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Concept

Direct multiple shooting method

Related publications (11)

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Jan Sickmann Hesthaven

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...

SPRINGER/PLENUM PUBLISHERS2020

Dynamic Optimization of Constrained Semi-Batch Processes Using Pontryagin’s Minimum Principle – An Effective Quasi-Newton Approach

Dominique Bonvin

This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirect methods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise ...

Elsevier2017

Communication-aware adaptive parareal with application to a nonlinear hyperbolic system of partial dierential equations

Jan Sickmann Hesthaven, Allan Svejstrup Nielsen, Gilles Brunner

In the strong scaling limit, the performance of conventional spatial domain decomposition techniques for the parallel solution of PDEs saturates. When sub-domains become small, halo-communication and other overheard come to dominate. A potential path beyon ...

2017

Fault Tolerance in the Parareal Method

Jan Sickmann Hesthaven, Allan Svejstrup Nielsen

Parallel-in-time integration is an often advocated approach for extracting parallelism in the solution of PDEs beyond what is possible using spacial domain decomposition tech- niques. Due to the comparatively low parallel efficiency of parallel-in-time int ...

Assoc Computing Machinery2016

An Adjoint Approach for Stabilizing the Parareal Method

Jan Sickmann Hesthaven, Allan Svejstrup Nielsen

The parareal algorithm seeks to extract parallelism in the time-integration direction of time-dependent differential equations. While it has been applied with success to a wide range of problems, it suffers from some stability issues when applied to non-di ...

2015

Enumeration-based approach to solving parametric linear complementarity problems

Colin Neil Jones

This paper presents a solution method for parametric linear complementarity problems (PLCP) that relies on an enumeration technique to discover all feasible bases. The enumeration procedure is based on evaluating all possible combinations of active constra ...

Elsevier2015

Calibration of optical tweezers with non-spherical probes via high-resolution detection of Brownian motion

László Forró, Richard Gaal, Sylvia Jeney, Flavio Maurizio Mor

Optical tweezers are commonly used and powerful tools to perform force measurements on the piconewton scale and to detect nanometer-scaled displacements. However, the precision of these instruments relies to a great extent on the accuracy of the calibratio ...

Elsevier Science Bv2015

On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method

Jan Sickmann Hesthaven

We propose a modified parallel-in-time - parareal-multi-level time integration method that, in contrast to previously proposed methods, employs a coarse solver based on a reduced model, built from the information obtained from the fine solver at each itera ...

Springer Int Publishing Ag2014

Splitting methods in control

Colin Neil Jones, Ye Pu, Georgios Stathopoulos, Alexander Szücs

The need for optimal control of processes under a restricted amount of resources renders first order optimization methods a viable option. Although computationally cheap, these methods typically suffer from slow convergence rates. In this work we discuss t ...

IEEE2014

On the evaluation of hyper-singular double normal derivative kernels in surface integral equation methods

Juan Ramon Mosig, Athanasios Polymeridis

A stable and efficient numerical scheme for the evaluation of surface integrals with 1/R-3-type singularities is presented. The method is based on the combination of the direct evaluation method and the singularity subtraction technique. The proposed metho ...

Elsevier2013

Spectral element approximation of the incompressible Navier-Stokes equations in a moving domain and applications

In this thesis we address the numerical approximation of the incompressible Navier-Stokes equations evolving in a moving domain with the spectral element method and high order time integrators. First, we present the spectral element method and the basic to ...

EPFL2009