AARMS (the Atlantic Association for Research in the Mathematical Sciences), the AARMS Collaborative Research Group in Numerical Analysis and Scientific Computing at Memorial University of Newfoundland, , and the Department of Mathematics and Statistics at Dalhousie University will bring researchers interested in parallel methods for partial differential equations to a 5-day workshop in beautiful Halifax, NS, Canada.
The meeting will consist of a 2-day short course on domain decomposition methods for PDEs taught by leading expert Dr. Martin Gander (University of Geneva), research level talks by experts in the area of domain decomposition and parallel methods, and talks by academic and industrial researchers with applied problems who have an interest in exploring parallel techniques. The final part of the workshop will be interactive, linking the applied researchers with domain decomposition experts to investigate the process of introducing parallelism to their simulations.
Travel Claim form for US based participants
Travel claim for all other participants promised funds - Coming Soon
Check workshop program for details!Registration is now live at this link . Registration fees are set at $160 for faculty or participants from industry, $110 for post-doctoral researchers, and $90 for undergraduate or graduate students. The registration fee includes the domain decomposition short course, access to all talks, all breaks and social activities. NOTE: Registration fee cancellations/refunds will only be available for a limited time. Please contact the organizers for details. Please contact me (rhaynes AT mun.ca) if you have questions about the workshop before you register.
There are three ways to participate in the meeting
Many simulations must be followed over time intervals that are long compared to the shortest timescales in the system, e.g., convective versus acoustic timescales in aerodynamics, ocean turnover versus gravity wave timescales in climate, plasma discharge versus Alfven timescales in tokamaks, piston travel versus fast reaction timescales in internal combustion. Often, the phenomena associated with the shortest timescales may be assumed to be in equilibrium relative to dynamics of interest; however, they control the computational timestep if an explicit method is used, with the result that even weak scaling cannot be achieved. Often, as well, one would ideally employ a high-order timestepping scheme and take relatively large timesteps for computational economy; however, if operator splitting techniques are used the lower order splitting error thwarts this objective. For these and other reasons, fully implicit methods are increasingly important for the nonlinear multiscale applications that pace large-scale simulations in energy, environment, and other complex systems. The good news is that advances in domain decomposition methods for distributed memory parallel computers, globalization algorithms, and software that implements them without demanding that the user constructs a full Jacobian make implicit methods practical alternatives. Moreover, we argue that computational challenges on the immediate horizon - uncertainty quantification, inverse problems, multiphysics coupling, etc. - are most naturally tackled with fully nonlinearly implicit formulations for the underlying forward problems well in hand. We illustrate these claims for systems governed by partial differential equations.
The main motivation to build a roust coarse space for a two-level additive Schwarz method is to achieve scalability when solving highly heterogeneous problems i.e. for which the convergence properties do not depend on the variation of the coefficient. Recently, for scalar elliptic problems, operator dependent coarse spaces have been built in the case where coefficients are not resolved by the subdomain partition. A very useful tool for building coarse spaces for which the corresponding two-level method is robust, regardless of the partition into subdomains and of the coefficient distribution, is the solution of local generalised eigenvalue problems. In this spirit, for the Darcy problem, we proposed to solve local generalised eigenvalue problems on overlapping coarse patches and local contributions are then "glued together" via a partition of unity to obtain a global coarse space. We proposed a coarse space construction based on Generalized Eigenproblems in the Overlap (which we will refer to as the GenEO coarse space). This particular construction has been applied successfully to positive definite systems of PDEs discretized by finite elements with only a few extra assumptions.
In optimal control problems, the goal is to find, for a given mechanical or biological system, the forcing function with minimal cost that drives the system to a desired target state. The numerical solution of optimal control problems under PDE constraints has become an active area of research in the past decade, with a growing list of applications such as the control of fluid flow governed by the Navier-Stokes equations, quantum control and medical applications related to the optimization of radiotherapy administration. When the governing PDE is parabolic, one must solve a coupled system of two PDEs, one forward in time (the state PDE) and another backward in time (the adjoint PDE). The tight coupling between these equations leads to extreme computational and storage requirements, so parallelization is essential. A natural idea is to apply Schwarz preconditioners to the large space-time discretized problem. Because the problem is essentially a two-point boundary value problem in time, it is possible to parallelize in time just as effectively as in space. We present a convergence analysis for a class of Schwarz methods applied to a decomposition of the time horizon into many subintervals. We show that just applying a classical Schwarz method in time already implies better transmission conditions than the ones usually used in the elliptic case, and we propose an even better variant based on optimized Schwarz theory.
Time parallel time integration methods have received renewed interest over the last decade because of the advent of massively parallel computers, which is mainly due to the clock speed limit reached on today's processors. When solving time dependent partial differential equations, the time direction is usually not used for parallelization. But when parallelization in space saturates, the time direction offers itself as a further direction for parallelization. The time direction is however special, and for evolution problems there is a causality principle: the solution later in time is affected (it is even determined) by the solution earlier in time, but not the other way round. Algorithms trying to use the time direction for parallelization must therefore be special, and take this very different property of the time dimension into account. I will show in this talk how time domain decomposition methods were invented, and give an overview of the existing techniques. Time parallel methods can be classified into four different groups: methods based on multiple shooting, methods based on domain decomposition and waveform relaxation, space-time multigrid methods and direct time parallel methods. I will show for each of these techniques the main inventions over time by choosing specific publications and explaining the core ideas of the authors. This talk is for people who want to quickly gain an overview of the exciting and rapidly developing area of research on time parallel methods.
The purpose of this presentation is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDE). The presentation is kept as much as possible at an elementary level with a special focus on the definitions of these methods in terms both of PDEs and of the sparse matrices arising from their discretizations. We also provide implementations written in an open source finite element software FreeFem++ linked to the MPI-C++ framework HPDDM. In addition, we consider a number of methods that are not present in other libraries.
Reference: V. Dolean, P. Jolivet and F. Nataf, Introduction to Domain Decomposition Methods: algorithms, theory and parallel implementation", 2015.
The university dorms at Dalhousie are the most economical choice for accommodations.
NEW!! Reservations can be made by fax: 902-494-1219, e-mail: stay@dal.ca, or phone: 902-494-8840 (local) or 1-888-271-9222
We have 30 rooms per night from Aug. 1st (day after the AARMS summer school ends) up to including the 7th (check out on the 8th). Cost for Student single rooms is $32.65 (tax in) and for Casual single rooms (apparently nicer than the student rooms?) the cost is $49.50 (taxes in).
We have also reserved a block of rooms at the Cambridge Suites Hotel, please make your own reservations using
Everyone (students, faculty, invited experts!) are responsible for booking and paying for their own accomodations and travel arrangements! Anyone receiving (partial) reimbursements will pay for all of their expenses and submit a travel claim form at the end of the workshop. All participants are expected to have a means of paying for all expenses (travel, food, accommodations) during the workshop.
Local information about Halifax, getting here and so on, is available
Opening Reception: Monday August 3 @ 6pm Cambridge Suites Hotel Map
Pub Night: Thursday August 6 @ 5:30 pm Tug's Pub Map
Atlantic Association for Research in the Mathematical Sciences
National Science Foundation (US)
Natural Science and Engineering Research Council of Canada
Springboard AtlanticThe Fields Institute for Research in Mathematical Sciences
Dept of Mathematics and Statistics, MUN
Dept of Math and Stats, Dalhousie
Dept of Math and Computing Science, Saint Mary's University
Office of the Vice President - Research, MUN
