GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A local convergence theory for combined inexact-Newton/finite-difference projection methods
SIAM Journal on Numerical Analysis
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
ACM Transactions on Mathematical Software (TOMS)
Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
ACM Transactions on Mathematical Software (TOMS)
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
Mathematics of Computation
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows
Journal of Computational Physics
Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
Numerical analysis: an introduction
Numerical analysis: an introduction
ScaLAPACK user's guide
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
On the stability of implicit-explicit linear multistep methods
Applied Numerical Mathematics - Special issue on time integration
Convergence Analysis of Pseudo-Transient Continuation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Spanning the length scales in dynamic simulation
Computers in Physics
Conservative remapping and region overlays by intersecting arbitrary polyhedra
Journal of Computational Physics
Generalized Multistep Predictor-Corrector Methods
Journal of the ACM (JACM)
Journal of Computational Physics
Achieving high sustained performance in an unstructured mesh CFD application
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration
SIAM Journal on Scientific Computing
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Multigrid
Modern C++ design: generic programming and design patterns applied
Modern C++ design: generic programming and design patterns applied
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
FQMR: A Flexible Quasi-Minimal Residual Method with Inexact Preconditioning
SIAM Journal on Scientific Computing
Nonlinearly Preconditioned Inexact Newton Algorithms
SIAM Journal on Scientific Computing
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Spectral Element Methods for Transitional Flows in Complex Geometries
Journal of Scientific Computing
A multirate W-method for electrical networks in state-space formulation
Journal of Computational and Applied Mathematics
Estimation of modeling error in computational mechanics
Journal of Computational Physics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Digital filters in adaptive time-stepping
ACM Transactions on Mathematical Software (TOMS)
Multi-Adaptive Galerkin Methods for ODEs I
SIAM Journal on Scientific Computing
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
A Preconditioner for Substructuring Based on Constrained Energy Minimization
SIAM Journal on Scientific Computing
Coupling of atomistic and continuum simulations using a bridging scale decomposition
Journal of Computational Physics
A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations
Journal of Computational Physics
Multi-Adaptive Galerkin Methods for ODEs II: implementation and Applications
SIAM Journal on Scientific Computing
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Interface conditions for wave propagation through mesh refinement boundaries
Journal of Computational Physics
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
Studies of the accuracy of time integration methods for reaction-diffusion equations
Journal of Computational Physics
A framework approach for developing parallel adaptive multiphysics applications
Finite Elements in Analysis and Design - Special issue: The fifteenth annual Robert J. Melosh competition
Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
Journal of Computational Physics
SIAM Journal on Scientific Computing
International Journal of High Performance Computing Applications
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
International Journal of High Performance Computing Applications
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
International Journal of High Performance Computing Applications
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
PALM: a computational framework for assembling high-performance computing applications
Concurrency and Computation: Practice & Experience - Computational Frameworks
GCF: a general coupling framework
Concurrency and Computation: Practice & Experience - Computational Frameworks
IRKC: an IMEX solver for stiff diffusion-reaction PDEs
Journal of Computational and Applied Mathematics
A Massively Parallel Multigrid Method for Finite Elements
Computing in Science and Engineering
Conservative load transfer along curved fluid-solid interface with non-matching meshes
Journal of Computational Physics
Coupling pore-scale networks to continuum-scale models of porous media
Computers & Geosciences
Building complex coupled physical simulations on the grid with InterComm
Engineering with Computers
A component-based parallel infrastructure for the simulation of fluid–structure interaction
Engineering with Computers
Efficient distributed mesh data structure for parallel automated adaptive analysis
Engineering with Computers
libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
Engineering with Computers
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
Journal of Computational Physics
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Multirate Timestepping Methods for Hyperbolic Conservation Laws
Journal of Scientific Computing
Shape determination for deformed electromagnetic cavities
Journal of Computational Physics
Journal of Computational Physics
MultiScale Modeling of Physical Phenomena: Adaptive Control of Models
SIAM Journal on Scientific Computing
An A Posteriori-A Priori Analysis of Multiscale Operator Splitting
SIAM Journal on Numerical Analysis
Toward interoperable mesh, geometry and field components for PDE simulation development
Engineering with Computers
SIAM Journal on Numerical Analysis
A Multiphysics and Multiscale Software Environment for Modeling Astrophysical Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
An Agent-Based Coupling Platform for Complex Automata
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Hybrid Simulations of Reaction-Diffusion Systems in Porous Media
SIAM Journal on Scientific Computing
Multirate Explicit Adams Methods for Time Integration of Conservation Laws
Journal of Scientific Computing
Multiscale computation for bioartificial soft tissues with complex geometries
Engineering with Computers - Special Issue on Computational Bioengineering. Guest Editors: Suvranu De and Christopher R. Johnson
A posteriori error analysis for a transient conjugate heat transfer problem
Finite Elements in Analysis and Design
Journal of Computational Physics
Graphical Notation for Diagramming Coupled Systems
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
A Scalable and Adaptable Solution Framework within Components of the Community Climate System Model
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Journal of Computational Physics
Journal of Computational Physics
An algebraic theory for primal and dual substructuring methods by constraints
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
SIAM Journal on Numerical Analysis
Enabling high-fidelity neutron transport simulations on petascale architectures
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
SIAM Journal on Numerical Analysis
Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements
SIAM Journal on Numerical Analysis
Multiscale Methods: Bridging the Scales in Science and Engineering
Multiscale Methods: Bridging the Scales in Science and Engineering
A component-based architecture for parallel multi-physics PDE simulation
Future Generation Computer Systems
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Partitioned Time Stepping for a Parabolic Two Domain Problem
SIAM Journal on Numerical Analysis
Journal of Computational Physics
DDEMA: a data driven environment for multiphysics applications
ICCS'03 Proceedings of the 2003 international conference on Computational science
The Design and Implementation of the SWIM Integrated Plasma Simulator
PDP '10 Proceedings of the 2010 18th Euromicro Conference on Parallel, Distributed and Network-based Processing
Monolithic discretization of linear thermoelasticity problems via adaptive multimesh hp-FEM
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D
Journal of Scientific Computing
A second order self-consistent IMEX method for radiation hydrodynamics
Journal of Computational Physics
An Interoperable, Data-Structure-Neutral Component for Mesh Query and Manipulation
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Direct Numerical Simulation of Particulate Flows on 294912 Processor Cores
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements
SIAM Journal on Numerical Analysis
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
SIAM Journal on Numerical Analysis
The International Exascale Software Project roadmap
International Journal of High Performance Computing Applications
Extrapolated Implicit-Explicit Time Stepping
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction
SIAM Journal on Scientific Computing
Optimal Explicit Strong-Stability-Preserving General Linear Methods
SIAM Journal on Scientific Computing
Enabling Multi-physics Coupled Simulations within the PGAS Programming Framework
CCGRID '11 Proceedings of the 2011 11th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing
A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems
Journal of Computational Physics
Petascale block-structured AMR applications without distributed meta-data
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
Unified Embedded Parallel Finite Element Computations via Software-Based Fréchet Differentiation
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Computational performance of ultra-high-resolution capability in the Community Earth System Model
International Journal of High Performance Computing Applications
Computing the First Eigenpair of the p-Laplacian via Inverse Iteration of Sublinear Supersolutions
Journal of Scientific Computing
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
ACM Transactions on Mathematical Software (TOMS)
Hierarchical Krylov and nested Krylov methods for extreme-scale computing
Parallel Computing
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We consider multiphysics applications from algorithmic and architectural perspectives, where â聙聹algorithmicâ聙聺 includes both mathematical analysis and computational complexity, and â聙聹architecturalâ聙聺 includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.