Spline collocation methods, software and architectures for linear elliptic boundary value problems
Abstract
We consider new discretization methods for the numerical solution of linear second order boundary value problems in one and two dimensions. The methods considered belong to the class of finite elements and are based on collocation by quadratic splines. We study the formulation and convergence of these methods and their implementation on serial and parallel computer architectures. It is shown that these discretization methods, when compared with other methods that perform the same task and require input of similar nature, are efficient and can be applied to a broad class of linear second order differential operators. For the solution of the resulting linear system of collocation equations, we apply existing sequential algorithms and devise parallel solvers on MIMD architectures. Finally, we present an experimental study, that verifies the mathematical and computational behavior of the methods.
Degree
Ph.D.
Advisors
Houstis, Purdue University.
Subject Area
Computer science
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