To overlap or not to overlap: a note on a domain decomposition method for elliptic problems
SIAM Journal on Scientific and Statistical Computing
Domain decomposition algorithms with small overlap
SIAM Journal on Scientific Computing
Grid overlapping for implicit parallel computation of compressible flows
Journal of Computational Physics
Journal of Computational Physics
Overlapping Nonmatching Grid Mortar Element Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
The SPHERIGON: A Simple Polygon Patch for Smoothing Quickly Your Polygonal Meshes
CA '98 Proceedings of the Computer Animation
Journal of Computational Physics
Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems
Journal of Scientific Computing
Overlapping Schwarz and Spectral Element Methods for Linear Elasticity and Elastic Waves
Journal of Scientific Computing
Two-Level Schwarz Algorithms with Overlapping Subregions for Mortar Finite Elements
SIAM Journal on Numerical Analysis
Domain Decomposition for Less Regular Subdomains: Overlapping Schwarz in Two Dimensions
SIAM Journal on Numerical Analysis
Optimal a priori estimates for higher order finite elements for elliptic interface problems
Applied Numerical Mathematics
Topics in ultrascale scientific computing with application in biomedical modeling
Topics in ultrascale scientific computing with application in biomedical modeling
A new computational paradigm in multiscale simulations: application to brain blood flow
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Multiscale simulations of blood-flow: from a platelet to an artery
Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the campus and beyond
Journal of Computational Physics
Parallel multiscale simulations of a brain aneurysm
Journal of Computational Physics
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We address the failure in scalability of large-scale parallel simulations that are based on (semi-)implicit time-stepping and hence on the solution of linear systems on thousands of processors. We develop a general algorithmic framework based on domain decomposition that removes the scalability limitations and leads to optimal allocation of available computational resources. It is a non-intrusive approach as it does not require modification of existing codes. Specifically, we present here a two-stage domain decomposition method for the Navier-Stokes equations that combines features of discontinuous and continuous Galerkin formulations. At the first stage the domain is subdivided into overlapping patches and within each patch a C^0 spectral element discretization (second stage) is employed. Solution within each patch is obtained separately by applying an efficient parallel solver. Proper inter-patch boundary conditions are developed to provide solution continuity, while a Multilevel Communicating Interface (MCI) is developed to provide efficient communication between the non-overlapping groups of processors of each patch. The overall strong scaling of the method depends on the number of patches and on the scalability of the standard solver within each patch. This dual path to scalability provides great flexibility in balancing accuracy with parallel efficiency. The accuracy of the method has been evaluated in solutions of steady and unsteady 3D flow problems including blood flow in the human intracranial arterial tree. Benchmarks on BlueGene/P, CRAY XT5 and Sun Constellation Linux Cluster have demonstrated good performance on up to 96,000 cores, solving up to 8.21B degrees of freedom in unsteady flow problem. The proposed method is general and can be potentially used with other discretization methods or in other applications.