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Primal-Dual Optimization for Fluids

T. Inglis, M.-L. Eckert, J. Gregson, N. Thuerey
2017 Computer graphics forum (Print)  
We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal-Dual method, to achieve controllable and realistic fluid simulations.  ...  We demonstrate the fast convergence of our Primal-Dual method with a variety of test cases for both model problems.  ...  We proposed a generic version of the Primal-Dual based optimization scheme with fast convergence for general proximal operator subproblems.  ... 
doi:10.1111/cgf.13084 fatcat:aqcubq4lqba5ljtx4izxzeuzau

Primal-Dual Optimization for Fluids

T Inglis, M-L Eckert, J Gregson, N Thuerey
2017 Computer Graphics Forum   unpublished
Thuerey (2017), Primal-Dual Optimization for Fluids. Computer Graphics Forum.  ...  : Fast Primal-Dual Method [1] [1] T.  ... 
fatcat:i6v7etynszd7hpbzjlbtpswkj4

Generalised primal-dual grids for unstructured co-volume schemes

Darren Engwirda
2018 Journal of Computational Physics  
The performance of this new method is tested experimentally, with a range of complex, multi-resolution primal-dual grids generated for various coastal and regional ocean modelling applications.  ...  the simulation of fluid dynamics and hyperbolic transport.  ...  ; seeking to generate optimal primal-dual pairs appropriate for a co-volume type discretisation scheme.  ... 
doi:10.1016/j.jcp.2018.07.025 fatcat:svlmeafbmngnzcgibz3cx6vadq

Complementary variational principles via generalised geometric programming

C.H Scott, T.R Jefferson, B.R Lederer
1979 Journal of Mathematical Analysis and Applications  
For some time now, mathematical programmers have been interested in developing dual problems to various primal optimization problems.  ...  At optimality the following relations hold G@o) + WY,) = 0 <X0??,) = 0 (7) yo E Wxo) (8) where x0 , y. are the extremizing functions of the primal and dual problems respectively.  ... 
doi:10.1016/0022-247x(79)90160-4 fatcat:rrcvyiokrffqbpmedzy6xjadvm

Adjoint-based Control of Fluid-Structure Interaction for Computational Steering Applications

Y. Bazilevs, M.-C. Hsu, M.T. Bement
2013 Procedia Computer Science  
The primal and adjoint, time-dependent fluid-structure interaction (FSI) formulations are presented.  ...  A simple control strategy for FSI problems is formulated based on the information provided by the solution of the adjoint FSI problem.  ...  Because both primal and adjoint FSI problems involve coupling between the primal and dual fluid and structural mechanics degrees of freedom, the control strategy automatically takes FSI coupling into account  ... 
doi:10.1016/j.procs.2013.05.368 fatcat:3pfifgkxsvggxf7mzwcggaxd7u

A Two Stage CVT / Eikonal Convection Mesh Deformation Approach for Large Nodal Deformations [article]

Stephan Schmidt
2014 arXiv   pre-print
A two step mesh deformation approach for large nodal deformations, typically arising from non-parametric shape optimization, fluid-structure interaction or computer graphics, is considered.  ...  The methodology is available as a FEniCS shape optimization add-on at http://www.mathematik.uni-wuerzburg.de/~schmidt/femorph.  ...  primal and dual pressure in 3D.  ... 
arXiv:1411.7663v1 fatcat:z3mfxhlp5fb7lmdpyd5eok42ne

HOT

Patrick Mullen, Pooran Memari, Fernando de Goes, Mathieu Desbrun
2011 ACM SIGGRAPH 2011 papers on - SIGGRAPH '11  
We introduce Hodge-optimized triangulations (HOT), a family of well-shaped primal-dual pairs of complexes designed for fast and accurate computations in computer graphics.  ...  due to the induced orthogonality between primal and dual complexes.  ...  Acknowledgements The authors thank David Cohen-Steiner and Omid Amini for early support and feedback, as well as Pierre Alliez for data.  ... 
doi:10.1145/1964921.1964998 fatcat:fxlwiylk3neq5i6k2jxs7tqbfu

HOT

Patrick Mullen, Pooran Memari, Fernando de Goes, Mathieu Desbrun
2011 ACM Transactions on Graphics  
We introduce Hodge-optimized triangulations (HOT), a family of well-shaped primal-dual pairs of complexes designed for fast and accurate computations in computer graphics.  ...  due to the induced orthogonality between primal and dual complexes.  ...  Acknowledgements The authors thank David Cohen-Steiner and Omid Amini for early support and feedback, as well as Pierre Alliez for data.  ... 
doi:10.1145/2010324.1964998 fatcat:tx4kjox7cbcvdkn5pwf4vvb5em

Page 4352 of Mathematical Reviews Vol. , Issue 86i [page]

1986 Mathematical Reviews  
Starting from a neither primal nor dual feasible solution, we reach an optimal solution in a finite number of steps if it exists.  ...  If there is no optimal solution, then we show that there is no primal feasible or dual feasible solution. We prove the finiteness of this procedure.  ... 

Adaptive finite element methods for partial differential equations [article]

Rolf Rannacher
2003 arXiv   pre-print
Employing duality techniques as used in optimal control theory the error in the target quantities is estimated in terms of weighted 'primal' and 'dual' residuals.  ...  The performance of this Dual Weighted Residual Method is illustrated for a model situation in computational fluid mechanics: the computation of the drag of a body in a viscous flow, the drag minimization  ...  The simultaneous solution of primal and dual eigenvalue problems naturally occurs within an optimal multigrid solver of nonsymmetric eigenvalue problems.  ... 
arXiv:math/0305006v1 fatcat:twjhi7vuu5be7fdcwy3ljszpvu

Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows [article]

Niklas Kühl, Jörn Kröger, Martin Siebenborn, Michael Hinze, Thomas Rung
2020 arXiv   pre-print
Thus both the primal and the dual procedures are performed in pseudo time and the backward integration of the dual approach is performed around the (pseudo-temporal) converged primal field.  ...  The paper analyses the primal and adjoint equations for an engineering model problem.  ...  Their dual scheme rigorously mirrors the primal NVD stencils.  ... 
arXiv:2009.03957v1 fatcat:yakpg63dqvajflbpman6jteeky

A simplex based algorithm to solve separated continuous linear programs

Gideon Weiss
2008 Mathematical programming  
We characterize the form of its optimal solution, and present an algorithm which solves it in a finite number of steps, using simplex pivot iterations.  ...  for optimization.  ...  (ii) The two solutions are optimal and have the same objective value (no duality gap).Note that the dual variables for the integrated constraints (1.2) at time t are π(T − t), and the dual variables for  ... 
doi:10.1007/s10107-008-0217-x fatcat:ayrpdtj46rdljg6aba2vzwbtgq

A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint [article]

Ningyuan Chen, Guillermo Gallego
2021 arXiv   pre-print
The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly.  ...  We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion.  ...  Note that * and * are the primal/dual optimal solutions to the fluid approximation (2).  ... 
arXiv:1812.09234v3 fatcat:bbxbypwwgrf2bh3druvzlqoryi

Krasovskii's method in the stability of network control

Diego Feijer, Fernando Paganini
2009 2009 American Control Conference  
We consider network resource allocation problems based on convex optimization, and their decentralized solutions by means of primal, dual, or primal-dual subgradient control.  ...  We show how Krasovskii's method, that seeks Lyapunov functions which are quadratic forms of the vector field, provides new global stability proofs for various problems of this kind.  ...  Here, using fluid models, we embed the primal-dual case in a class of problems for which Krasovskii's method provides a Lyapunov stability proof.  ... 
doi:10.1109/acc.2009.5160529 dblp:conf/amcc/FeijerP09 fatcat:jvplgo3azbhvdcjt3ejdqt5oyi

Computing multiple solutions of topology optimization problems [article]

Ioannis P. A. Papadopoulos, Patrick E. Farrell, Thomas M. Surowiec
2021 arXiv   pre-print
The algorithm combines the techniques of deflation, barrier methods and primal-dual active set solvers in a novel way.  ...  In this paper, we present an algorithm to perform a systematic exploratory search for the solutions of the optimization problem via second-order methods without a good initial guess.  ...  For values of ρ close to one, α(ρ) is small, permitting fluid flow; for small values of ρ, α(ρ) is very large, restricting fluid flow.  ... 
arXiv:2004.11797v2 fatcat:u34rqqt35zbdpcopkrjjgfslwy
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