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Parallel (‖) ELLPACK: an expert system for parallel processing of partial differential equations

E.N. Houstis, J.R. Rice, T.S. Papatheodorou
1989 Mathematics and Computers in Simulation  
Ahstract We are developing an expen system environment for solving elliptic partial differential equations(pDEs) defined on two and three dimensional domains on MIMD type parallel machines.  ...  According to its design objectives, it will provide a uniform programming environment for implementing parallel MIMD PDE solution solvers, an automatic partitioning and allocation of the PDE computation  ...  GEOMETRY DECOMPOSITION BASED METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS The development of parallel algorithms for a given computation usually assumes the partitioning of the underlying computation  ... 
doi:10.1016/0378-4754(89)90143-2 fatcat:vgbqwicvangmjknom3wvpcsvwa

Parallel Reservoir Simulation with OpenACC and Domain Decomposition

Zhijiang Kang, Ze Deng, Wei Han, Dongmei Zhang
2018 Algorithms  
Meanwhile, domain decomposition is not well used for GPU-based reservoir simulations.  ...  In order to address the problems, we propose a parallel method with OpenACC to accelerate serial code and reduce the time and effort during porting an application to GPU.  ...  In last experiment, we compare two kinds of parallel reservoir simulation methods which differentiate from the other depending on whether the domain decomposition is used.  ... 
doi:10.3390/a11120213 fatcat:swrmqhkzujc3fjvozi3jckd7rm

Design and Optimization of OpenFOAM-based CFD Applications for Hybrid and Heterogeneous HPC Platforms [article]

Amani AlOnazi, David Keyes, Alexey Lastovetsky, Vladimir Rychkov
2015 arXiv   pre-print
Hardware-aware design and optimization is crucial in exploiting emerging architectures for PDE-based computational fluid dynamics applications.  ...  We propose a number of optimizations of the dominant kernel of the Krylov solver, aimed at acceleration of the overall execution of the applications on modern GPU-accelerated heterogeneous platforms.  ...  Parallel Approach A common approach for parallelizing partial differential equations is domain decomposition.  ... 
arXiv:1505.07630v1 fatcat:ncqycx2hmvbaxjbfeavwhyw3v4

Implementing Overlapping Domain Decomposition Methods on a Virtual Parallel Machine [chapter]

David Darjany, Burkhard Englert, Eun Heui Kim
2006 Lecture Notes in Computer Science  
To solve many partial differential equations of different types domain decomposition techniques were developed.  ...  We first develop suitable domain decomposition algorithms for our virtual parallel machine.  ...  To solve many partial differential equations of different types domain decomposition techniques were developed.  ... 
doi:10.1007/11942634_74 fatcat:hm2qv3i3abggrhhh3cmnydiive

PELLPACK: a problem-solving environment for PDE-based applications on multicomputer platforms

E. N. Houstis, J. R. Rice, S. Weerawarana, A. C. Catlin, P. Papachiou, K.-Y. Wang, M. Gaitatzes
1998 ACM Transactions on Mathematical Software  
The system employs several parallel reuse methodologies based on the decomposition of discrete geometric data to map sparse PDE computations to parallel machines.  ...  This paper presents the software architecture and implementation of the problem solving environment (PSE) PELLPACK for modeling physical objects described by partial differential equations (PDEs).  ...  PELLPACK is supported by a library of parallel PDE modules for the numerical solution of stationary and time dependent single equation PDE models on two and three dimensional regions.  ... 
doi:10.1145/285861.285864 fatcat:ekapzyflknhuffw4tswnptnwya

Performance of preconditioners for the distributed vector finite-element time-domain algorithm

A. Nicolas, L. Nicolas, C. Vollaire, B. Butrylo
2005 IEEE transactions on magnetics  
Index Terms-Edge elements, finite-element (FE) method, iterative solver, parallel numerical algorithms, time-domain algorithm.  ...  The properties of the solver are estimated for concurrent three-dimensional formulation of the finite-element time-domain method.  ...  The first one is the typical fixed speedup of the algorithm (2) where is the latency time of the PCG solver in a single step of the time-domain algorithm.  ... 
doi:10.1109/tmag.2005.846055 fatcat:brt2afl43zbojitsj5iic35pke

Parallel FEM Software for CFD Problems

Arnas Kačeniauskas, Peter Rutschmann
2004 Informatica  
Domain decomposition strategy and parallel iterative GM-RES solver have been adapted to the universal space-time FEM code FEMTOOL, which allows implementation of any partial differential equation with  ...  The present paper describes the development and the performance of parallel FEM software for solving various CFD problems.  ...  Eric De Sturler for helpful suggestions and useful discussions related with some important topics of this work.  ... 
doi:10.15388/informatica.2004.066 fatcat:cbv6m4whmbdspnt56l2cj7dzju

Hybrid Iterative-Direct Solution Strategy For Improving The Scalability Of Nuclear Waste Management Simulations

Emmanuel Agullo
2017 Zenodo  
The enabling numerical tool is a domain decomposition solution strategy for the sparse system of linear equations resulting from the spatial discretization of the underlying PDEs (Partial Differential  ...  A concrete application is considered for assessing the benefits of using a domain decomposition sparse linear solution strategy as compared to the originally used approach, which is based on a more classical  ...  Enabling numerical tool: domain decomposition solver Domain decomposition methods are flexible and powerful techniques for the parallel numerical solution of systems of PDEs.  ... 
doi:10.5281/zenodo.826134 fatcat:hqymvtg4kbchhme2lt5a5m6hii

Domain Decomposition Based High Performance Parallel Computing [article]

Mandhapati P. Raju, Siddhartha Khaitan
2009 arXiv   pre-print
The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers.  ...  Hence, the parallelization of sparse direct solvers is done using domain decomposition techniques. A highly efficient sparse direct solver PARDISO is used in this study.  ...  Acknowledgments Author would like to thank the Ohio Supercomputing Centre for proving the computing facility.  ... 
arXiv:0911.0910v1 fatcat:6xujlwd52bhq5czdj42vvfjd2u

Finite Element Tearing and Interconnecting Method and its Algorithms for Parallel Solution of Magnetic Field Problems

Dániel Marcsa, Miklós Kuczmann
2013 Electrical, Control and Communication Engineering  
Domain decomposition methods (DDMs) for parallel solution of linear systems of equations are based on the partitioning of the analyzed domain into sub-domains which are calculated in parallel while doing  ...  In this case, the non-overlapping domain decomposition method is the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method.  ...  ACKNOWLEDGEMENT This paper was supported by the TÁMOP-4.2.2.A-11/1/KONV-2012-0012 : Basic research for the development of hybrid and electric vehicles -The Project is supported by the Hungarian Government  ... 
doi:10.2478/ecce-2013-0011 fatcat:yqdcht2ldrclzek26it3r4qgbi

A Schur Complement Method for DAE/ODE Systems in Multi-Domain Mechanical Design [chapter]

David Guibert, Damien Tromeur-Dervout
2008 Lecture Notes in Computational Science and Engineering  
A Schur Complement DDM can then be applied. During some time steps, the Jacobian matrix can be frozen allowing to speed-up the Krylov solvers convergence by projecting onto the Krylov subspace.  ...  The large increase of unknowns in multi-domain mechanical modeling leads to investigate new parallel implementation of ODE and DAE systems.  ...  Conclusion A Schur domain decomposition method has been investigated to solve systems of ordinary/algebraic differential equations.  ... 
doi:10.1007/978-3-540-75199-1_67 fatcat:mpne7l43zbhgde4sr74jydklle

Fast parallelized algorithms for on-line extended-term dynamic cascading analysis

Siddhartha Kumar Khaitan, Chuan Fu, James McCalley
2009 2009 IEEE/PES Power Systems Conference and Exposition  
described as a set of differential algebraic equations (DAEs).  ...  This paper reports on the design Index Terms--high-speed extended term time domain simulation, Differential algebraic equation, Recursive Projection method, Waveform relaxation method, linear solver, multifrontal  ...  PROBLEM FORMULATION Time domain simulation of power system involves the solution of a large number of differential algebraic equations (DAEs), which are constructed based on the modeling of the power system  ... 
doi:10.1109/psce.2009.4840238 fatcat:nzgvqpbszbfubfww75gdruhwte

Agent Architecture for Mesh Based Simulation Systems [chapter]

K. Banaś
2006 Lecture Notes in Computer Science  
As an example a framework for finite element simulations, employing a modular architecture (described in [1]), is considered.  ...  The paper presents an analysis of requirements for building simulation systems with tightly coupled components, such as typical mesh based PDE approximation software.  ...  reordering linear equations linear solver which is considered an external software in the proposed architecture Domain Decomposition for FEM Core For parallel execution the extension shown in Fig.  ... 
doi:10.1007/11758532_97 fatcat:4rezeumctbbcxju2zigaf46gcy

High Order Finite Element Schemes And Domain Decomposition Solvers For Large-Scale Simulations In Electromagnetics

Stéphane Lanteri
2017 Zenodo  
The enabling numerical tool is a domain decomposition solution strategy for the sparse system of linear equations resulting from the spatial discretization of the underlying PDEs (Partial Differential  ...  The PDEs at hand here are the frequency-domain (or time-harmonic) Maxwell equations.  ...  Enabling numerical tool: domain decomposition solver Domain decomposition methods are flexible and powerful techniques for the parallel numerical solution of systems of PDEs.  ... 
doi:10.5281/zenodo.830354 fatcat:zdaf5nmg3bbntevadby5i737ym

Primal Domain Decomposition Method with Direct and Iterative Solver for Circuit-Field-Torque Coupled Parallel Finite Element Method to Electric Machine Modelling

Daniel Marcsa, Miklos Kuczmann
2015 Advances in Electrical and Electronic Engineering  
In this paper, the primal Domain Decomposition Method (DDM) with parallel forward-backward and with parallel Preconditioned Conjugate Gradient (PCG) solvers are introduced in two-dimensional parallel time-stepping  ...  Simulation results of a rotating machine is also presented. Keywords Field-circuit-torque coupling, parallel finite element method, primal domain decomposition method.  ...  However, it can be concluded based on the presented results, the parallel direct solver is more efficient for the smaller problems, whereas the iterative solver is more useful for larger problem.  ... 
doi:10.15598/aeee.v13i5.1410 fatcat:cqubceqg7vcppmj32zojdvxi5m
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