Relevant Reading
ICIS Multiphysics Workshop Website
ICiS Multiphysics Workshop: Below are links to some relevant reading.
Report from this ICiS workshop:
Multiphysics Simulations: Challenges and Opportunities, D. E. Keyes, L. C. McInnes, C. Woodward, W. Gropp, E. Myra, M. Pernice, J. Bell, J. Brown, A. Clo, J. Connors, E. Constantinescu, D. Estep, K. Evans, C. Farhat, A. Hakim, G. Hammond, G. Hansen, J. Hill, T. Isaac, X. Jiao, K. Jordan, D. Kaushik, E. Kaxiras, A. Koniges, K. Lee, A. Lott, Q. Lu, J. Magerlein, R. Maxwell, M. McCourt, M. Mehl, R. Pawlowski, A. P. Randles, D. Reynolds, B. Riviere, U. Ruede, T. Scheibe, J. Shadid, B. Sheehan, M. Shephard, A. Siegel, B. Smith, X. Tang, C. Wilson, and B. Wohlmuth, International Journal of High Performance Computing Applications, 27(1): 4-83, 2013. Special issue. DOI 10.1177/1094342012468181.
Applied Mathematics at the U.S. Department of Energy: Past, Present, and View to the Future, D. Brown et al., May, 2008
See in particular section 2.1.1: Multiscale, multiphysics, and complex hybrid models
DOE workshop reports:
Scientific Grand Challenges: Crosscutting Technologies for Computing at the Exascale, Chairs D. Brown and P. Messina, February, 2010
See in particular 'Mathematical Models and Algorithms' (pages 19-49)
Report of the First Multiscale Mathematics Workshop: First Steps toward a Roadmap, P. Colella, T. Hou, and L. Petzold (Eds.); U. S. Department of Energy – Office of Science Workshop Report, August 2004
Final Report: Second DOE Workshop on Multiscale Problems, D. Estep, J. N. Shadid, and S. J. Tavener (Eds.); Broomsfield, Colorado, U. S. Department of Energy – Office of Science Workshop Report, October 2004
Multiscale Mathematics Initiative: A Roadmap, J. Dolbow, M. A. Khaleel, J. Mitchell, J., (Eds.), U.S. Department of Energy – Office of Science Workshop Report, December 2004
Mathematical Research Challenges in Optimization of Complex Systems, B. A. Hendrickson and M. H. Wright (Eds.), U. S. Department of Energy – Office of Science Workshop Report, December 2006
Fusion Energy Science and the Role of Computing at the Extreme Scale, W. Tang, D. Keyes et al., U.S. Department of Energy, Workshop Report, March 2009
See in particular 'Algorithms for Fusion Energy Sciences at Extreme Scale' (pages 93-107)
References suggested by workshop participants:
Fluid-Structure Interaction II -- Modeling, Simulation, Optimisation, H.-J. Bungartz, M. Mehl, and M. Schafer (Eds.), Springer, Lecture Notes in Computational Science and Engineering, vol 73, 2010.
ref suggested by M. Mehl: This book is an overview of research on fluid-structure interaction using different approaches (monolithic, partitioned, ALE, Eulerian,...) and different tools (commercial and in-house); some of the insights could easily be extended to general multiphysics applications.
Implicitly Balanced Solution of the Two-Phase Flow Equations Coupled to Nonlinear Heat Convection, V. A. Mousseau, Journal of Computational Physics, vol 200, pages 104-132, 2004.
ref suggested by B. Sheehan: This paper describes the application of a Jacobian-free Newton-Krylov method with a physics-based preconditioner to a multiphysics problem. In this case the physics-based preconditioner is a solution method based on operator splitting, in conjunction with single physics solvers, which can be used by itself to solve the original problem. The concept of using "older" methods with single physics solvers as preconditioners is of particular interest to me, especially in the case where the single physics components require different sized timesteps.
Nonlinearly Preconditioned Inexact Newton Algorithms, X.-C. Cai and D. E. Keyes, SIAM J. Sci. Comput., vol 24, pages 183-200, 2002.
ref suggested by D. Keyes: From a discrete algebraic solver viewpoint, partitioning by "physics" is no different than partitioning by domain, though, of course, there are convergence rate and data structure differences when subspace projections are employed as preconditioners. Physics-based preconditioning and fully implicit Jacobian-free Newton solvers are interesting for multiphysics coupling, as mentioned in the second-last paragraph of this reference, with respect to the algorithm in Section 4.
Error Estimation for Multiscale Operator Decomposition for Multiphysics Problems, D. Estep, chapter 11 of the book Bridging the Scales in Science and Engineering, Editor J. Fish, Oxford University Press, 2010.
ref suggested by D. Estep: This chapter on a posteriori analysis for solution of coupled multiphysics applications presents an overview of a posteriori error analysis, Green's functions, and stability. It then briefly explains how solution of multiphysics problems raises new issues for accurate error estimation and how these can be addressed.
Studies on the Accuracy of Time-Integration Methods for the Reaction-Diffusion Equation, D. Ropp, J. Shadid, and C. Ober, Journal of Computational Physics, vol 194, pages 544-574, 2004.
ref suggested by M. Pernice: This manuscript illustrates the strengths and weaknesses of semi-implicit and operator split time integration methods on a set of carefully selected example problems. One of the most important points made here is the need for improved understanding of the circumstances where the different methods can be used, the shortcomings of a priori accuracy estimates, and the need for thorough algorithmic verification to support claims of accuracy.
Provably Second-order Time-accurate Loosely-Coupled Solution Algorithms for Transient Nonlinear Computational Aeroelasticity, C. Farhat, G. van der Zee, and P. Geuzaine, Computer Methods in Applied Mechanics and Engineering, vol 195, pages 1973-2001, 2006.
ref suggested by C. Farhat: This paper describes a methodology for designing provably second-order time-accurate and yet loosely-coupled partitioned procedures for the solution of nonlinear fluid–structure interaction (FSI) problems on moving grids. In particular, focusing on a complex application involving a full-scale F-16 figther aircraft in transonic flows, it shows that for a large class of FSI problems, a well-designed loosely-coupled solution procedure can perform as well as any so-called implicit coupled solution methodology while offering practical and computational advantages.
Implicit Methods for Plasma Physics, S. Jardin, Journal of Computational Physics, in press, 2011.
ref suggested by S. Jardin: I consider this paper to be multiphysics as it addresses problems that occur on multiple timescales (plasma stability, transport, and reconnection).
Comparison of Multimesh hp-FEM to Interpolation and Projection Methods for Spatial Coupling of Thermal and Neutron Diffusion Calculations, L. Dubcova, P. Solin, G. Hansen, and H. Park, Journal of Computational Physics, vol 230, pages 1182-1197, 2011.
ref suggested by G. Hansen: This paper describes an approach of spatial coupling distinct phenomena with differing spatial resolution requirements, using an adaptive multiple-mesh hp-FEM method. It compares the accuracy of the proposed method with selected approaches based on field transfer between meshes, and discusses some pros and cons of multiple mesh spatial integration.
Direct Numerical Simulation of Particulate Flows on 294912 Processor Cores, J. Götz, K. Iglberger, M. Stürmer, U. Rüde, SC'10, Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, New Orleans, Nov 13-19, 2010.
ref suggested by U. Rüde: This paper describes a fully resolved computational model of particulate flows based on the Lattice Boltzmann method that is coupled to a so-called "physics engine" for simulating the dynamics of rigid objects with full geometrical resolution. The latter includes collision detection and handling frictional contacts. The coupling is achieved by an explicit fluid-structure interaction technique. The coupled codes are fully parallelized and scale up to beyond 100 000 processor cores.
An Approximate Block Newton Method for Coupled Iterations of Nonlinear Solvers: Theory and Conjugate Heat Transfer Applications, A. Yeckel, L. Lun, and J. Derby, Journal of Computational Physics, vol 228, pages 8566-8588, 2009.
ref suggested by M. McCourt: This paper discusses the use of Newton solvers on coupled systems where each component has a specially designed black box solver. Results are compared against more traditional Gauss-Seidel methods and the Block Newton solver converges in a wider set of cases.
A Fluid-Fluid Interaction Method Using Decoupled Subproblems and Differing Time Steps, J. Connors and J. Howell, Numerical Methods for Partial Differential Equations, Wiley Online Library, May 2011.
ref suggested by J. Connors: This paper addresses decoupling fluid-fluid interaction (atmosphere-ocean motivated) by semi-implicit time stepping. We assume the majority of the energy in the two flows is associated with different time scales, so taking different time step sizes for the subproblems is important for efficiency.
A Taxonomy and Comparison of Parallel Block Multi-level Preconditioners for the Incompressible Navier-Stokes Equations, H. Elman, V. Howle, J. Shadid, R. Shuttleworth, R. Tuminaro, Journal of Computational Physics, vol 227, pages 1790-1808, 2008.
ref suggested by A. Lott: This paper develops a taxonomy of block preconditioners based on an adaptation of a generalized approximate factorization of the Navier–Stokes system, and discusses the role in which approximations to the Schur complement operator plays in providing an efficient block preconditioner.
Advanced Physics Calculations Using a Multi-fluid Plasma Model, U. Shumlak, R. Lilly, N. Reddell, E. Sousa and B. Srinivasan, Computer Physics Communications, vol 182, issue 9, pages 1767-1770, 2011.
ref suggested by A. Hakim: This paper applies the discontinous-Galerkin scheme to the multi-fluid plasma equations. The system is very stiff: the very small electron/ion mass ratio and speed of light means that the system displays physics on very different time-scales. This paper outlines the need for really good preconditioners that explicitly take into account the physics of the problem.
Consistent and Accurate Schemes for Coupled Neutronics Thermal-hydraulics Reactor Analysis, J. C. Ragusa and V. S. Mahadevan, Nuclear Engineering and Design, vol 239, issue 3, pages 566–579, 2009.
ref suggested by D. Kaushik: This paper proposes some remedies to inconsistencies resulting from the treatment of nonlinear terms in an operator-split method (commonly used for multiphysics simulations). This often leads to small time steps to maintain accuracy. This work demonstrates that nonlinearly consistent adaptive time stepping methods (implemented for 0D point-kinetics/thermal-hydraulics lumped model and a 1D neutronics/heat conduction/enthalpy balance model) provide better accuracy and reliability in the solution fields than constant time stepping methods.
A Theory Manual for Multiphysics Code Coupling in LIME, Version 1.0, R. Pawlowski, R. Bartlett, N. Belcourt, R. Hooper, R. Schmidt, Sandia Report SAND2011-2195, March, 2011.
ref suggested by R. Pawlowski: This manual defines multiphysics coupling in the context of the CASL project, including the domain model for multiphysics coupling, various interaction models with physics codes depending on what they can provide (how much of a black-box it is), and various coupling techniques.
DG Approximations of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition, Vi. Girault and B. Riviere, SIAM J. Numer. Anal. vol 47, number 3, pages 2052-2089, 2009.
Ref suggested by B. Riviere: This paper addresses the mathematical analysis of weak and numerical solution to a multiphysics problem.
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations, C. Kennedy and M. Carpenter, Applied Numerical Mathematics, vol 44, pages 139-181, 2003.
ref suggested by D. Reynolds: This paper provides a thorough comparison of leading ARK-IMEX methods, including analysis of coupling errors between the explicit and implicit components, as well as numerical tests on a variety of difficult multi-scale ODE and PDE problems.
Heterogeneous Multiscale Methods: A Review, Weinan E., B. Engquist, X. Li, W. Ren and E. Vanden-Eijnden, Communications in Computational Physics, vol 2, number 3, pages 367-450, 2007.
ref suggested by D. Reynolds: This paper provides a thorough overview of both theory and implementation of HMM methods for multiscale modeling, focusing on continuum-particle and continuum-continuum coupling between coarse and fine-grain models.
Hybrid Atomistic Simulation Methods for Materials Design, N. Bernstein, J. Kermode, and G. Csanyi, Reports on Progress in Physics 72 (2009) 026501.
ref suggested by E. Kaxiras: This article provides an overview of the technical issues that arise in coupling quantum and classical atomistic regimes in materials simulations.
The Quasicontinuum Method: Overview, Applications, and Current Directions, R. Miller and E. Tadmor, Journal of Computer-Aided Materials Design, vol 9, pages 203-239, 2002.
ref suggested by E. Kaxiras: This paper provides an overview of the quasi-continuum method that couples classical atomistic and continuum regimes for materials simulations.
Overview of Multiscale Simulation of Materials, G. Lu and E. Kaxiras, Chapter 22, Handbook of Theoretical and Computational Nanotechnology, M. Rieth and W. Schommers, editors, 2005.
ref suggested by E. Kaxiras: This chapter is a general overview of different types of approaches (concurrent and sequential) for coupling length scales and time scales in materials simulations.
Accuracy Analysis of a Spectral Element Atmospheric Model Using a Fully Implicit Solution Framework, K. Evans, M. Taylor, J. Drake, Monthly Weather Review, vol 138, issue 8, pages 3333-3341, 2010.
ref suggested by K. Evans: This paper analyzes the accuracy of using a fully implicit scheme versus an operator split method and fully explicit method in the shallow water version of the Community Atmosphere model. We analyze the temporal convergence of all three and evaluate an appropriate time step for each.
FACETS - A Framework for Parallel Coupling of Fusion Components, J. Cary, A. Hakim, M. Miah, S. Kruger, A. Pletzer, S. Shasharina, S. Vadlamani, A. Pankin, R. Cohen, T. Epperly, T. Rognlien, R. Groebner, S. Balay, L. McInnes, H. Zhang, Proceedings of the 18th Euromicro International Conference on Parallel, Distributed and Network-Based Computing. Pisa, Italy, 2010.
ref suggested by A. Hakim: This paper describes the software design of the FACETS coupling framework for fusion simulations, including features needed for any in-memory coupling system that works with both newly written components and legacy components. The paper also indicates the particular choices made in a large coupling framework that has been successfully applied to a number of fusion problems.
Local-in-time Adjoint-based Method for Design Optimization of Unsteady Flows, N. Yamaleev, B. Diskin, E. Nielsen, Journal of Computational Physics, vol 229, pages 539-5407, 2010.
ref suggested by K. H. Lee: This paper describes how transient adjoint analysis in local time could be applied to obtain sensitivity of a simulation with respect to the quantity of interest. With a clever formulation of the objective function, which is composed of solution variables from multiphysics domains to represent the multiphysics coupling, the adjoint values can be used to quantify the strength of the coupling.