Abstract : Many applications in computational sciences and engineering involve multiple physical quantities. Accurate simulations of multiphysics problems involve the solution of large sparse linear equation systems consisting of blocks that correspond to the different physics and their coupling. This has to be taken into account when designing scalable and efficient solvers for such kind of problems.
This minisymposium addresses the development and implementation of the solution strategies for large-scale complex multiphysics systems as well as the presentation of results on modern supercomputers.
01054 (1/3) : 4D @E507 [Chair: Alexander Heinlein]
[01909] On the Use of Algebraic Multigrid in Various Applications on High Performance Computers
Format : Talk at Waseda University
Author(s) :
Ulrike Meier Yang (Lawrence Livermore National Laboratory)
Abstract : The hypre software library provides a variety of parallel linear solvers implemented for high performance computers. Its focus is on algebraic multigrid methods (AMG), which provide excellent scalability. With the increasing inclusion of accelerators into current and future high-performance computers, various new programming models have been added to take advantage of the increased performance potential of GPUs. This talk will discuss porting challenges and present results of use of hypre’s GPU-enabled multigrid solvers within several application codes.
[03924] Implications of multiphysics problems in multigrid methods from a linear algebra view point
Format : Talk at Waseda University
Author(s) :
Matthias Bolten (University of Wuppertal)
Abstract : Multiphysics problems require special attention in multigrid methods, as standards methods often do not converge. To overcome this, different approaches have been considered, e.g, special smoothers and special grid transfer and coarse grid selection. We are studying methods for block matrices, as they arise when systems of PDEs are considered. Different approaches for block matrices are presented, including block smoothers as well as analysis of multigrid methods resulting in requirements on grid transfer operators.
[03818] Parallel scalable solvers for Helmholtz problems
Format : Talk at Waseda University
Author(s) :
Cornelis Vuik (Delft University of Technology)
Jinqiang Chen (Delft University of Technology)
Vandana Dwarka (Delft University of Technology)
Abstract : A matrix-free, parallel multi-level deflation preconditioning method is proposed for Helmholtz problems. The method integrates the geometric multi-grid-based Complex Shifted Laplace Preconditioner (CSLP) and higher-order deflation, employing re-discretization schemes derived from Galerkin coarsening approach for a matrix-free parallel implementation. The method shows close to wavenumber-independent convergence and satisfactory strong, and weak parallel scalability. Numerical experiments demonstrate the effectiveness of our approach for complex mo problems, solving large-scale heterogeneous Helmholtz problems with minimized pollution error.
[02018] Reynolds-robust preconditioners for the stationary incompressible viscoresistive MHD equations
Format : Talk at Waseda University
Author(s) :
Patrick Emmet Farrell (University of Oxford)
Fabian Laakmann (University of Oxford)
Abstract : We present an augmented Lagrangian preconditioner for the incompressible viscoresistive equations of magnetohydrodynamics. For stationary problems, our solver achieves robust performance with respect to the Reynolds and coupling numbers. We extend our method to fully implicit methods for time-dependent problems. Our approach relies on specialized parameter-robust multigrid methods for the hydrodynamic and electromagnetic blocks. The scheme ensures exactly divergence-free approximations of both the velocity and the magnetic field up to solver tolerances.
01054 (2/3) : 4E @E507 [Chair: Alexander Heinlein]
[05039] Immersed Mesh Methods for Coupled Multiphysics Problems
Format : Talk at Waseda University
Author(s) :
Rolf Krause (Euler Institute, USI, Lugano)
Patrick Zulian (Euler Institute, USI, Lugano)
Maria Nestola (Euler Institute, USI, Lugano)
Abstract : We present overlapping domain domain decomposition methods coupling different discretizations in the volume, along surfaces, or between surfaces and volumes. Central element of our approach is a massively parallel discrete $L^2$ projection, which allows for stable variational transfer between different physical models. Examples from fluid structure interaction (FSI), i.e. artificial heart valves, or flow in fracture networks, as well as from contact mechanics coupled with FSI illustrate our approach.
[04232] Robust nonlinear domain decomposition methods for problems with micro-heterogeneous structures
Format : Talk at Waseda University
Author(s) :
Alexander Heinlein (Delft University of Technology (TU Delft))
Axel Klawonn (University of Cologne)
Martin Lanser (University of Cologne)
Abstract : Nonlinear domain decomposition methods (DDMs) are efficient alternatives to classical Newton-Krylov-DDMs.
In contrast to the latter ones, in nonlinear DDMs, the nonlinear partial differential equation is decomposed into
subdomains before linearization, which often improves the nonlinear convergence behavior. To obtain robustness
applying nonlinear DDMs to heterogeneous multiscale or multiphysics problems, a global and coarse second level
should be included. In this talk, several two-level nonlinear Schwarz methods for heterogeneous problems are
discussed and compared.
[04600] Towards a scalable multilevel domain decomposition solver for immersed boundary finite element method
Format : Talk at Waseda University
Author(s) :
Jakub Sistek (Institute of Mathematics of the Czech Academy of Sciences)
Abstract : We develop multilevel balancing domain decomposition by constraints (BDDC) method tailored to the solution of the linear systems arising in the context of immersed boundary FEM with parallel adaptive grid refinement. A crucial challenge is presented by fragmenting of subdomains. We present these concepts, the challenges, our implementation, and numerical results for the Poisson problem on complex geometries from engineering. This is joint work with Fehmi Cirak, Eky Febrianto, Matija Kecman, and Pavel Kus.
01054 (3/3) : 5B @E507 [Chair: Alexander Heinlein]
[03836] Co-Design of Modelling and Monolithic Overlapping Schwarz Solvers in Chemo-Mechanics
Format : Talk at Waseda University
Author(s) :
Friederike Röver (TU Bergakademie Freiberg)
Bjoern Kiefer (TU Bergakademie Freiberg)
Stefan Prüger (TU Bergakademie Freiberg)
Oliver Rheinbach (TU Bergakademie Freiberg)
Abstract : The focus of this talk is the co-design of the variational formulations arising from model problems in chemo-mechanics and parallel iterative solvers from domain decomposition.
We choose the FROSch framework of the Trilinos Software library as a parallel solver. It contains a parallel implementation of the GDSW preconditioner, which allows an algebraic construction.
We present results applying FROSch to a fully coupled deformation-diffusion boundary value problem of a swelling hydrogel. For the FE-implementation, we use the deal.II software library and incorporate FROSch as a solver framework.
[03397] A tensor-preserving domain decomposition preconditioner for high-order implicit methods
Format : Talk at Waseda University
Author(s) :
Jing-Yuan Wang (University of Macau)
Yingzhi Liu (University of Macau)
Xiao-Chuan Cai (University of Macau)
Abstract : We investigate high-order block implicit methods for solving parabolic and unsteady Stokes problems, including the fully implicit Runge-Kutta method as a special case. These methods provide high accuracy with relatively large time step size, but the large, often nonsymmetric, and highly ill-conditioned stiffness matrix limits its practical use. To overcome this, we propose one- and two-level tensor-preserving domain decomposition preconditioners. Numerical experiments show the effectiveness and scalability of this approach for parabolic and Stokes flows.
