This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms.
The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics.
This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied mathematicians, computer scientists and all scientists using mathematical methods.
Author(s): T Carraro, M Geiger, S Körkel, R Rannacher (eds.)
Series: Contributions in Mathematical and Computational Sciences 9
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 424
Tags: Computational Mathematics and Numerical Analysis; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization; Numeric Computing; Engineering Fluid Dynamics; Applications of Mathematics
Front Matter....Pages i-x
Direct Multiple Shooting and Generalized Gauss-Newton Method for Parameter Estimation Problems in ODE Models....Pages 1-34
Direct and Indirect Multiple Shooting for Parabolic Optimal Control Problems....Pages 35-67
50 Years of Time Parallel Time Integration....Pages 69-113
Direct Multiple Shooting for Nonlinear Optimum Experimental Design....Pages 115-141
Parameter Estimation for High-Dimensional PDE Models Using a Reduced Approach....Pages 143-157
Direct Multiple Shooting for Parabolic PDE Constrained Optimization....Pages 159-181
Multiple Shooting in a Microsecond....Pages 183-201
Preconditioners Based on “Parareal” Time-Domain Decomposition for Time-Dependent PDE-Constrained Optimization....Pages 203-232
Space-Time Discontinuous Galerkin Methods for Optimal Control Problems Governed by Time Dependent Diffusion-Convection-Reaction Equations....Pages 233-261
Reducing Memory Requirements in Scientific Computing and Optimal Control....Pages 263-287
Optimal Control of Heat and Fluid Flow for Efficient Energy Utilization....Pages 289-304
A Unified Approach to Integration and Optimization of Parametric Ordinary Differential Equations....Pages 305-314
A Variational Approach for Physically Based Image Interpolation Across Boundaries....Pages 315-354
Statistics for Model Calibration....Pages 355-375
On Time Discretizations of Fluid-Structure Interactions....Pages 377-400
Parareal Time-Stepping for Limit-Cycle Computation of the Incompressible Navier-Stokes Equations with Uncertain Periodic Dynamics....Pages 401-422
