417 Advances in Iterative Solution Methods for Multiphysics Systems

John Shadid, Sandia National Laboratories
Haim Waisman, Columbia University
Survranu De, Rensselaer Polytechnic Institute
A current challenge before the computational science and numerical mathematics community is the efficient computational solution of multiphysics systems (see e.g. [1,2,3]). These systems are strongly coupled, highly nonlinear and characterized by multiple physical phenomena spanning a very large range of length- and time-scales. To enable stable, accurate, and efficient numerical approximation of these systems a wide range of spatial discretization methods are commonly employed (e.g. finite difference, finite volume, and finite element methods). For effective time integration of the longer time-scale response of these systems some form of implicitness is also required.

These characteristics make the robust, efficient, and scalable, numerical solution of these systems extremely challenging. The intention of this set of mini-symposium sessions is to focus on recent advances in nonlinear and linear iterative methods, scalable preconditioning techniques, and computational solution algorithms for complex, strongly coupled multiphysics problems
in a wide range of important scientific and engineering applications.

[1] D.E. Keyes, L.C. McInnes, C. Woodward, W. Gropp, et. al., Multiphysics simulations: Challenges and opportunities,. Int. J. High Performance Computing App.., 27:4–83, 2013. 

[2] J. Dongarra and J. Hittinger. Applied mathematics research for exascale computing. Technical Re- port https://science.energy.gov/ /media/ascr/pdf/research/am/docs/EMWGreport.pdf, DOE Office of Science ASCR, 2015.

[3] D. L. Brown et. al, Applied Mathematics at the US Department of Energy: Past, Present and Future, DOE Office of Science Advanced Scientific Computing Research Program., Technical Report, 2008