Performance Modeling of PDE Solvers
نویسندگان
چکیده
In this chapter, we collect actual CPU time measurements of a number of prototypical PDE simulators for solving the Poisson equation, the linear elasticity equation, the heat conduction equation, the equations of nonlinear water waves, the incompressible Navier-Stokes equations, and many more. We show how these measurements can be used to establish performance models of the form: t = C n, which describes the CPU consumption as a function of the size of a discretized problem. The models can, in particular, quantify the efficiency of some standard numerical methods for solving the linear system in a particular problem. Different numerical methods can thus be compared, and we also hope that the performance models may form a basis for roughly estimating the consumption of CPU time by more complicated PDE simulators.
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