6 papers · 1 filter
Schwarz Modulus Based Matrix Splittings with Minimal Polynomial Extrapolation Acceleration for linear complementarity problems arising from American option pricing
Martin J. Gande, Si-Wei Liao, Liu-Di Lu
Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem…
From PDEs constrained optimization to controllability problems via time domain decomposition
Pierre-Henri Cocquet, Liu-Di Lu
This paper focuses on the application of time domain decomposition to solve partial differential equations constrained optimization problems and controllability problems. After cla…
Weak Scalability of time parallel Schwarz methods for parabolic optimal control problems
Liu-Di Lu, Tommaso Vanzan
Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be tre…
Optimized Schwarz methods for heterogeneous heat transfer problems
Martin J. Gander, Liu-Di Lu, Tingting Wu
We present here nonoverlapping optimized Schwarz methods applied to heat transfer problems with heterogeneous diffusion coefficients. After a Laplace transform in time, we derive t…
Non-overlapping Schwarz methods in time for parabolic optimal control problems
Martin Jakob Gander, Liu-Di Lu
We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neum…
New time domain decomposition methods for parabolic optimal control problems II: Neumann-Neumann algorithms
Martin Jakob Gander, Liu-Di Lu
We present new Neumann-Neumann algorithms based on a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, the…