Concept

Direct multiple shooting method

Related publications (21)

Efficient algorithms for wave problems

Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...

EPFL2021

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

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

Dominique Bonvin

2016

An Adjoint Approach for Stabilizing the Parareal Method

Jan Sickmann Hesthaven, Allan Svejstrup Nielsen, Yvon Maday

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

A Parareal Method for Time-fractional Differential Equations

Jan Sickmann Hesthaven

In this paper, a parareal method is proposed for the parallel-in-time integration of time-fractional differential equations (TFDEs). It is a generalization of the original parareal method, proposed for classic differential equations. To match the global fe ...

Elsevier2015

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, Flavio Maurizio Mor, Sylvia Jeney

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

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