Concurrent scientific computing
Concurrent scientific computing
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Stiff differential equations solved by Radau methods
Proceedings of the on Numerical methods for differential equations
Software and algorithms for sensitivity analysis of large-scale differential algebraic systems
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
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Fast algorithms for simulating mathematical models of coupled blood-tissue transport and metabolism are critical for the analysis of data on transport and reaction in tissues. Here, by combining the method of characteristics with the standard grid discretization technique, a novel algorithm is introduced for solving a general blood-tissue transport and metabolism model governed by a large system of one-dimensional semilinear first order partial differential equations. The key part of the algorithm is to approximate the model as a group of independent ordinary differential equation (ODE) systems such that each ODE system has the same size as the model and can be integrated independently. Thus the method can be easily implemented in parallel on a large-scale multiprocessor computer. The accuracy of the algorithm is demonstrated for solving a simple blood-tissue exchange model introduced by Sangren and Sheppard [W.C. Sangren, C.W. Sheppard, A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment, Bull. Math. Biophys. 15 (1953) 387-394], which has an analytical solution. Numerical experiments made on a distributed-memory parallel computer (an HP Linux cluster) and a shared-memory parallel computer (a SGI Origin 2000) demonstrate the parallel efficiency of the algorithm.