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Full-Text Articles in Physical Sciences and Mathematics
Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, Stephen Guffey
Masters Theses & Specialist Projects
In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the …
Mapping Algorithms And Software Environment For Data Parallel, Nikos Chrisochoides, Elias Houstis, John Rice
Mapping Algorithms And Software Environment For Data Parallel, Nikos Chrisochoides, Elias Houstis, John Rice
John R Rice
We consider computations associated with data parallel iterative solvers used for the numerical solution of Partial Differential Equations (PDEs). The mapping of such computations into load balanced tasks requiring minimum synchronization and communication is a difficult combinatorial optimization problem. Its optimal solution is essential for the efficient parallel processing of PDE computations. Determining data mappings that optimize a number of criteria, like workload balance, synchronization and local communication, often involves the solution of an NP-Complete problem. Although data mapping algorithms have been known for a few years there is lack of qualitative and quantitative comparisons based on the actual performance …