art nanofabrication techniques are used to realize plasmonic devices, their performance is severely impacted by fabrication uncertainties arising from extreme manufacturing constraints. Mathematical modeling and numerical simulation are therefore essential to accurately predict the response of the physical system, and must be incorporated in the design process. Nonetheless, plasmonic simulations present notable challenges. From the physical perspective, the realistic behavior of conduction electrons in metallic nanostructures is not captured by Maxwell's equations, thus requiring additional modeling. From the simulation perspective, the disparity in length scales stemming from the extreme field localization exceeds the capabilities of most numerical simulation schemes. In addition, relevant data such as optical constants or geometry specifications are typically subject to measurement and manufacturing errors, hence simulations need to accommodate uncertainty in the data. In this thesis we present a collection of numerical methods to efficiently simulate electromagnetic wave propagation through metallic nanostructures. Firstly, we develop the hybridizable discontinuous Galerkin (HDG) method for Maxwell's equations augmented with the hydrodynamic model for metals, which accounts for the nonlocal interactions between electrons that become predominant at nanometric regimes. Secondly, we develop a reduced order modeling (ROM) framework for Maxwell's equations with the HDG method, enabling the incorporation of material and geometric uncertainties in the simulations. The result is a family of surrogate models that produces accurate yet inexpensive simulations of plasmonic devices. Finally, we apply these approaches to the study of periodic annular nanogaps, and present parametric analyses, verification with experimental data and design of novel structures.by Ferran Vidal-Codina.Ph. D
A reduced-basis method for input-output uncertainty propagation in stochastic PDEs
No full textThesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 123-132).Recently there has been a growing interest in quantifying the effects of random inputs in the solution of partial differential equations that arise in a number of areas, including fluid mechanics, elasticity, and wave theory to describe phenomena such as turbulence, random vibrations, flow through porous media, and wave propagation 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 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 very efficiently. In particular, we apply a reduced-basis technique to the Hybridizable Discontinuous Galerkin (HDG) approximation of the underlying PDE, which allows for a rapid and accurate evaluation of the input-output relationship represented by a functional of the solution of the PDE. The method has been devised for problems where an affine parametrization of the PDE in terms of the uncertain input parameters may be obtained. This particular structure enables us to seek an offline-online computational strategy to economize the output evaluation. Indeed, the offline stage (performed once) is computationally intensive since its computational complexity depends on the dimension of the underlying high-order discontinuous finite element space. The online stage (performed many times) provides rapid output evaluation with a computational cost which is several orders of magnitude smaller than the computational cost of the HDG approximation. In addition, we incorporate two ingredients to the reduced-basis method. First, we employ the greedy algorithm to drive the sampling in the parameter space, by computing inexpensive bounds of the error in the output on the online stage. These error bounds allow us to detect which samples contribute most to the error, thereby enriching the reduced basis with high-quality basis functions. Furthermore, we develop the reduced basis for not only the primal problem, but also the adjoint problem. This allows us to compute an improved reduced basis output that is crucial in reducing the number of basis functions needed to achieve a prescribed error tolerance. Once the reduced bases have been constructed, we employ Monte-Carlo based sampling methods to perform the uncertainty propagation. The main achievement is that the forward evaluations needed for each Monte-Carlo sample are inexpensive, and therefore statistics of the output can be computed very efficiently. This combined technique renders an uncertainty propagation method that requires a small number of full forward model evaluations and thus greatly reduces the computational burden. We apply our approach to study the heat conduction of the thermal fin under uncertainty from the diffusivity coefficient and the wave propagation generated by a Gaussian source under uncertainty from the propagation medium. We shall also compare our approach to stochastic collocation methods and Monte-Carlo methods to assess the reliability of the computations.by Ferran Vidal-Codina.S.M
Proyecto constructivo de una E.D.A.R. y colectores en Orís (Osona)
No full textEl proyecto de construcción de la Estación Depuradora de Aguas Residuales
(E.D.A.R.) para el municipio de Orís es una de las actuaciones previstas en el Plan de
Saneamiento y Depuración de Aguas Residuales Urbanas de Catalunya, aprobado por
el Gobierno de la Generalitat en fecha de 7 de noviembre de 1995.
Actualmente las aguas residuales del núcleo de Orís son vertidas sin tratamiento
previo en las aguas del río Ter, que discurre en sus alrededores. Dando lugar a una
situación sanitario-ambiental degradada.
El PSARU 2005 se enmarca dentro de la directiva 91/271/CEE sobre el tratamiento de
aguas residuales urbanas y la directiva 2000/60/CE mediante la cual se establece un
marco comunitario de actuación en el ámbito de política de aguas. Dicho programa de
saneamiento tiene por objetivo la definición de todas las actuaciones destinadas a la
reducción de la contaminación originada por el uso doméstico del agua.
El término municipal de Orís se encuentra englobado dentro de las infraestructuras
propuestas por el PSARU 2005. La construcción de la E.D.A.R. de Orís y los
correspondientes colectores están incluidos en el segundo escenario de actuación
como consecuencia del obligado cumplimiento de la directiva europea 91/271/CE.
Por esta razón, se decide redactar como Proyecto Final de Carrera, el Proyecto
Constructivo de la Estación Depuradora de Aguas Residuales de Orís, situado en la
comarca de Osona
Optimal collapse simulator for three-dimensional structures
Full text linkIn this project limit analysis for 3D structures is studied. The goal is to obtain for a certain structure the load factor that applied to the external loads induces collapse to the structure. The static theorem of limit analysis is the theoretical basis for the Structural Collapse Simulator (SCS), that is nding a stress distribution in equilibrium that does not violate yield criteria anywhere. This theorem is employed combined with linear programming techniques. Thereby a tutorial on LP problems is presented rst. Then a brief summary of the progresses in study of limit analysis for structures is o ered, being a useful introduction for understanding the very nature of SCS functioning. Moreover, limit analysis is developed and written as a LP problem, which consists of the maximization of the collapse load factor subject to
equilibrium and yield criteria.
Two major contributions are presented for nding the collapse load. Firstly,
the yield curve of standard 2D beam cross sections is adaptively approximated with inscribed and circumscribed polygons that yield to lower and upper bounds of respectively. Secondly, an interesting approach for accounting with uniform distributed loads is shown, producing bounding of the load factor. Combining these two techniques the bound gap can be reduced
arbitrarily, observing convergence of the upper and the lower bounds to the exact load factor. A tutorial for using SCS and computing structures is provided, and numerical examples are thoroughly studied in order to illustrate the functioning of the program and the limits of the method. Finally, recent developments and future branches of research are detailed in order to
widen the applicability range of SCS, the most important being the adaptive approximation of the yield surface for 3D beams
Proyecto constructivo de una E.D.A.R. y colectores en Orís (Osona)
No full textEl proyecto de construcción de la Estación Depuradora de Aguas Residuales
(E.D.A.R.) para el municipio de Orís es una de las actuaciones previstas en el Plan de
Saneamiento y Depuración de Aguas Residuales Urbanas de Catalunya, aprobado por
el Gobierno de la Generalitat en fecha de 7 de noviembre de 1995.
Actualmente las aguas residuales del núcleo de Orís son vertidas sin tratamiento
previo en las aguas del río Ter, que discurre en sus alrededores. Dando lugar a una
situación sanitario-ambiental degradada.
El PSARU 2005 se enmarca dentro de la directiva 91/271/CEE sobre el tratamiento de
aguas residuales urbanas y la directiva 2000/60/CE mediante la cual se establece un
marco comunitario de actuación en el ámbito de política de aguas. Dicho programa de
saneamiento tiene por objetivo la definición de todas las actuaciones destinadas a la
reducción de la contaminación originada por el uso doméstico del agua.
El término municipal de Orís se encuentra englobado dentro de las infraestructuras
propuestas por el PSARU 2005. La construcción de la E.D.A.R. de Orís y los
correspondientes colectores están incluidos en el segundo escenario de actuación
como consecuencia del obligado cumplimiento de la directiva europea 91/271/CE.
Por esta razón, se decide redactar como Proyecto Final de Carrera, el Proyecto
Constructivo de la Estación Depuradora de Aguas Residuales de Orís, situado en la
comarca de Osona
Optimal collapse simulator for three-dimensional structures
No full textIn this project limit analysis for 3D structures is studied. The goal is to obtain for a certain structure the load factor that applied to the external loads induces collapse to the structure. The static theorem of limit analysis is the theoretical basis for the Structural Collapse Simulator (SCS), that is nding a stress distribution in equilibrium that does not violate yield criteria anywhere. This theorem is employed combined with linear programming techniques. Thereby a tutorial on LP problems is presented rst. Then a brief summary of the progresses in study of limit analysis for structures is o ered, being a useful introduction for understanding the very nature of SCS functioning. Moreover, limit analysis is developed and written as a LP problem, which consists of the maximization of the collapse load factor subject to
equilibrium and yield criteria.
Two major contributions are presented for nding the collapse load. Firstly,
the yield curve of standard 2D beam cross sections is adaptively approximated with inscribed and circumscribed polygons that yield to lower and upper bounds of respectively. Secondly, an interesting approach for accounting with uniform distributed loads is shown, producing bounding of the load factor. Combining these two techniques the bound gap can be reduced
arbitrarily, observing convergence of the upper and the lower bounds to the exact load factor. A tutorial for using SCS and computing structures is provided, and numerical examples are thoroughly studied in order to illustrate the functioning of the program and the limits of the method. Finally, recent developments and future branches of research are detailed in order to
widen the applicability range of SCS, the most important being the adaptive approximation of the yield surface for 3D beams
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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