Iterative methods for the solution of elliptic problems on regions partitioned into substructures
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
Introduction to Parallel & Vector Solution of Linear Systems
Introduction to Parallel & Vector Solution of Linear Systems
International Journal of Supercomputer Applications and High Performance Engineering
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Iterative methods for nonsymmetric systems in DAEs and stiff ODEs codes
Mathematics and Computers in Simulation
A comparison of preconditioned nonsymmetric Krylov methods on a large-scale MIMD machine
SIAM Journal on Scientific Computing
Hierarchical control of congested urban traffic—mathematical modelling and simulation
MIM-S2 '93 Papers from the symposium on Second mathematical and intelligent models in system simulation
Balancing domain decomposition for problems with large jumps in coefficients
Mathematics of Computation
Efficient Mapping Algorithms for a Class of Hierarchical Systems
IEEE Transactions on Parallel and Distributed Systems
A collection of parallel linear equations routines for the Denelcor HEP
Parallel Computing
A class of Lanczos-like algorithms implemented on parallel computers
Parallel Computing
Efficient traffic flow simulation computations
Mathematical and Computer Modelling: An International Journal
Traffic flow simulation through high order traffic modelling
Mathematical and Computer Modelling: An International Journal
An analysis of queuing network simulation using GPU-based hardware acceleration
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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Computational Fluid Dynamics (CFD) methods for solving traffic flow continuum models have been studied and efficiently implemented in traffic simulation codes in the past. This is the first time that such methods are studied from the point of view of parallel computing. We studied and implemented an implicit numerical method for solving the high-order flow conservation traffic model on parallel computers. Implicit methods allow much larger time-step than explicit methods, for the same accuracy. However, at each time-step a nonlinear system must be solved. We used the Newton method coupled with a linear iterative method (Orthomin). We accelerated the convergence of Orthomin with parallel incomplete LU factorization preconditionings. We ran simulation tests with real traffic data from an 12-mile freeway section (in Minnesota) on the nCUBE2 parallel computer. These tests gave the same accuracy as past tests, which were performed on one-processor computers, and the overall execution time was significantly reduced.