1# Library to Find Best eBook for Read
Author : Dirk Klindworth
Release : 2011
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Certified Reduced Basis Methods for Parametrized Parabolic Partial Differential Equations with Non-affine Source Terms by : Dirk Klindworth
Download or read book Certified Reduced Basis Methods for Parametrized Parabolic Partial Differential Equations with Non-affine Source Terms written by Dirk Klindworth. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin A. Grepl
Release : 2011
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Certified Reduced Basis Methods for Nonaffine Linear Time-varying Partial Differential Equations by : Martin A. Grepl
Download or read book Certified Reduced Basis Methods for Nonaffine Linear Time-varying Partial Differential Equations written by Martin A. Grepl. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt:
Author : National Aeronautics and Space Administration (NASA)
Release : 2018-06-19
Genre :
Kind : eBook
Book Rating : 370/5 ( reviews)
Book Synopsis Reliable Real-Time Solution of Parametrized Partial Differential Equations by : National Aeronautics and Space Administration (NASA)
Download or read book Reliable Real-Time Solution of Parametrized Partial Differential Equations written by National Aeronautics and Space Administration (NASA). This book was released on 2018-06-19. Available in PDF, EPUB and Kindle. Book excerpt: We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. Prudhomme, C. and Rovas, D. V. and Veroy, K. and Machiels, L. and Maday, Y. and Patera, A. T. and Turinici, G. and Zang, Thomas A., Jr. (Technical Monitor) Langley Research Center
Author : Dimitrios Vasileios Rovas
Release : 2003
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Reduced-basis Output Bound Methods for Parametrized Partial Differential Equations by : Dimitrios Vasileios Rovas
Download or read book Reduced-basis Output Bound Methods for Parametrized Partial Differential Equations written by Dimitrios Vasileios Rovas. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: 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 low-dimensional spaces with certain problem-specific approximation properties. Reliability is obtained by a posteriori error estimation methods - relaxations of the standard error-residual equation that provide inexpensive but sharp and rigorous bounds for the error in outputs of interest. Special affine parameter dependence of the differential operator is exploited to develop a two-stage off-line/on-line blackbox computational procedure. In the on-line stage, for every new parameter value, we calculate the output of interest and an associated error bound. The computational complexity of the on-line stage of the procedure scales only with the dimension of the reduced-basis space and the parametric complexity of the partial differential operator; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. The theory and corroborating numerical results are presented for: symmetric coercive problems (e.g. problems in conduction heat transfer), parabolic problems (e.g. unsteady heat transfer), noncoercive problems (e.g. the reduced-wave, or Helmholtz, equation), the Stokes problem (e.g flow of highly viscous fluids), and certain nonlinear equations (e.g. eigenvalue problems).
Author : Jan S Hesthaven
Release : 2015-08-20
Genre : Mathematics
Kind : eBook
Book Rating : 700/5 ( reviews)
Book Synopsis Certified Reduced Basis Methods for Parametrized Partial Differential Equations by : Jan S Hesthaven
Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven. This book was released on 2015-08-20. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
